Alpa P. Rajai

I am Alpa Rajai, Completed my Masters in science with specialization in Physics. I am very enthusiastic about Writing about my understanding towards Advanced science. I assure that my words and methods will help readers to understand their doubts and clear what they are looking for. Apart from Physics, I am a trained Kathak Dancer and also I write my feeling in the form of poetry sometimes. I keep on updating myself in Physics and whatever I understand I simplify the same and keep it straight to the point so that it deliver clearly to the readers.

Does Amplitude Of Wave Decrease: When,Why ,How And Detailed Facts

January 21, 2024April 18, 2022 by Alpa P. Rajai

We got an answer to the question “does amplitude of wave change?” in the previous post. So in this post, we will look at the topic “does amplitude of wave decrease? when, why, and how?” So let us get started.

The amplitude of a wave is one of its most important characteristics, as it enables us to determine the wave’s energy. As a result, as the energy or power (the amount of energy delivered by a wave per unit time) drops over time, the wave amplitude decreases.

Before we go into the depth of our questions, does amplitude of wave decrease, how, when, and why? First, let us start with a basic understanding of a wave and its amplitude.

⇢ Significance of the wave:

In physics, the term wave has a basic but broad meaning.

It can be thought of as an oscillation or, more accurately, a disturbance that travels across space-time carrying energy. As a result, wave motion is defined as a motion that transmits energy from one point to another by causing a disturbance.

Source: Wikipedia

The motion of the disturbance does not cause the displacement of particles in that medium. As a result, while the wave conveys energy, it is not related to mass transport. Waves are classified into two categories, which are listed below:

Longitudinal waves: Sound waves come under this category.
Transverse waves: Electromagnetic waves (Light waves) come under this category.

Now, the amplitude of a wave is another term we should be familiar with.

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⇢ Significance of the wave amplitude:

The maximum displacement of a particle due to a disturbance in a medium from its resting point is defined as the amplitude of the wave. The particle’s maximum displacement is measured in meters. The amplitude of a wave is half of a wavelength.

gV2pkBzKJHSVk1b174ruTSUKl553gHo4lXdBJlIuuiXXIyFz — Image Credits: Geoff Ruth, Crest trough wavelength amplitude, CC BY-SA 3.0

In the case of sound waves, the amplitude is just the loudness. The amplitude defines the brightness or intensity of light compared to other light waves of the same wavelength when it comes to light waves.

Now, the focus of our article is: does amplitude of wave decrease? So let us make a move in that direction.

Does amplitude of wave decrease?

⇨ The amplitude of a wave is unquestionably important, yet it is not a consistent property. The amplitude of a wave can alter depending on environmental elements such as energy, distance, time, and speed.

As per these factors’ proportionality (it can be directly proportional, inversely proportional, etc.) with amplitude causes a change in amplitude. For example, a drop in amplitude is caused by a loss in energy and an increase in distance.

Thus, if a sound wave has a larger amplitude than another, it has a higher loudness, whereas a sound wave with a lower amplitude has a lower loudness. When it comes to light waves, more amplitude does not imply higher loudness, but rather high intensity, whereas low amplitude term implies low intensity.

Why does amplitude of wave decrease?

⇨ Both frequency and amplitude are wave qualities that are related to energy.

The wave frequency is directly proportional to the wave energy, and so is the square of the wave amplitude. Because the frequency is the identity of a wave, if it changes with a change in energy, the wave will not remain the same. As a result, when energy drops, wave amplitude reduces.

When does amplitude of wave decrease?

⇨ Whenever any wave passes through a medium, it experiences losses. When any wave passes through the medium, it spreads out in the medium.

Moreover, during that propagation, some part of the wave is absorbed by the medium. As the wave carries energy, spreading out and absorption of the wave indicates the spreading and absorption of energy. Thus, losses of energy experienced by the wave will materialize in the reduction of wave amplitude.

Does wave amplitude decrease over time?

⇨ The amplitude of a wave should not change with time if we assume ideal conditions.

However, we live in the actual world, where the wave loses energy over time due to environmental factors. This causes the wave amplitude to drop.

Why does the amplitude of a wave decrease over time?

⇨ There are no frictionless systems in the actual world.

To overcome the friction in the frictional system, the wave loses its own energy in order to propagate. As a result, as time passes, energy is lost as the wave spreads and attempts to overcome friction, resulting in a fall in amplitude.

When considering a simple harmonic motion, the amplitude of the simple harmonic wave drops exponentially over time, which is referred to as damping. The graph below shows damping as a function of time in a simple harmonic wave.

o4lHulkuZvOiwXThwywTIEr2hYjZzDIv2C2xoRTq K4 xAhQTYAqw7REkbeR3AUde2BysQtKxIKLNUeAnlaIVV7cQ19i797cER0SN33HnwUe30mE vU0X9spMAnwYdKWSe1UvUQR — Image Credits: anonymous, Damped sinewave, CC BY-SA 3.0

Does the amplitude decrease over distance?

⇨ Distance is another crucial aspect that influences the amplitude of a wave.

As time passes, the distance increases, causing energy loss by the propagating wave. Thus, distance increases, and amplitude increases as the wave comes far from the source. That is why the brightness of the light is high near the source, and as you go far, you can notice lesser brightness.

Why does the amplitude decrease over distance?

⇨ When a wave travels through a medium, it loses energy as it travels further.

The wave spreads out over a larger and larger area as the distance between it and its source rises. The wave loses energy in the medium as it spreads, and the amplitude of the wave decreases as a result.

Frequently Asked Question (FAQs) on Amplitude reduction:

Q: Why does the amplitude of a wave decrease after diffraction?

Ans: Diffraction is a physical phenomenon that is used when a wave encounters an obstacle or travels through small openings, as seen in the figure below.

When a wave undergoes diffraction, it expands out over a larger area. The energy of a wave reduces as its area rises, and hence its amplitude lowers as well.

Q: When we look up at the sky, why does the sun appear brighter than other stars that are larger than it?

Ans: When the energy comes from the star and the sun in the form of a light wave, they have to overcome the medium coming in their way. To continue the propagation, the stars lose their energy in the medium.

If the star is larger than the sun, it has higher energy than the sun. But as the sun’s distance from the earth is less than any other larger star, the energy loss is also less. Thus the amplitude of a light wave or the sun’s brightness is higher than the star larger than it.

We hope we were able to offer you with acceptable responses to your questions. Does amplitude of wave decrease? Why does amplitude of wave decrease? When does amplitude of wave decrease? Why does the amplitude of a wave decrease over time? Why Does the amplitude decrease over distance? To read more science-related articles, please visit our website.

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Does Amplitude Of Wave Change:When,Why,How And Detailed Facts

January 21, 2024March 30, 2022 by Alpa P. Rajai

The amplitude of a wave is a critical property. So, if you want to know, “Does amplitude of wave change?” When, why, and how are these things going to happen? Then go ahead and read.

The energy transported by an electromagnetic wave, an acoustic wave, or any other wave is directly proportional to the amplitude square of that wave. Thus, whenever there is a change in the wave’s energy, then its effect impacts the amplitude of the wave.

Before we go into the depth of our questions, does amplitude of wave change, how, when, and why? Let us first get brief information about the wave and its amplitude.

Wave: In physics, a wave is considered an energy transport phenomenon that transmits energy along with a medium without carrying any matter. As a result, we think of it as a medium disturbance that transports energy but not mass. There are primarily two types of waves, which are listed below:

1. Longitudinal: Sound waves
2. Transverse: Electromagnetic waves or light waves

Amplitude: The total distance between a wave’s resting position and the maximum displacement it can span is referred to as its amplitude.

Wavelength: The size or length of a single wave is known as its wavelength. It is calculated as the distance or gap between two consecutive peaks.

Frequency: The frequency of a wave tells us how many waves pass by a certain spot in a given amount of time.

Does Amplitude Of Wave Change:When,Why,How And Detailed Facts 5 — Image Credits: Geoff Ruth, Crest trough wavelength amplitude, CC BY-SA 3.0

If you are considering sound waves, their amplitude determines how loud the sound is. A higher amplitude of a sound wave means its loudness is higher, and a lower amplitude means lower loudness.

When we study a light wave, the amplitude of the wave is nothing but the brightness or intensity of the wave in comparison to other light waves of the same wavelength. Light with a greater amplitude has a greater intensity or brightness, while light with a smaller amplitude has a lesser intensity or brightness.

Now the question is, does amplitude of wave change? Let us see how things turn out.

Does amplitude of wave change?

⇒ The wave’s amplitude is a crucial characteristic.

The amplitude of a wave is not a constant characteristic. As a result, it is subject to change due to situational factors.

When does amplitude of wave change?

⇒ We know that the energy of the wave is always conserved, which means it cannot be destroyed or generated.

Any wave’s frequency and amplitude are independent properties. However, frequency change leads to a change in energy. Thus, the amplitude of every wave, whether longitudinal or transverse, changes with energy in order to conserve the total energy.

Why does amplitude of wave change?

⇒ The amplitude of a wave can vary with the change in energy of the wave.

The wave’s energy and the amplitude of the wave are closely related to each other. The relation between the energy of the wave and the amplitude of the wave is given as below:

E ∝ A²

Where letter E denotes the wave’s energy, and letter A denotes the wave’s amplitude.

We can see that the wave’s energy is directly proportional to the square of the amplitude of the wave. Thus, if there is a slight change in energy, it results in a squared change in amplitude.

We can deduce from the energy and amplitude of wave relationships that if the energy of a wave is large, its amplitude will be high. The amplitude of a low-energy wave will be similar to that of a low-energy wave. Both scenarios are represented in the diagram below.

Thus, we can say that any change in the wave’s energy leads to a change in the wave’s amplitude.

How does amplitude of wave change?

⇒ A change in energy is the most likely cause of the amplitude variation, but it might also be a change in wave speed. The wave’s energy can go up or down.

If you have a wave driver, you can use it to increase the energy and, therefore, the amplitude. However, when a wave travels through a medium, some of the energy is diluted, resulting in a reduction in amplitude. Sometimes it’s not the energy but the change in wave speed that also results in a change in wave amplitude, as seen in the ocean waves.

Let us look at some real-life examples to see what we’re talking about.

We have already discussed in detail that the wave’s amplitude depends on the energy carried by that wave. Now we know that every medium has friction. There is no such thing as a frictionless medium or an ideal medium. As a result, as a wave moves through a medium, it experiences friction. The energy of the wave will dilute as it spreads out in the medium, overcoming the friction of the medium. The loss of energy will result in attenuation or reduction of the amplitude of that wave.

