How to Find Acceleration in Free Fall: A Comprehensive Guide

In the fascinating world of physics, one concept that captures our attention is free fall. Free fall occurs when an object experiences a downward motion under the sole influence of gravity, without any other forces acting upon it. During free fall, the object accelerates due to the force of gravity pulling it towards the center of the Earth. In this blog post, we will explore the intricacies of calculating acceleration in free fall, uncovering the formulas and step-by-step processes involved. We will also delve into some special cases and additional concepts related to this captivating phenomenon.

How to Find Acceleration in Free Fall

The Basic Formula and Its Explanation

To understand how to find acceleration in free fall, we need to turn to the basic formula of physics:

$a = \frac{F}{m}$

where:
– $a$ represents the acceleration,
– $F$ stands for the force acting on the object, and
– $m$ denotes the mass of the object.

When an object is in free fall, the only force acting upon it is the force of gravity. In most cases on Earth, we can approximate the force of gravity as $9.8 \, \text{m/s}^2$ . However, keep in mind that this value can vary slightly depending on the location.

Hence, when calculating the acceleration in free fall, we can substitute $F$ with the force of gravity $g$ and $m$ with the mass of the object. The formula then becomes:

$a = \frac{g}{m}$

Step-by-Step Process to Calculate Acceleration

Now that we have the formula, let’s walk through the step-by-step process of calculating acceleration in free fall:

Begin by determining the mass of the object. This can usually be found in the problem statement or given as part of the question.
Next, identify the acceleration due to gravity. On Earth, this is typically $9.8 \, \text{m/s}^2$ , but as mentioned earlier, it may vary slightly depending on the location or if you’re dealing with a different celestial body.
Finally, plug the values of mass and acceleration due to gravity into the formula $a = \frac{g}{m}$ to calculate the acceleration in free fall.

Worked Out Examples

Let’s solidify our understanding of how to find acceleration in free fall with some worked-out examples:

Example 1:
Suppose we have a ball with a mass of 2 kg. What is the acceleration of the ball during free fall?

Solution:
Given: Mass of the ball $\( m$ ) = 2 kg

Using the formula $a = \frac{g}{m}$ , we can substitute the values:
$a = \frac{9.8 \, \text{m/s}^2}{2 \, \text{kg}} = 4.9 \, \text{m/s}^2$

Hence, the acceleration of the ball during free fall is $4.9 \, \text{m/s}^2$ .

Example 2:
Let’s consider a feather with a mass of 0.02 kg. What is the acceleration of the feather during free fall?

Solution:
Given: Mass of the feather $\( m$ ) = 0.02 kg

Using the formula $a = \frac{g}{m}$ , we can substitute the values:
$a = \frac{9.8 \, \text{m/s}^2}{0.02 \, \text{kg}} = 490 \, \text{m/s}^2$

Remarkably, the feather experiences an acceleration of $490 \, \text{m/s}^2$ during free fall, just like any other object!

Special Cases in Finding Acceleration in Free Fall

Calculating Free-Fall Acceleration on the Moon

As we explored earlier, the acceleration due to gravity can vary depending on the celestial body. Let’s consider the example of determining the free-fall acceleration on the Moon.

The acceleration due to gravity on the Moon is approximately $1.6 \, \text{m/s}^2$ . By following the same process as before, we can calculate the acceleration in free fall on the Moon for a given object. Simply substitute $g$ with $1.6 \, \text{m/s}^2$ in the formula $a = \frac{g}{m}$ , and proceed with the calculations using the mass of the object.

Finding the Free Fall Acceleration of a Planet

To find the free fall acceleration of a planet, we need to consider the mass and radius of the planet. The formula to calculate the acceleration due to gravity on a planet is:

$g = \frac{G \cdot M}{r^2}$

where:
– $g$ represents the acceleration due to gravity,
– $G$ is the gravitational constant $\( 6.67 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2$ ),
– $M$ denotes the mass of the planet, and
– $r$ is the radius of the planet.

By using this formula, we can calculate the free fall acceleration on any given planet.

Determining the Surface Free Fall Acceleration

The surface free fall acceleration refers to the acceleration an object experiences when it is close to the surface of a massive object, such as Earth. It can be calculated using the formula $g = \frac{GM}{R^2}$ , where $G$ is the gravitational constant, $M$ is the mass of the massive object, and $R$ is the distance from the center of the object to the object’s surface.

Additional Concepts Related to Free Fall Acceleration

Image by User:Mekala Harika – Wikimedia Commons, Wikimedia Commons, Licensed under CC0.

How to Find Final Velocity in Free Fall

When an object is in free fall, we can also calculate its final velocity. The formula to find the final velocity in free fall is:

$v = u + at$

where:
– $v$ represents the final velocity,
– $u$ denotes the initial velocity $usually \( 0 \, \text{m/s}$ during free fall),
– $a$ is the acceleration, and
– $t$ stands for the time taken for the object to fall.

By plugging in the values of acceleration and time, we can determine the final velocity of an object in free fall.

How to Find Displacement in Free Fall

The displacement of an object in free fall can be calculated using the formula:

$s = ut + \frac{1}{2} a t^2$

where:
– $s$ represents the displacement,
– $u$ denotes the initial velocity,
– $a$ is the acceleration, and
– $t$ stands for the time taken for the object to fall.

By using this formula, we can determine the displacement of an object during free fall.

Understanding the Acceleration of a Free Falling Pendulum

A pendulum is an object that swings back and forth. When a pendulum is released from a certain height and allowed to swing freely, it becomes a free falling pendulum. The acceleration of a free falling pendulum can be calculated using the formula:

$a = \frac{g \cdot \sin(\theta)}{L}$

where:
– $a$ represents the acceleration,
– $g$ is the acceleration due to gravity,
– $\theta$ denotes the angle the pendulum makes with the vertical, and
– $L$ is the length of the pendulum.

The acceleration of a free falling pendulum depends on the angle and the length of the pendulum.

LSI Integration:

During our exploration of how to find acceleration in free fall, we encountered various intriguing concepts and equations. The acceleration of gravity, free fall equations, terminal velocity, falling objects, Newton’s Laws of Motion, acceleration calculation, air resistance, kinematics, force of gravity, conservation of energy, kinetic energy, velocity of falling objects, momentum, trajectory, and friction naturally emerged during our discussion. By understanding these interconnected ideas, we deepen our understanding of the captivating world of physics.

So, whether you’re analyzing the motion of a falling object or contemplating the acceleration of a free falling pendulum, the concepts and formulas we explored in this blog post will equip you with the tools to unravel the mysteries of free fall acceleration. With a solid foundation in hand, you can now confidently dive into the intricacies of this captivating phenomenon. Happy calculating!

Numerical Problems on how to find acceleration in free fall

Problem 1:

A ball is dropped from a height of 50 meters. Calculate the acceleration of the ball during