Now one can also increase the amount of energy using the driver of the wave. Here, “wave driver” simply means the consistent work done on that wave. Consider the case of a helical spring that is initially at rest. As you stretch it in a horizontal direction, a transverse wave or pulse is produced. In other words, as you apply force to the spring, it will deviate from its rest position in proportion to the force applied.

To achieve a higher amplitude or maximum displacement, more energy must be applied or more work must be performed. Finally, the energy that a transverse pulse or wave carries across the medium is related to its amplitude. The wavelength, frequency, and speed of a transverse pulse or wave are unaffected by putting a lot of energy into it. The amount of energy applied to a pulse or wave will only change the amplitude of that pulse or wave.

Ocean Wave:

The change in the amplitude of ocean waves is caused by the slowing of the wave speed. Slowing the wave allows energy to be converted into higher amplitude waves since the frequency and energy level carried by the wave cannot change. When watching ocean waves approaching shallower water, this effect is very noticeable. As the propagation speed slows, the wave crests become crowded together. The wave heights or the amplitude increase as a result of the crowding until the wave breaks.

Frequently Asked Questions (FAQs):

Q: Does amplitude change over time?

Ans.: Ideally, the amplitude of the wave should not alter over time. However, as we live in the real world, things are changing.

There is no such thing as a frictionless system in the actual world. As a result, as the wave loses energy, the amplitude of the wave decreases over time. When we study a simple harmonic motion, we can see that the amplitude of the simple harmonic wave decreases exponentially over time.

The following graph represents the damping of the wave over time:

FjHLuagptrIEytid7BikC tZl9YU10xhEOHhtQ3P9XGGPbV5N6ipQ — Image Credits: anonymous, Damped sinewave, CC BY-SA 3.0

Q.: Does the amplitude of the wave change when the wave changes the medium of propagation?

Ans.: When the wave propagates from one medium to another, some part of the wave goes through the medium, and the remaining part of it will reflect back.

The portion of the wave that goes through the medium signifies the portion of the wave’s energy that has been lost in the medium. Reflected waves are considered the remaining energy. As changing media causes a decrease in energy, it directly leads us towards the change (more precisely, reduction) of amplitude.

Q.: What happens when the amplitude of the wave is doubled?

Ans.: The amplitude of a wave has a direct connection with energy, which is given below:

E ∝ A²

When the amplitude of a wave is doubled, the energy of the wave increases by four times. As a result, doubling the wave’s amplitude signifies quadrupling of the energy transferred by the wave.

Similarly, if the amplitude of a wave is tripled, it implies a nine fold increase in the supply of energy delivered by the wave.

Click here to know how to find the amplitude of a wave.

We hope we have provided you with appropriate answers to your queries. Does amplitude of wave change? When does amplitude of wave change? Why does amplitude of wave change? How does amplitude of wave change? Please visit our website to read more science-related articles.

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Can Velocity Be Negative: Why,When,How,Different Scenarios And Problems

January 21, 2024March 13, 2022 by Alpa P. Rajai

If you are already looking for an answer to the query, can velocity be negative or not, you have come to the right place. This post will also answer how and when it can be negative.

As velocity is classified as a vector quantity, it has both a magnitude (value) and a direction. Whenever an object or body moves in a positive direction described by the coordinate system, its velocity is considered positive. Its velocity is termed negative if it goes in the opposite direction.

How can velocity be negative?

Velocity, as a vector quantity, not only has a magnitude (vector length) but also has a direction.

Any vector’s magnitude or vector length, including velocity, is always positive because it is just a value. The direction of any vector, however, is determined by the frame of reference. As a result, the negative sign for any vector only denotes the vector’s direction. As a result, velocity can be negative.

When can velocity be negative?

The magnitude of velocity cannot be negative; only the direction results in a negative or positive sign. The coordinate system decides the vector’s positive and negative signs.

Consider an object or body traveling in one dimension, or we can say that along a straight line. The positive direction denotes motion in a positive direction specified by the coordinate system, while the negative direction denotes motion oppositely.

Can velocity be negative in graph?

Velocity can be positive, negative, and zero in the graph too.

In the velocity vs. time graph, if the graph’s line lies under the graph’s negative region, i.e., below the X-axis as shown in the below graph, we can say that the object or body is moving with negative velocity. The graph shows that the object or body is moving in a negative direction.

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So, based on the graphs above, we can conclude that whether the slope of the line is increasing or decreasing, if it is in the negative region, the velocity of the object is negative. Similarly, if the line of the graph is in the positive region, the object is said to have positive velocity. Finally, suppose the graph line passes over the X axis from positive to negative region or from negative to positive region. We can say that the object or body has changed its direction in that case.

Now you may be wondering when acceleration is positive or if the situation is similar to free fall. Is it possible for velocity to be negative at that moment as well? Let’s see how it goes.

Can velocity be negative when acceleration is positive?

Yes, it is possible to have negative velocity when acceleration is positive.

Consider a body or an object moving in a negative direction, having a negative velocity and acceleration. If the object slows down, its acceleration vector will be in the opposite direction from its motion, i.e., positive. It means that while velocity is negative, acceleration is positive.

Go through this article to learn more about motion with negative velocity and positive acceleration.

Problem: Suppose a car is going with a speed of 15 m/s from east to west (which we consider negative direction. The driver applies the breaks after 4 seconds at a distance of 30 m. What would be the acceleration of the car? Is the acceleration in this scenario positive or negative?

Given:

Initial velocity of car v₁ = -15 m/s

Finale velocity of car v₂ = 0 m/s (As break applies)

Time taken by car to t = 4 s

Distance traveled by the car d = 30 m

To Find:

Acceleration of the car a = ?

Solution:

As we know acceleration is given by:

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Can Velocity Be Negative: Why,When,How,Different Scenarios And Problems 11

Can Velocity Be Negative: Why,When,How,Different Scenarios And Problems 12

∴ a = 3.8 m/s²

As a result, even though the initial velocity is negative when the driver applies the brakes after 4 seconds, the acceleration is positive since it is in the opposite direction of motion.

Can velocity be negative in free fall?

Free fall is just a negative acceleration. More specifically, it denotes that something is moving faster in the downward direction.

In the Cartesian coordinate system, we usually consider the downward direction to be the negative and the upward direction to be positive. As a result, when an object is in free fall, we estimate its velocity to be negative due to the downward direction.

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Problem: Consider a tennis ball and a plastic ball falling from the same height and at the same time. The plastic ball takes 4 seconds to reach the ground, whereas the tennis ball takes 6 seconds. What are their velocities?

Given:

Time taken by plastic ball t_p = 4 sec

Time taken by tennis ball t_t = 6 sec

Acceleration due to gravity g = -9.8 m/s² (as it is in the downward direction)

To Find:

Velocity of plastic ball v_p = ?

Velocity of tennis ball v_t= ?

Solution:

In the case of free fall velocity is given by:

v = gt

∴ Velocity of the plastic ball:

v_p= gt_p

∴ v_p = -9.8 * 4 = -39.2 m/s

∴ Velocity of the tennis ball:

v_t= gt_t

∴ v_t = -9.8 * 6 = -58.8 m/s

As a result, the tennis ball has a higher velocity than the plastic ball.

Let us now analyze if various velocities such as average velocity, final velocity, initial velocity, terminal velocity, angular velocity, relative velocity, instantaneous velocity, and so on can be negative or not.

Can average velocity be negative?

Average velocity, just like velocity, is also a vector quantity. Its direction is also the same as the direction of the object’s motion.

When the average velocity is positive, an object moves forward from its initial point. When the average velocity is negative, it simply means that an object is moving backward from its initial point. AS a result, a negative average velocity just indicates the object’s backward motion.

Problem: Calculate the average velocity over a given time interval of a person if he moves 5 m in 3 s along the positive x-axis and 15 m in 7 s along the negative x-axis?

Given:

Initial displacement of the person, x_i = 5 m

Final displacement of the person, x_f = -15 m (As he travels in negative x direction)

Initial time interval t_i = 3 s

Final time interval t_f = 7 s

To Find:

Average velocity of the person v_avg = ?

Solution:

Average velocity of the person is given by:

v_avg = (x_f – x_i) / (t_f – t_i)

Putting the values in the above equation:

∴ v_avg = (-15-5) / (7-3)

∴ v_avg= -20/4 = -5m/s

Can initial velocity be negative?

The initial velocity might be either positive, negative, or zero.

If an object or body is going backward or downwards, its initial velocity is considered negative. Similarly, if it is traveling forward or upward, we consider it to have a positive initial velocity. We consider a body or object to have zero initial velocity if it is not moving at all.

Problem: Within 3 seconds, John completes the bicycle ride with a final velocity of 9 m/s and an acceleration of 4 m/s². Determine the initial velocity of John.

Given:

Final velocity v = 9 m/s

Acceleration a = 4 m/s²

Time interval t = 3 s

To Find:

Initial velocity u = ?

Solution:

To find the initial velocity, we will apply the equation of motion, which is given by:

v = u + at

∴ u = v – at

Putting the values in the above equation:

∴u = 9 – (4 * 3) = 9 -12 =-3 m/s

As we get negative initial velocity, we can say that John was initially going in the backward direction with a speed of 3 m/s and then in the forward direction with a speed of 9 m/s.

Can final velocity be negative?

The final velocity can also be either positive, negative, or zero, like the initial velocity.

If an object or body is going backward or downwards, its final velocity is considered negative. Similarly, if it is traveling forward or upward, we consider it to have a positive final velocity. If a body or object comes to a complete halt, we consider it to have zero final velocity.

Problem: Suppose a man travels a certain distance in the positive x direction at a speed of 18 m/s. Now, if his acceleration is -5 m/s², calculate the final velocity at 4 seconds.

Given:

Initial velocity u = 18 m/s

Acceleration a = -5 m/s²

Time interval t = 4 s

To Find:

Final velocity v = ?

Solution:

To find the final velocity, we will apply the equation of motion, which is given by:

v = u + at

Putting the values in above equation:

∴v = 18 +(-5)*4 = 18-20 =-2 m/s

As the person eventually switches direction, we get a negative final velocity.

Can instantaneous velocity be negative?

The gradient of an object’s displacement is nothing but called instantaneous velocity.

If the gradient of displacement at a given instant is negative, the instantaneous velocity is negative as well. This indicates that velocity is in the opposite direction of the positive direction you selected in terms of physics.

Problem: A particle moves along the x-axis according to x(t) = 15t – 3t². What is the instantaneous velocity at t = 2 s and t = 3 s?

Given:

x(t) = 15t – 3t² ……….(1)

Time t₁ = 2 sec

Time t₂ = 3 sec

To Find:

Instantaneous velocity of a particle v(t) = ?

Solution:

The motion of the particles is described by Equation (1) in terms of displacement as a function of time. We may find the equation of motion in terms of velocity by taking the derivative of the above equation.

∴v(t) = 15 – 6t

Instantaneous velocity at time t₁ = 2 sec

v(2 s) = 15 – 6*2 = 15-12= 3 m/s

Instantaneous velocity at time t₂ = 3 sec

v(3 s) = 15 – 6*3 = 15-18= -3 m/s

Can relative velocity be negative?

When we consider the velocity of an object or body with respect to another, this velocity is called the relative velocity.

When two objects or bodies are moving in the opposite direction, their relative velocity is given by the difference between their velocities. Thus, the relative velocity of oppositely moving objects ends up being negative.

Consider two objects are moving with different velocities in opposite directions. Thus, the velocity of object 2 with respect to object 1 is given by:

v₂₁ = v₂ – v₁

Problem: Two east-west train tracks run parallel to one other. Train A moves east with a speed of 54 km/h, while train B moves west with a speed of 90 km/h. What is the velocity of train B with respect to train A?

Given:

The positive direction of the x axis has been chosen to be from west to east. Thus,

Velocity of train A v_A = 54 km/h = 15 m/s

Velocity of train B v_B = -90 km/h = -25 m/s

To Find:

Velocity of train B with respect to train A v_BA = ?

Solution:

v_BA = v_B – v_A

Putting the values of velocities in the above equation:

∴v_BA =-25-15 = -40 m/s

As a result, we can conclude that train B looks to be moving at a speed of 40 m/s from east to west.

Can angular velocity be negative?

Angular velocity is also a vector quantity that contains both the direction and magnitude.

When the rotation is counterclockwise, then angular velocity is taken as positive, and when rotation is clockwise, then angular velocity is taken as negative. Furthermore, when angular displacement is decreasing, angular velocity is negative, and angular velocity is positive when it is increasing.

Problem: Calculate the angular velocity of a wheel with an initial angular displacement of π rad and an angular displacement of -π rad after 2 seconds.

Given:

Initial angular displacement ????_i = π rad

Final angular displacement ????_f=-π rad

Time interval t = 2 sec

To Find:

Angular velocity of a wheel ⍵ = ?

Solution:

Angular velocity is given by:

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Thus,

⍵ =(-π-π)/2 =-1 rad/s

Can maximum velocity be negative?

Maximum velocity is considered to be obtained when the derivative of velocity is zero. There is no way to gain any additional speed after this point.

The negative and positive only show which way the object or body is moving when it reaches its maximum velocity. More precisely, if we consider the coordinate system, we can see in which region, positive or negative, the object has the maximum velocity.

Can terminal velocity be negative?

The highest constant velocity obtained by an object as it falls through a fluid (which can be any gas or liquid) is known as terminal velocity.

The viscous force balances its weight as soon as a spherical body is submerged in a viscous liquid. If the spherical body’s density is less than the density of the surrounding fluid, the body will begin to migrate upward. Negative terminal velocity is applied to this upward directional terminal velocity.

Can change in velocity be negative?

When we take the difference between the body’s final velocity and its initial velocity, it is called the change in velocity of that body.

Because both the final and initial velocity can be negative, the velocity change can likewise be negative. Furthermore, if the final velocity differs from the initial velocity in a negative direction, the velocity change will be negative.

We hope that we have provided you with satisfactory solutions to your queries about can velocity be negative, how can velocity be negative, when can velocity be negative, and many more. Please visit our website to read more articles related to science.

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How To Find Acceleration With Velocity And Distance:3 Probs!

January 28, 2024February 16, 2022 by Alpa P. Rajai

To compute acceleration $a$ using initial velocity $u$ , final velocity $v$ , and distance $d$ , apply the formula $a = \frac{v^2 - u^2}{2d}$ . This equation originates from the kinematic relation $v^2 = u^2 + 2ad$ , assuming linear motion and constant acceleration. Acceleration, being a vector, encompasses both magnitude and direction; this formula calculates the magnitude. In cases of non-uniform acceleration, integration of the velocity function $v(t)$ is necessary. Consistent unit usage is crucial: $v$ and $u$ in meters per second ( $\text{m/s}$ ), $d$ in meters ( $\text{m}$ ), yielding $a$ in meters per second squared ( $\text{m/s}^2$ ).

How to find acceleration with velocity and distance without time

To find acceleration without time, use $a = \frac{v^2 - u^2}{2s}$ , where $a$ is acceleration, $v$ final velocity, $u$ initial velocity, $s$ distance. This derives from $v^2 = u^2 + 2as$ , a kinematic equation for constant acceleration, ensuring precise calculation when time data is unavailable.

How to find acceleration with distance time and initial velocity

To find acceleration with distance, time, and initial velocity, use $a = \frac{2(s - ut)}{t^2}$ . Here, $a$ is acceleration, $s$ distance, $u$ initial velocity, $t$ time. This formula accurately calculates acceleration, particularly in linear motion with uniform acceleration, providing a precise assessment in scenarios where final velocity is unknown.

Acceleration: A Quantitative Overview

Formula Derivation

Acceleration, denoted as a, is defined as the rate of change of velocity (v) over time (t). In situations where only velocity and distance (s) are known, the equation used is:

$a=2sv2−u2$

Here, v is the final velocity, u is the initial velocity, and s is the distance covered.

Underlying Physics

This formula is derived from kinematic equations under constant acceleration, integrating the principle of work-energy where the kinetic energy difference equates to the work done against the force causing acceleration.

Advanced Calculation Techniques

Case Study: Variable Acceleration

In cases of variable acceleration, calculus is employed. The velocity function v(t) is integrated over time to find distance, and its derivative gives acceleration:

$\int f(x) \, dx$

$s = \int v(t) \, dt$

$a(t) = \frac{dv(t)}{dt}$

Real-World Example: A Car’s Acceleration

For instance, a car accelerating from 0 to 60 km/h over 100 meters. Using our formula:

$a = \frac{(60^2 - 0^2) \times \left(\frac{5}{18}\right)^2}{2 \times 100} \approx 2.47 \, \text{m/s}^2$
$a = \frac{2 \times 100}{(60^2 - 0^2) \times \left(\frac{18}{5}\right)^2} \approx 2.47 \, \text{m/s}^2$

Practical Application: Experimental Approach

Setup and Measurement Techniques

Equipment: Motion sensor, track, and data analysis software.
Procedure: Release an object on the track, recording its velocity.
Data Analysis: Plot velocity vs. time, calculate acceleration.

Experiment: Verifying Theoretical Values

Conduct experiments, e.g., an object sliding down an inclined plane, measure the distance and final velocity, then calculate and compare the theoretical and experimental acceleration.

Challenges in Accurate Determination

Factors Affecting Accuracy

Air Resistance: Affects results, especially at high velocities.
Measurement Errors: Inaccurate distance or velocity measurements lead to erroneous acceleration calculations.
Friction: Introduces opposing force, affecting acceleration.

The Constant Acceleration Equations OR The Kinematics Formulas:

Kinematics formulas that are only relevant when an object or body moves with a constant acceleration within a given time interval are known as constant acceleration equations. When it comes to constant acceleration, the acceleration caused by gravity is the best real world example. It is commonly symbolized by the letter ‘g,’ whose value on the earth’s surface is 9.8 m/s².

The kinematic formulas, often known as constant acceleration equations, are a series of formulas that link the five kinematic variables given below.

a Constant Acceleration
v₀ Initial Velocity
v Finale Velocity
t Time Interval
ð›¥x Distance traveled by an object in one direction

Suppose an object or body is under constant acceleration, and three of these five kinematic variables (a, v, v₀, t, x) are known. In that case, we can use the kinematic equations given below to solve one of the unknown variables.

1. v = v₀ + at

2. ð›¥x = v₀t + (1/2)at²

3. v² = v₀² + 2að›¥x

How do you choose and apply a constant acceleration formula?

In kinematics, we have three equations of constant acceleration. Out of five kinematic variables, four are present in each equation.

We must select the constant acceleration equation that incorporates both the unknown variable we are looking for and three of the known kinematic variables. By introducing known variable values into the equation, we can find the unknown variable that is only unknown in the equation.

Consider the case of dragging a box that was initially steady. After 5 seconds, its velocity had increased to 10 m/s. Consider a constant acceleration for 5 seconds. Because we have v₀, v, and t, we can find the value of the unknown constant acceleration by applying the equation v = v₀ + at.

Let us see some problems of finding acceleration using velocity and distance.

But our primary concern for this article is to figure out how to calculate acceleration using velocity and distance. So, let us now talk about how to find acceleration with velocity and distance.

How to find acceleration with velocity and distance?

The constant acceleration equation is the one that is used in kinematics to find acceleration using velocity and distance.

If we have an initial velocity, a final velocity, and a distance but don’t know the time interval, we can apply the constant acceleration equation v² = v₀² + 2að›¥x to get the acceleration.

We have three known quantities and one unknown quantity in the above equation. We can calculate the constant acceleration by placing all three known values in an equation and making acceleration the subject of the equation. As a result, acceleration is determined by rearranging the above equation and given by:

We can find acceleration with velocity and distance using the equation above. Keep in mind that the constant acceleration equations only work if the acceleration is constant (as the name suggests) and in one direction. When dealing with two-dimensional or three-dimensional motion, things become more complicated. However, by applying the above equations for constant acceleration, one may build equations of motion for each direction separately. These simple equations aren’t used when acceleration is changing; instead, complex calculus is used.

Problem: A bike constantly accelerates from rest to a speed of 10 m/s across a distance of 20 m. Determine the acceleration of the bike.

Given:

The initial velocity of the bike v₀ = 0 m/s (As initially, the bike is at rest)

Finale velocity of the bike v = 10 m/s

Distance traveled by the bike ð›¥x = 20 m

To Find:

Constant acceleration of the bike a = ?

Solution:

Putting the values in the above equation:

âˆ´ a = 2.5 m/s²

As a result, the bike’s acceleration is 2.5 m/s².

Problem: From a height of 1.40 meters, a feather is dropped onto the moon. If the feather’s velocity is 2.135 m/s, then determine the acceleration of gravity on the moon.

Image Credits: Wikipedia

Given:

Initial velocity of the feather v₀ = 0 m/s (As in free falling initial velocity is zero)

Finale velocity of the feather v = 2.135 m/s

Distance traveled by the feather ð›¥x = 1.40 m

To Find:

Acceleration due to gravity on the surface of the moon a = ?

Solution:

Putting the values in the above equation:

âˆ´ a = 1.625 m/s²

Problem: At a speed of 12 m/s, a racing boat crosses the finish line and continues straight ahead. It came to a halt 18 meters from the finish line. What is the magnitude of the acceleration of the racing boat if it instantly decelerates till it comes to a stop?

Given:

Initial velocity of the racing boat v₀ = 12 m/s

Explore the advanced science and research posts to learn more.

Finale velocity of the racing boat v = 0 m/s (As it comes to a stop)

Distance traveled by the racing boat ð›¥x = 18 m

To find:

Constant acceleration of the racing boat a = ?

Solution:

Putting the values in the above equation:

âˆ´ a = -4 m/s²

The negative sign indicates that the racing boat’s acceleration decreases and its value is 4 m/s².

We hope we have answered all of your questions on how to find acceleration with velocity and distance.

Explore the advanced science and research posts to learn more.

Also Read:

Does Constant Acceleration Mean Constant Velocity: Detailed Facts

January 21, 2024February 1, 2022 by Alpa P. Rajai

Constant velocity and constant acceleration are phrases that you could come upon. Does constant acceleration mean constant velocity? Let us have a look at this article to find out the answer.

When an object moves with a constant velocity, it means that the moving object has no acceleration. However, when an object moves with constant acceleration, its velocity changes by a constant amount throughout the same time interval.

Before delving into the answer, it is important to understand what you mean by constant velocity and constant acceleration. Let us have a look at it first.

Constant Velocity:

Velocity is the physical term that gives information about the rate of change of an object or body’s displacement. Thus, if an object changes its displacement from x_i to x_f over a time interval t, its velocity v may be calculated using the following formula:

gNf3oQ6yATGlMUBga7KDzY74vFdwMi1b3flYHh07Kqcq4t8wS7eTo62Kx3EcAEX2423F6pUHijUNwJ9lqT3HYnPfvPK145jEH75N5ARCAnZKaBOGPNZ5rvyG5zb jA1bhbqX3Cgd

Thus, when the distance traveled in one direction is the same during each time interval, then the velocity of an object or body is said to be constant.

As a result, having a constant velocity does not imply that the object is stable. If a graph of displacement vs time is drawn, it will be parallel to the X axis, the time axis, i.e. a horizontal line as shown in the figure below.

5ELE81ZZdkRvQHWEf9F jOigRvXY qvClvLOFZge HStWXDnAuSV4ga WSgrHUz2VFsr8DPKe T5OBo8zq7hRViiKtoQVmB 6cBMfLtUlf2pgjzmGeeswMZrM fC2 C8yKX9KqNg

Constant Acceleration:

Acceleration is also the physical term that gives information about the rate of change of an object or body’s velocity. Thus, when a moving object is changing, its speed in one direction is the same during each time interval, then the acceleration of an object or body is said to be constant. Thus, if an object changes its velocity from v_i to v_fover a time interval t, its acceleration a may be calculated using the following formula:

As a result, same as the constant velocity, having a constant acceleration also does not imply that the object is stable. If a graph of velocity vs time is drawn, it will be parallel to the X axis, the time axis, i.e. a horizontal line as shown in the figure below.

Learn more about the graph of constant velocity vs. time by reading this article.

Does constant acceleration mean constant velocity?

Constant acceleration and constant velocity are two physics expressions that have different meanings.

When anything has constant acceleration, it means that its velocity change is the same in each time interval. It means it is subjected to the same amount of force throughout the motion. As a result, constant acceleration does not imply constant velocity at all.

You might wonder what are the differences between constant velocity and constant acceleration? Let us look at the differences between constant velocity and constant acceleration.

Constant velocity vs Constant acceleration:

Motion with constant velocity and constant acceleration has totally different meanings. The followings are the differences between constant velocity and constant acceleration:

Suppose any object or body is traveling with constant velocity. It means that it continuously travels at the same speed and also in the same direction. If the velocity of an object or body is constant, then its velocity is not changing, and thus, it has no acceleration with time. Consider you are driving on the highway on one way where your speedometer indicates the same speed, then it is said that you are traveling with constant velocity.

Constant acceleration is quite different from constant velocity. Suppose any object or body is moving with constant acceleration. It means that the velocity of an object or body is changing, but the rate at which it is changing is always constant. The best example of constant acceleration is the acceleration due to gravity.

Consider an object is falling from some height, which happened due to the earth’s gravitational force. If you are considering the earth’s gravitational force, then the gravitational acceleration due to earth has a constant value of 9.8 m/s2. The gravitational force on the moon is 1/6^th of that of the earth. Thus, the gravitational acceleration of the moon is also 1/6th of that of the earth, so its value is 1.625 m/s2.

Frequently Asked Questions (FAQs)

Q: Does constant velocity mean no acceleration?

Ans: Acceleration is a physics term that describes the rate at which velocity changes.

When a moving item has constant velocity, it means that time is changing, but its velocity is not. As a result, according to the definition of acceleration, if the object’s velocity does not change, it does not have acceleration. As a result, we might conclude that constant velocity implies no acceleration.

Q: What is the cause of the object’s zero acceleration?

Ans: Zero acceleration term denotes that the velocity of an object or body remains constant across time.

When no net force is exerted on a moving object, the object will continue to move in the same direction and speed, or more accurately, velocity. As a result, given those circumstances, we can say that it has zero acceleration.

Problems of finding velocity and acceleration:

Problem 1: At time t = 25 seconds, a boat is moving at a velocity of 50 m/s, and at time t = 50 seconds, the same boat is moving at a velocity of 100 m/s. Find the constant acceleration by calculating the change in velocity and time.

Given:

Initial time t_i = 25 s

Finale time t_f = 50 s

At time t1 velocity of a boat v_i = 50 m/s

At time t2 velocity of the same boat v_f = 100 m/s

To find:

Change in velocity Δv = ?

Time interval Δt = ?

Acceleration a = ?

Solution:

Change in velocity:

Δv = v_f– v_i = (100 – 50) m/s = 50 m/s

Time interval:

Δt = t_f – t_i = (50 – 25) s = 25 s

Constant acceleration of the boat:

a = Δv/Δt =(50 m/s) / 25 s

∴a = 2 m/s²

Thus, the constant acceleration of the boat is 2 m/s².

Problem 2: Consider a car is moving in the east direction, and in each second, it travels the distance of 7 m. Find its velocity and acceleration.

Given:

Time interval Δt = 1 s

Change in displacement Δx = 7 m

To find:

Velocity v = ?

Acceleration a = ?

Solution:

Velocity of the car:

v = Δx / Δt

∴ v = 7 m / 1 s = 7 m/s

As each second car is traveling a distance of 7 m, we can say that its velocity is constant, and its value is 7 m/s.

Acceleration of the car:

As the car has constant velocity we can say that Δv = 0.

Thus, acceleration of the car a = 0 m/s².

Also Read:

Constant Velocity vs Time Graph: Graphs And Detailed Analysis

January 21, 2024January 27, 2022 by Alpa P. Rajai

The phrase “constant” refers to a state of being stable. What happens when an object’s velocity remains constant? Let’s look at a constant velocity vs. time graph to see what we are talking about.

When a body or object moves at a constant velocity, the constant velocity vs time graph will have no slope. And because velocity remains constant, i.e., it does not change even when time does, there will be no acceleration.

Velocity vs Time Graph:

The velocity of an object or body is nothing but its speed in a particular direction. It means that if two objects or bodies are moving at the same speed but not in the same direction, their velocities will differ.

In the velocity vs time graph, there will be time on the horizontal axis (X-axis) as it is the independent variable. At the same time, on the vertical axis (Y-axis), there will be the object’s velocity as it is time dependent. The velocity vs. time graph is the one that is used to compare how velocity is changing with time. Moreover, using this graph, velocity and its direction of motion, acceleration of an object, and displacement of an object can be found. The slope of the line in the velocity vs time graph will give us the object’s acceleration. The area under that line, on the other hand, will give us the object’s displacement.

Meaning of the slope of the velocity vs. time graph:

In the velocity vs time graph, the slope of the graph gives us acceleration. As we know, if we divide the change in the y-axis to change in the x-axis, it gives us the slope of the graph. As a result, we can write:

vW1BLbC0dDu WBm0olYoPfQrWN17KYjHk OVQgSJ69gAQMuXT24ODomASWdt 5XhSnmBtT8hV0Tiu4BR r AFyejc8HCEJQCTAntB3d

We now know that velocity is measured on the y axis, and time is measured on the x axis. As a result of plugging in the y axis and x axis values, we get:

Constant Velocity vs Time Graph: Graphs And Detailed Analysis 23

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However, dividing the change in velocity by the passage of time yields the value of acceleration. As a result, by looking at the slope of the velocity vs time graph, one can calculate the acceleration. Thus, we can write:

Slope = Acceleration a

When the slope is steeper, its value is higher, so the acceleration is greater. And when the slope is less steep, or we might say shallower, its value is less, so the acceleration is lower.

The meaning of the shape of velocity vs. time graph:

The slope of the graph not only gives the magnitude of acceleration but also tells us how the object is accelerating, i.e., if it is increasing, decreasing, or not accelerating. If the graph has a positive slope, it will also have a positive acceleration. Similarly, if the slope of the graph is negative, it means acceleration is also negative. Lastly, if the graph has no slope or zero slope, the object is not accelerating or has zero acceleration.

To further grasp positive, negative, and zero acceleration, consider the example of boating. The boat is initially stationary on the riverbank. A group of folks decided to take a river trip by boat after some time had passed. As a result, turning on the motor increases the boat’s velocity, and the boat begins to move. The boat is now going at a consistent speed as they approach the middle of the river. They slowed down and then finally came to a halt when they noticed familiar faces on another boat. They restart the boat after some conversation time. This is how the velocity vs. time graph for the entire scenario will look:

If we analyze the graph, we can observe that the boat has no velocity because it is standing on the river bank. As people start the boat’s engine, the velocity increases with time. As a result, its slope will be positive, so its acceleration will be positive. When the boat is moving with constant speed, the graph will be a straight line, and thus it will have no acceleration. After that, as the boat slows down and comes to a halt, its slope will be negative and thus will have negative acceleration, which is also called deceleration.

If you want to know how to find acceleration in the velocity-time graph, go through this article. Let us now focus on the constant velocity vs time graph, which is the primary goal of this article.

Constant Velocity vs Time Graph:

In each time interval, if a body or the object is traveling the same distance in the same direction, then we can say that its velocity is constant. Because velocity does not change with time, the plot of the constant velocity vs. time graph will be a horizontal line parallel to the x axis or the time axis. The line on the graph has no slope because it is horizontal. As a result, we can conclude that the object which is moving with constant velocity has no acceleration.

Consider a car is moving in the east direction with a constant velocity of 7 m/s, i.e., in each second, it travels the distance of 7 m.

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If the velocity vs. time graph is plotted for the given data of the car, then the graph will look like the following.

We can observe that because the motion of the car is continuous, the graph of velocity vs. time is a horizontal line. As we know, the horizontal line has no slope; hence there is no acceleration. It can be proved mathematically as follows:

yMHwu4SAaVKh5WMU nY49cvvx HQJItCemyeCJuVK2oYWAjdv asiheDjdMtlmQ1jWLPAf VQqdvoDryGrRbmvgzR 2uFJWUND4V2SYlc88xjOoCj8vwwj9Y9Z0Egebq7 R7YRkh

∴ a = 0 m/s²

Frequently Asked Questions (FAQs):

Q: How can you tell when velocity is constant of a velocity time graph?

Ans: The slope of the velocity vs time graph reveals information regarding velocity and acceleration.

Consider an object moving with any velocity and plot the velocity vs. time graph to know its motion. If an object moves at a constant velocity, it shows that there is no change in velocity with time. Thus the graph has no slope. It means if the graph of velocity vs. time is a horizontal line, then we can say that its velocity is constant.

Q: If the object is not accelerating, does it mean that it is stable?

Ans: The object is said to be accelerating if its velocity keeps on changing with time.

The term “stable” refers to an object that has no velocity and consequently no acceleration. Furthermore, if an object moves at a constant velocity (one that does not change over time), it will not accelerate. As a result, we can conclude that if the acceleration is zero, it is not necessarily stable; it can be traveling at a constant velocity.

Q: How can an object with zero acceleration move?

Ans: An object or body can move only if it is under the influence of force.

As per Newton’s second law, if the acceleration of an object or body is zero, it means there is no net force acting on it. The net force is zero means the opposite force acting on an object or body cancels each other. As a result, we can say that an object or a body can move even without acceleration.

Also Read:

How To Find Acceleration With A Constant Velocity: Facts And Problem Examples

February 17, 2024January 18, 2022 by Alpa P. Rajai

How to Find Acceleration with a Constant Velocity

Acceleration is a fundamental concept in physics and plays a crucial role in understanding the motion of objects. In this blog post, we will explore how to find acceleration with a constant velocity. We will delve into the relationship between acceleration and constant velocity, the mathematical formula for acceleration, and provide step-by-step guides and examples to calculate acceleration in different scenarios.

Understanding the Concept of Acceleration

Acceleration refers to the rate of change of velocity. It measures how quickly an object’s velocity changes over a specific time interval. In simpler terms, acceleration describes how an object’s speed or direction of motion changes over time.

The Relationship between Acceleration and Constant Velocity

In physics, velocity and acceleration are closely related but distinct concepts. Velocity describes the speed and direction of an object’s motion, while acceleration measures the change in velocity.

When an object moves with a constant velocity, it means that both its speed and direction remain unchanged over time. In this scenario, the object’s acceleration is zero. This is because there is no change in velocity, and acceleration is defined as the rate of change of velocity.

The Mathematical Formula for Acceleration

The mathematical formula for acceleration is derived from the definition of acceleration as the rate of change of velocity. It can be expressed as:

$a = frac{Delta v}{Delta t}$

Where:
– $a$ represents acceleration
– $Delta v$ represents the change in velocity
– $Delta t$ represents the change in time

This formula allows us to calculate the acceleration of an object by dividing the change in velocity by the change in time. The resulting unit of acceleration is typically meters per second squared (m/s^2).

The Difference between Velocity and Acceleration

To gain a deeper understanding of finding acceleration with a constant velocity, we must first differentiate between velocity and acceleration.

Defining Velocity and Acceleration

Velocity is a vector quantity that describes the speed and direction of an object’s motion. It is represented by a velocity vector, which contains both magnitude (speed) and direction. For example, if an object is moving at a constant speed of 10 meters per second (m/s) to the right, its velocity vector would be represented as 10 m/s to the right.

Acceleration, on the other hand, is also a vector quantity but represents the rate at which an object’s velocity changes. It is defined as the change in velocity divided by the time interval over which the change occurs. Acceleration is typically measured in m/s^2.

How Velocity and Acceleration Relate to Each Other

Velocity and acceleration are related in a straightforward manner. When an object is moving with a constant velocity, its acceleration is zero. This means that the object’s speed and direction of motion remain unchanged over time.

However, it’s important to note that an object can have a constant velocity while still experiencing changes in speed or direction. For example, if an object is moving in a circular path at a constant speed, its velocity is constant, but its acceleration is not. This is because the object is constantly changing its direction of motion.

Calculating Acceleration with Constant Velocity and Time

Now let’s explore how to calculate acceleration when we have constant velocity and time. In this scenario, we can determine the acceleration by simply dividing the change in velocity by the change in time.

The Role of Time in Acceleration Calculation

Time plays a crucial role in calculating acceleration. It represents the time interval over which the change in velocity occurs. By measuring the time taken for the velocity to change, we can determine the rate at which the object’s velocity is changing.

Step-by-Step Guide to Calculate Acceleration

To calculate acceleration with constant velocity and time, follow these steps:

Determine the initial velocity of the object.
Determine the final velocity of the object.
Calculate the change in velocity by subtracting the initial velocity from the final velocity.
Determine the time interval over which the change in velocity occurs.
Divide the change in velocity by the time interval to calculate the acceleration.

Let’s illustrate this with an example:

Example:
An object starts with an initial velocity of 20 m/s and ends with a final velocity of 40 m/s. The time interval over which this change in velocity occurs is 5 seconds.

Using the formula for acceleration, we can calculate:

$a = frac{Delta v}{Delta t}$

$a = frac{40 , text{m/s} - 20 , text{m/s}}{5 , text{s}}$

$a = frac{20 , text{m/s}}{5 , text{s}}$

$a = 4 , text{m/s}^2$

Therefore, the acceleration of the object is 4 m/s^2.

Determining Acceleration with Velocity and Distance

Another way to calculate acceleration is by using velocity and distance. In this scenario, we need to consider the distance covered by the object along with its velocity.

The Importance of Distance in Acceleration Calculation

Distance is a key factor in determining acceleration as it allows us to measure the displacement of the object. Displacement refers to the change in position of an object and is a vector quantity. By considering the distance covered, we can determine the object’s change in velocity over that distance.

Detailed Process to Determine Acceleration with Velocity and Distance

To determine acceleration using velocity and distance, we can follow these steps:

Determine the initial velocity of the object.
Determine the final velocity of the object.
Measure the distance covered by the object.
Calculate the change in velocity by subtracting the initial velocity from the final velocity.
Divide the change in velocity by the distance covered to calculate the acceleration.

Let’s look at an example to clarify this process:

Example:
An object starts with an initial velocity of 10 m/s and ends with a final velocity of 30 m/s. During this time, it covers a distance of 50 meters.

Using the formula for acceleration, we can calculate:

$a = frac{Delta v}{d}$

$a = frac{30 , text{m/s} - 10 , text{m/s}}{50 , text{m}}$

$a = frac{20 , text{m/s}}{50 , text{m}}$

$a = 0.4 , text{m/s}^2$

Hence, the acceleration of the object is 0.4 m/s^2.

The Magnitude of Acceleration with a Constant Velocity

Image by SweetWood – Wikimedia Commons, Wikimedia Commons, Licensed under CC0.

When discussing acceleration with a constant velocity, the magnitude of acceleration refers to the absolute value of acceleration without considering its direction.

What is Magnitude in Terms of Acceleration

Magnitude describes the size or quantity of a vector without taking into account its direction. In the context of acceleration, magnitude refers to the absolute value of acceleration, disregarding whether it is positive or negative.

How to Calculate the Magnitude of Acceleration

To calculate the magnitude of acceleration, we can simply take the absolute value of acceleration. This is done by removing the positive or negative sign associated with the value.

For example, if the acceleration is -5 m/s^2, the magnitude of acceleration would be 5 m/s^2.

Examples of Determining the Magnitude of Acceleration with a Constant Velocity

Let’s consider an example to determine the magnitude of acceleration with a constant velocity:

Example:
An object moves with a constant velocity of 8 m/s. In this scenario, the acceleration is zero since the velocity remains constant. Therefore, the magnitude of acceleration is also zero.

Understanding how to find acceleration with a constant velocity is essential in the study of physics and motion. By recognizing the relationship between acceleration and constant velocity, as well as employing the appropriate formulas and calculations, we can determine the acceleration of an object in various scenarios. This knowledge allows us to analyze and describe the motion of objects accurately, providing valuable insights into the behavior of the physical world.

How can I find constant acceleration with a given velocity and time?

To find constant acceleration when given velocity and time, it is necessary to understand the relationship between these variables. By utilizing the equation for average acceleration (acceleration equals change in velocity divided by the change in time), one can calculate the constant acceleration. The article “Finding Constant Acceleration: Velocity and Time” provides a detailed explanation on how to apply this formula and obtain the constant acceleration value by using the given velocity and time.

Numerical Problems on how to find acceleration with a constant velocity

Problem 1

A car is moving with a constant velocity of 20 m/s. After 10 seconds, the car’s velocity increases to 30 m/s. Calculate the acceleration of the car during this time period.

Solution:

Given:
Initial velocity, $u = 20 , text{m/s}$
Final velocity, $v = 30 , text{m/s}$
Time, $t = 10 , text{s}$

Acceleration ( $a$ ) can be calculated using the formula:

$a = frac{{v - u}}{{t}}$

Substituting the given values:

$a = frac{{30 , text{m/s} - 20 , text{m/s}}}{{10 , text{s}}}$

$a = frac{{10 , text{m/s}}}{{10 , text{s}}}$

$a = 1 , text{m/s}^2$

Therefore, the acceleration of the car during this time period is $1 , text{m/s}^2$ .

Problem 2

A cyclist is moving with a constant velocity of 12 km/h. After 5 minutes, the cyclist’s velocity increases to 20 km/h. Calculate the acceleration of the cyclist during this time period.

Solution:

Given:
Initial velocity, $u = 12 , text{km/h}$
Final velocity, $v = 20 , text{km/h}$
Time, $t = 5 , text{minutes} = 5 times 60 , text{s} = 300 , text{s}$

Acceleration ( $a$ ) can be calculated using the formula:

$a = frac{{v - u}}{{t}}$

Substituting the given values:

$a = frac{{20 , text{km/h} - 12 , text{km/h}}}{{300 , text{s}}}$

$a = frac{{8 , text{km/h}}}{{300 , text{s}}}$

$a = frac{{8 , text{km/h}}}{{300 , text{s}}} times frac{{1000 , text{m}}}{{1 , text{km}}} times frac{{1 , text{h}}}{{3600 , text{s}}}$

$a = frac{{8 times 1000}}{{300 times 3600}} , text{m/s}^2$

$a = frac{{8000}}{{1080000}} , text{m/s}^2$

$a = frac{{4}}{{135}} , text{m/s}^2$

Therefore, the acceleration of the cyclist during this time period is $frac{{4}}{{135}} , text{m/s}^2$ .

Problem 3

A train is moving with a constant velocity of 80 m/s. After 15 seconds, the train’s velocity decreases to 60 m/s. Calculate the acceleration of the train during this time period.

Solution:

Given:
Initial velocity, $u = 80 , text{m/s}$
Final velocity, $v = 60 , text{m/s}$
Time, $t = 15 , text{s}$

Acceleration ( $a$ ) can be calculated using the formula:

$a = frac{{v - u}}{{t}}$

Substituting the given values:

$a = frac{{60 , text{m/s} - 80 , text{m/s}}}{{15 , text{s}}}$

$a = frac{{-20 , text{m/s}}}{{15 , text{s}}}$

$a = -frac{{20 , text{m/s}}}{{15 , text{s}}}$

Therefore, the acceleration of the train during this time period is $-frac{{20 , text{m/s}}}{{15 , text{s}}}$ or approximately $-1.33 , text{m/s}^2$ .

Also Read:

What is the wavelength of photon: How to Find, Several Insights And Facts

January 21, 2024January 11, 2022 by Alpa P. Rajai

The wavelength of photons tells us about their energy. So in this article, we will look at what is the wavelength of photons and how to find it. Let us begin.

Photons travel through electromagnetic waves. As the photon is ultimately a part of the electromagnetic wave, its wavelength will be the same as the electromagnetic wave. If the energy and frequency of a photon are known, then from that, one can easily find the wavelength of the photon.

Before we get into the wavelength of a photon, let’s have a look at what a photon is.

Photon:

As the energy that is contained by photons is not divisible, they are often described as energy packets. Maxwell has described photons as electric fields which are traveling through space. Or, to put it another way, photon energy is stored in the form of an oscillating electric field that can oscillate at any frequency. Thus a quantum of electromagnetic radiation or energy is called a photon.

Photons are particles that have neither a charge nor a mass. As a result, they are able to travel at the speed of light. The speed of the electric field can decide the speed of the photons in free space. The emission of photons is possible by means of the action of the charged particles and some other methods like radioactive decay.

What is the wavelength of photon?

The properties of photons are the same as those of electromagnetic waves. As a result, each photon is associated with its unique frequency and wavelength.

Photons travel in waves, as though each one is riding a roller coaster that only uses the same track repeatedly. The wavelength of a photon wave is the length of the wave, or more precisely, the distance between two consecutive points of the same phase of the wave.

Three different wavelengths are shown in the diagram below. Although photons do not have color, they will correspond to the light of that particular color.

What is the wavelength of photon — Image Credits: Wikipedia

How to find wavelength of a photon?

The length of an electric field wave, or a photon wave, is the wavelength of a photon.

To determine the wavelength of a photon, either its energy or frequency is used. As a result, if any of them are known, the wavelength of a photon can be found easily.

Let’s look at how to find wavelength of a photon using frequency and energy.

How to find wavelength of a photon with frequency?

The frequency and the wavelength of a photon are related to each other.

The length of the photon wave gives the wavelength of the photon wave. While the number of photon wavelengths that propagates every second gives us the frequency of photon waves. As a result, if a photon’s wavelength is short, its frequency will be high, and its frequency will be low if its wavelength is long.

As one increases while the other decreases, we can say that they have an inverse relationship. Let us derive a mathematical equation that reflects the link between photon frequency and wavelength.

Several quantities such as wavelength, period, frequency, and so on can be used to describe a wave. As we know, the frequency of a photon wave determines the number of photon waves that propagate each second. As a result, the frequency of a photon wave can be calculated as follows:

……….(1)

Where f is the frequency of the photon wave, and T is the period of the photon wave, i.e., the time it takes for the photon wave to complete one cycle.

After one period, every wave point returns to the same value. This happens because in a wave during one period, one oscillation occurs, and each oscillation travels a distance of one wavelength in that time.

The distance traveled by any wave in a unit of time determines its speed. But as the wave is traveling with the speed of light, thus we denote it with the letter c, and it can be given by:

……….(2)

From equations (1) and (2), we can write:

c = ????f ……….(3)

Thus, the wavelength of the photon is given by:

……….(4)

Because the speed of light c is constant and has a value of 3 X 10⁸ m/s, we may deduce from the above equation that the wavelength of a photon is inversely proportional to its frequency.

How to calculate wavelength of a photon given energy?

The frequency of a photon relates to both its energy and wavelength. As a result, the photon’s wavelength is also connected to its energy.

The photon wave’s wavelength contains information about its energy. A shorter wavelength photon wave will have a higher frequency and consequently higher energy. Similarly, a photon wave with a longer wavelength will have a lower frequency and thus less energy.

Also, in this case, a longer wavelength corresponds to lower wave energy, whereas a shorter wavelength corresponds to higher wave energy. As a result, we can state that the wavelength of the photon wave and its energy are inversely proportional. In terms of an equation, let’s look at the relationship between energy and wavelength of the photon wave.

According to the great scientist Max Plank, light is composed of discrete packets of energy known as quanta of light, which are also known as photons. The energy of light can only have discrete values. Plank further said that energy is given by the product of photon frequency and a constant known as Plank’s constant. We can express it mathematically as follows:

E = hf ……….(5)

Where h = Plank’s constant (6.626 X 10^-34 J s)

When we compare equations (4) and (5), we get the following expression for energy:

……….(6)

Rearranging Plank’s equation, the wavelength of a photon in terms of energy is given by:

……….(7)

Thus, if the energy of a photon or light wave is known, the wavelength of the photon can be determined using Plank’s equation.

Some problems of finding the wavelength of the photon using frequency and energy:

Problem: What is the wavelength of a light wave with a frequency of 7 X 10¹⁴ Hz?

Given parameters:

Frequency of photon f =7 X 10¹⁴ Hz

Speed of light c = 3 X 10⁸ m/s

To Find:

Wavelength of photon ???? = ?

Solution:

???? = c / f

???? = 3 X 10⁸ / 7 X 10¹⁴

∴ ???? = 0.428 X 10^-6 m

∴ ???? = 428 nm

As a result, a photon with a frequency of 7 X 10¹⁴ Hz has a wavelength of 428 nm.

Problem: What wavelength will a photon have if its energy is4 X 10^-15 J?

Given parameters:

Energy of photon E = 4 X 10^-15 J

Plank’s constant h = 6.626 x 10^-34 Js

Speed of light c = 3 X 10⁸ m/s

To Find:

Wavelength of photon ???? = ?

Solution:

???? = hc/ E

???? = 6.626 X 10^-34 X 3 X 10⁸ / 4 X 10^-15

∴ ???? = 5 X 10^-11 m

∴ ???? = 500 nm

As a result, a photon with an energy of 4 X 10^-15 J has a wavelength of 500 nm.

Problem: If the energy of a photon is 2.19 × 10¹¹ ev, determine the wavelength of that photon.

Given parameters:

Energy of photon E = 2.19 × 10¹¹ ev

∴ E = 2.19 × 10¹¹ X 1.6 X 10-19

∴ E = 3.05 × 10^-8 J =350 X 10^-10 J

Plank’s constant h = 6.626 x 10^-34 Js

Speed of light c = 3 X 10⁸ m/s

To Find:

Wavelength of photon ???? = ?

Solution:

???? = hc/ E

???? = 6.626 X 10^-34 X 3 X 10⁸ / 350 X 10^-10

∴ ???? = 0.056 X 10^-16 m

As a result, a photon with an energy of 2.19 × 10¹¹ ev has a wavelength of 0.056 X 10^-16 m.

Also Read:

How To Find Normal Force With Tension: The Complete Guide !

January 21, 2024January 6, 2022 by Alpa P. Rajai

How to Find Normal Force with Tension

Understanding the concept of normal force and its relationship with tension is crucial in the field of physics. In this blog post, we will explore the intricacies of finding the normal force with tension, providing step-by-step guidance, worked-out examples, and debunking common misconceptions along the way. So, let’s dive right in!

A. Understanding the Concept of Normal Force

The normal force is a fundamental concept in physics that arises when an object comes into contact with a surface. It is a force exerted perpendicular to the surface, opposing the force of gravity acting on the object. The magnitude of the normal force depends on various factors such as the weight of the object, the angle of inclination, and the presence of other forces.

B. The Role of Tension in Determining Normal Force

tension, on the other hand, is a force that occurs when an object is pulled or stretched by a rope, cable, or any other similar medium. It acts in the direction of the rope, opposing the force applied to it. When tension is present, it affects the value of the normal force experienced by an object, especially in scenarios where the object is suspended or connected to a system of ropes.

C. The Relationship between Normal Force and Tension

The relationship between normal force and tension can be understood through Newton’s third law of motion, which states that every action has an equal and opposite reaction. When an object is at rest or in equilibrium, the tension force within a rope or cable is equal to the normal force experienced by the object. This means that the tension force and the normal force have the same magnitude but act in opposite directions.

Step-by-Step Guide to Calculate Normal Force with Tension

Image by Cdang – Wikimedia Commons, Wikimedia Commons, Licensed under CC BY-SA 3.0.

how to find normal force with tension — Image by Joseasorrentino – Wikimedia Commons, Wikimedia Commons, Licensed under CC BY-SA 4.0.

Now that we have a solid understanding of the concept, let’s explore a step-by-step guide to calculate the normal force with tension.

A. Identifying the Variables

To calculate the normal force with tension, we need to identify the variables involved in the system. These variables may include the mass of the object, the angle of inclination, the force applied, and the presence of friction. By recognizing and understanding these variables, we can apply the appropriate formulas and equations to solve for the normal force.

B. Applying the Correct Formulas

To calculate the normal force with tension, we often utilize the principles of trigonometry and Newton’s laws of motion. For example, when dealing with an object on an inclined plane, we can use the formula:

$N = mg\cos(\theta)$

where N represents the normal force, m is the mass of the object, g is the acceleration due to gravity, and θ is the angle of inclination.

C. Worked out Examples of Calculating Normal Force with Tension

Let’s walk through a practical example to better understand how to calculate the normal force with tension. Suppose we have a box with a mass of 10 kg resting on an inclined plane with an angle of inclination of 30 degrees. The box is connected to a rope that makes an angle of 45 degrees with the horizontal. We want to find the normal force acting on the box.

First, we determine the weight of the box using the formula:

$W = mg = 10 kg \times 9.8 m/s^2 = 98 N$

Next, we calculate the gravitational force component acting parallel to the incline:

$F_{\text{parallel}} = mg\sin(\theta) = 10 kg \times 9.8 m/s^2 \times \sin(30^\circ) = 49 N$

Then, we find the tension force in the rope:

$T = \frac{F_{\text{parallel}}}{\cos(\phi)} = \frac{49 N}{\cos(45^\circ)} = 69.296 N$

Finally, using Newton’s third law of motion, we conclude that the normal force acting on the box is 69.296 N.

Common Misconceptions about Normal Force and Tension

Image by Sanpaz – Wikimedia Commons, Wikimedia Commons, Licensed under CC BY-SA 3.0.

Let’s address some common misconceptions that often arise when discussing the concepts of normal force and tension.

A. Is Tension a Normal Force?

No, tension is not a normal force. tension refers to the force experienced by an object when being pulled or stretched by a rope or cable. On the other hand, the normal force is the force exerted by a surface perpendicular to the object in contact with it.

B. Does Tension Equal Force?

In certain scenarios, tension can be equal to the force applied to it. However, in the context of finding the normal force with tension, tension and the normal force have the same magnitude but act in opposite directions due to Newton’s third law of motion.

C. Does Tension Force Do Work?

Yes, tension force can do work. When an object is lifted or moved by a rope or cable, the tension force applied by the rope transfers energy to the object, thereby doing work on it.

How can the coefficient of friction be used to calculate the normal force in a system?

Calculating normal force with coefficient is a crucial concept in physics. One can understand this concept better by exploring the relationship between tension and normal force. By understanding how to find the normal force with the coefficient of friction, one can gain insight into the mechanics of objects in contact with each other. To explore this topic further, you can refer to the article on Calculating normal force with coefficient.

How to Find Tension Force without Acceleration

In certain cases, we may need to find the tension force acting on an object without considering acceleration. Let’s explore the process of finding the tension force in such scenarios.

A. Understanding the Scenario

When an object is in equilibrium or at rest, the net force acting on it is zero. In this case, we can determine the tension force by considering the forces acting on the object and applying the principle of equilibrium.

B. The Calculation Process

To find the tension force without acceleration, we need to analyze the forces acting on the object. By considering the weight force and any other forces involved, we can set up an equation that ensures the object is in equilibrium. Solving this equation will give us the tension force.

C. Example Problems for Better Understanding

Let’s consider a simple example to illustrate how to find the tension force without acceleration. Suppose we have a mass of 5 kg hanging from a rope attached to a ceiling. The mass is at rest, and we want to find the tension force in the rope.

First, we recognize that the weight force of the object is 5 kg multiplied by the acceleration due to gravity (9.8 m/s^2), which gives us 49 N. Since the object is at rest, the tension force in the rope must equal the weight force, resulting in a tension force of 49 N.

By following this process, we can accurately determine the tension force acting on an object without acceleration.

Also Read:

How to Calculate Force Without Acceleration: In-depth Guide

January 21, 2024December 14, 2021 by Alpa P. Rajai

How to Calculate Force without Acceleration

In physics, force is a fundamental concept that describes the influence that can cause an object to accelerate. However, there are situations where we need to calculate force without knowing the acceleration. Understanding how to calculate force without acceleration is essential in various fields, such as mechanics and engineering. In this blog post, we will delve into the concept of force without acceleration, discuss the role of mass in these calculations, explore different types of forces, and provide worked-out examples to solidify our understanding.

Understanding the Concept of Force without Acceleration

Force, in simple terms, can be defined as a push or pull on an object. It is a vector quantity, which means that it has both magnitude and direction. When an object experiences an acceleration, the force acting on it can be calculated using Newton’s second law of motion:

$F = ma$

where $F$ is the force, $m$ is the mass of the object, and $a$ is the acceleration. However, in certain scenarios, the acceleration may be unknown or zero. This is where calculating force without acceleration becomes necessary.

The Role of Mass in Calculating Force without Acceleration

Mass plays a crucial role in calculating force without acceleration. Mass is a measure of an object’s inertia, or its resistance to changes in motion. When an object is at rest or moving with a constant velocity (zero acceleration), the net force acting on it is zero. According to Newton’s first law of motion, an object will remain at rest or continue moving in a straight line at a constant velocity unless acted upon by an external force.

In these situations, the force required to sustain the object’s motion without acceleration can be calculated using the equation:

$F = mg$

where $F$ is the force, $m$ is the mass of the object, and $g$ is the acceleration due to gravity. This equation allows us to calculate the force exerted by an object’s weight, commonly known as the gravitational force.

The Importance of Direction in Force Calculation

When calculating force without acceleration, it is essential to consider the direction of the force. As mentioned earlier, force is a vector quantity, meaning it has both magnitude and direction. Two forces with the same magnitude but opposite directions can cancel each other out, resulting in a net force of zero.

For example, when an object is placed on a horizontal surface, the force of gravity acts vertically downward, while the normal force exerted by the surface acts perpendicular to it. The normal force balances the force of gravity, resulting in zero net force in the vertical direction. In this case, the normal force can be calculated as:

$F_{text{normal}} = mg$

where $F_{text{normal}}$ is the normal force, $m$ is the mass of the object, and $g$ is the acceleration due to gravity.

The Challenge of Calculating Force without Knowing Acceleration

Calculating force without knowing the acceleration can present a challenge. Without the knowledge of acceleration, we cannot use Newton’s second law directly to determine the force acting on an object. However, there are techniques and methods that can help us overcome this challenge.

Overcoming the Challenge: Techniques and Methods

One technique to calculate force without acceleration is by considering the equilibrium of forces. When an object is in equilibrium, the net force acting on it is zero. This means that all the forces acting on the object are balanced, and the object remains at rest or moves with a constant velocity.

To calculate force in an equilibrium situation, we can analyze the forces acting on the object and set up an equation that equates the magnitudes of the opposing forces. By solving this equation, we can determine the force we are interested in.

Worked Out Examples: Calculating Force without Acceleration

Let’s work through a couple of examples to solidify our understanding of calculating force without acceleration.

Example 1: Calculating Normal Force

Suppose we have a rock resting on a flat surface. The mass of the rock is 5 kg. We want to determine the magnitude of the normal force exerted by the surface on the rock.

In this case, the force of gravity acting on the rock is given by $F_{text{gravity}} = mg = 5 , text{kg} times 9.8 , text{m/s}^2$ . Since the rock is at rest, the normal force must balance the force of gravity. Therefore, the magnitude of the normal force is equal to the magnitude of the force of gravity:

$F_{text{normal}} = F_{text{gravity}} = 5 , text{kg} times 9.8 , text{m/s}^2$

Example 2: Calculating Friction Force

Consider an object with a mass of 10 kg being pushed along a horizontal surface with a force of 50 N. The object moves with a constant velocity, indicating zero acceleration. We want to determine the magnitude of the frictional force acting on the object.

Since the object is moving at a constant velocity, the net force acting on it must be zero. This means that the force of friction, which opposes the applied force, must balance it. Therefore, the magnitude of the frictional force is equal to the magnitude of the applied force:

$F_{text{friction}} = 50 , text{N}$

These examples demonstrate how to calculate specific types of forces without knowing the acceleration. By understanding the equilibrium of forces and balancing opposing forces, we can determine the forces at play in various situations.

Calculating Specific Types of Force without Acceleration

In addition to calculating the normal force and frictional force, there are other specific types of forces that can be determined without knowing the acceleration. Let’s explore a few examples:

A. How to Determine Tension Force without Acceleration

Tension force is the force transmitted through a string, rope, or cable when it is pulled taut. When an object is connected to a rope and is stationary or moving with a constant velocity, the tension force in the rope must balance the opposing forces.

To determine the tension force, consider the forces acting on the object connected to the rope. The net force in the direction of the rope must be zero. By setting up an equation that equates the magnitudes of the opposing forces, we can solve for the tension force.

B. How to Measure Friction Force without Acceleration

Friction force is the force that opposes the relative motion or tendency of motion between two surfaces in contact. To calculate the friction force without knowing the acceleration, we can consider the equilibrium of forces.

For example, when an object is on a flat surface and is not moving, the force of static friction balances the opposing forces, such as the force of gravity. By setting up an equation that equates the magnitudes of these opposing forces, we can determine the friction force.

C. How to Calculate Normal Force without Acceleration

The normal force is the force exerted by a surface to support the weight of an object resting on it. When an object is at rest on a horizontal surface, the normal force must balance the force of gravity.

By considering the equilibrium of forces in the vertical direction, we can calculate the normal force. The magnitude of the normal force is equal to the magnitude of the force of gravity.

The Role of Centripetal Force in Non-Accelerating Systems

In non-accelerating systems, another important force to consider is the centripetal force. Centripetal force is the force that acts on an object moving in a circular path, always directed towards the center of the circle.

Understanding Centripetal Force without Acceleration

In a non-accelerating system, the centripetal force is responsible for keeping an object moving in a circular path with a constant speed. By understanding the concept of centripetal force and its relationship to acceleration, we can calculate the centripetal force without knowing the acceleration.

Calculating Centripetal Force without Acceleration

The centripetal force can be calculated using the formula:

$F_{text{centripetal}} = frac{mv^2}{r}$

where $F_{text{centripetal}}$ is the centripetal force, $m$ is the mass of the object, $v$ is the velocity, and $r$ is the radius of the circular path.

Worked Out Examples: Centripetal Force Calculations

Let’s go through an example to illustrate how to calculate centripetal force without knowing the acceleration.

Example: Calculating Centripetal Force

Suppose a car of mass 1000 kg is traveling in a circular path with a radius of 50 meters at a constant speed of 20 m/s. We want to determine the magnitude of the centripetal force acting on the car.

Using the formula for centripetal force, we can calculate:

$F_{text{centripetal}} = frac{(1000 , text{kg})(20 , text{m/s})^2}{50 , text{m}}$

Simplifying the equation, we find:

$F_{text{centripetal}} = 8000 , text{N}$

Thus, the magnitude of the centripetal force acting on the car is 8000 N.

The Relationship between Force, Mass, and Acceleration

Force, mass, and acceleration are interconnected concepts in physics. Newton’s second law of motion states that the force acting on an object is directly proportional to its mass and acceleration:

$F = ma$

This equation highlights the relationship between force, mass, and acceleration. When the acceleration is zero, the net force acting on the object is also zero.

What Happens when there is No Acceleration?

When there is no acceleration, it means that all the forces acting on an object are balanced, resulting in a state of equilibrium. In equilibrium, the net force is zero, and the object remains at rest or moves at a constant velocity.

Calculating force without acceleration becomes crucial in determining the forces that balance each other in equilibrium situations. By understanding the forces at play, we can analyze various scenarios and make accurate calculations.

Worked Out Examples: Force, Mass, and Acceleration Calculations

To further solidify our understanding of force, mass, and acceleration, let’s work through a couple of examples.

Example 1: Calculating Force given Mass and Acceleration

Suppose an object with a mass of 2 kg experiences an acceleration of 3 m/s^2. We want to determine the force acting on the object.

Using Newton’s second law of motion, we can calculate:

$F = (2 , text{kg})(3 , text{m/s}^2)$

Simplifying the equation, we find:

$F = 6 , text{N}$

Therefore, the force acting on the object is 6 N when it has a mass of 2 kg and experiences an acceleration of 3 m/s^2.

Example 2: Calculating Acceleration given Force and Mass

Consider an object with a mass of 5 kg experiencing a force of 20 N. We want to determine the acceleration of the object.

Rearranging Newton’s second law of motion, we can calculate:

$a = frac{F}{m} = frac{20 , text{N}}{5 , text{kg}}$

Simplifying the equation, we find:

$a = 4 , text{m/s}^2$

Thus, the object has an acceleration of 4 m/s^2 when a force of 20 N is applied to it.

Calculating force without acceleration is a fundamental concept in physics and engineering. By understanding the role of mass, considering the equilibrium of forces, and utilizing appropriate formulas, we can accurately determine various types of forces without knowing the acceleration. These calculations are essential in analyzing the behavior of objects in different scenarios, ensuring safety, and optimizing design in various fields. By mastering the art of calculating force without acceleration, we enhance our understanding of the intricate relationship between forces, mass, and acceleration.

How can we calculate force without acceleration and find acceleration with friction?

When determining force without acceleration, we can use the equation:

Force = mass × acceleration

However, when friction is involved, finding acceleration can be more complex. To simplify the process of finding acceleration with friction, we can utilize the concept of Finding acceleration with friction simplified. This approach streamlines the calculation by incorporating additional factors such as the coefficient of friction and normal force. By understanding this simplified method, we can accurately determine acceleration even in the presence of friction.

Numerical Problems on how to calculate force without acceleration

Problem 1:

A car of mass 1000 kg is moving at a constant velocity of 20 m/s. Calculate the force acting on the car.

Solution:
Given:
Mass of the car, $m = 1000$ kg
Velocity of the car, $v = 20$ m/s

Since the car is moving at a constant velocity, there is no acceleration $( a = 0$ ).

The force acting on the car can be calculated using the formula:

$F = m cdot a$

Substituting the given values, we get:

$F = 1000 , text{kg} cdot 0 , text{m/s}^2 = 0 , text{N}$

Therefore, the force acting on the car is 0 N.

Problem 2:

A block of mass 5 kg is placed on a table. Calculate the force exerted by the table on the block if it is at rest.

Solution:
Given:
Mass of the block, $m = 5$ kg
Acceleration due to gravity, $g = 9.8$ m/s $^2$

Since the block is at rest, the acceleration $( a$ ) is 0.

The force exerted by the table on the block can be calculated using the formula:

$F = m cdot a$

Substituting the given values, we get:

$F = 5 , text{kg} cdot 0 , text{m/s}^2 = 0 , text{N}$

Therefore, the force exerted by the table on the block is 0 N.

Problem 3:

A ball of mass 0.2 kg is thrown vertically upwards with an initial velocity of 10 m/s. Calculate the force acting on the ball at its highest point.

Solution:
Given:
Mass of the ball, $m = 0.2$ kg
Initial velocity, $u = 10$ m/s
Acceleration due to gravity, $g = 9.8$ m/s $^2$

At the highest point, the velocity $( v$ ) of the ball will be 0.

The force acting on the ball can be calculated using the equation of motion:

$v^2 = u^2 + 2as$

Since the final velocity $( v$ ) is 0, the equation becomes:

$0 = (10 , text{m/s})^2 + 2 cdot a cdot s$

Simplifying the equation, we get:

$100 = 2as$

Since the ball is at its highest point, the displacement $( s$ ) is also 0.

Therefore, the force acting on the ball at its highest point is 0 N.

Also Read:

⇢ Significance of the wave:

⇢ Significance of the wave amplitude:

Does amplitude of wave decrease?

Why does amplitude of wave decrease?

When does amplitude of wave decrease?

Does wave amplitude decrease over time?

Why does the amplitude of a wave decrease over time?

Does the amplitude decrease over distance?

Why does the amplitude decrease over distance?

Frequently Asked Question (FAQs) on Amplitude reduction:

Q: Why does the amplitude of a wave decrease after diffraction?

Q: When we look up at the sky, why does the sun appear brighter than other stars that are larger than it?

Does amplitude of wave change?

When does amplitude of wave change?

Why does amplitude of wave change?

How does amplitude of wave change?

Q: Does amplitude change over time?

Q.: Does the amplitude of the wave change when the wave changes the medium of propagation?

Q.: What happens when the amplitude of the wave is doubled?

How can velocity be negative?

When can velocity be negative?

Can velocity be negative in graph?

Can velocity be negative when acceleration is positive?

Problem: Suppose a car is going with a speed of 15 m/s from east to west (which we consider negative direction. The driver applies the breaks after 4 seconds at a distance of 30 m. What would be the acceleration of the car? Is the acceleration in this scenario positive or negative?

Can velocity be negative in free fall?

Problem: Consider a tennis ball and a plastic ball falling from the same height and at the same time. The plastic ball takes 4 seconds to reach the ground, whereas the tennis ball takes 6 seconds. What are their velocities?

Can average velocity be negative?

Problem: Calculate the average velocity over a given time interval of a person if he moves 5 m in 3 s along the positive x-axis and 15 m in 7 s along the negative x-axis?

Can initial velocity be negative?

Problem: Within 3 seconds, John completes the bicycle ride with a final velocity of 9 m/s and an acceleration of 4 m/s2. Determine the initial velocity of John.

Can final velocity be negative?

Problem: Suppose a man travels a certain distance in the positive x direction at a speed of 18 m/s. Now, if his acceleration is -5 m/s2, calculate the final velocity at 4 seconds.

Can instantaneous velocity be negative?

Problem: A particle moves along the x-axis according to x(t) = 15t – 3t2. What is the instantaneous velocity at t = 2 s and t = 3 s?

Can relative velocity be negative?

Problem: Two east-west train tracks run parallel to one other. Train A moves east with a speed of 54 km/h, while train B moves west with a speed of 90 km/h. What is the velocity of train B with respect to train A?

Can angular velocity be negative?

Problem: Calculate the angular velocity of a wheel with an initial angular displacement of π rad and an angular displacement of -π rad after 2 seconds.

Can maximum velocity be negative?

Can terminal velocity be negative?

Can change in velocity be negative?

How to find acceleration with velocity and distance without time

How to find acceleration with distance time and initial velocity

Acceleration: A Quantitative Overview

Formula Derivation

Underlying Physics

Advanced Calculation Techniques

Case Study: Variable Acceleration

Real-World Example: A Car’s Acceleration

Practical Application: Experimental Approach

Setup and Measurement Techniques

Experiment: Verifying Theoretical Values

Challenges in Accurate Determination

Factors Affecting Accuracy

The Constant Acceleration Equations OR The Kinematics Formulas:

How do you choose and apply a constant acceleration formula?

How to find acceleration with velocity and distance?

Problem: A bike constantly accelerates from rest to a speed of 10 m/s across a distance of 20 m. Determine the acceleration of the bike.

Problem: From a height of 1.40 meters, a feather is dropped onto the moon. If the feather’s velocity is 2.135 m/s, then determine the acceleration of gravity on the moon.

Problem: At a speed of 12 m/s, a racing boat crosses the finish line and continues straight ahead. It came to a halt 18 meters from the finish line. What is the magnitude of the acceleration of the racing boat if it instantly decelerates till it comes to a stop?

Constant Velocity:

Constant Acceleration:

Does constant acceleration mean constant velocity?

Constant velocity vs Constant acceleration:

Q: Does constant velocity mean no acceleration?

Q: What is the cause of the object’s zero acceleration?

Problem 1: At time t = 25 seconds, a boat is moving at a velocity of 50 m/s, and at time t = 50 seconds, the same boat is moving at a velocity of 100 m/s. Find the constant acceleration by calculating the change in velocity and time.

Problem 2: Consider a car is moving in the east direction, and in each second, it travels the distance of 7 m. Find its velocity and acceleration.

Velocity vs Time Graph:

Meaning of the slope of the velocity vs. time graph:

The meaning of the shape of velocity vs. time graph:

Constant Velocity vs Time Graph:

Q: How can you tell when velocity is constant of a velocity time graph?

Q: If the object is not accelerating, does it mean that it is stable?

Q: How can an object with zero acceleration move?

How to Find Acceleration with a Constant Velocity

Understanding the Concept of Acceleration

The Relationship between Acceleration and Constant Velocity

The Mathematical Formula for Acceleration

The Difference between Velocity and Acceleration

Problem: Within 3 seconds, John completes the bicycle ride with a final velocity of 9 m/s and an acceleration of 4 m/s². Determine the initial velocity of John.

Problem: Suppose a man travels a certain distance in the positive x direction at a speed of 18 m/s. Now, if his acceleration is -5 m/s², calculate the final velocity at 4 seconds.

Problem: A particle moves along the x-axis according to x(t) = 15t – 3t². What is the instantaneous velocity at t = 2 s and t = 3 s?

Problem: What is the wavelength of a light wave with a frequency of 7 X 10¹⁴ Hz?

Problem: What wavelength will a photon have if its energy is4 X 10^-15 J?

Problem: If the energy of a photon is 2.19 × 10¹¹ ev, determine the wavelength of that photon.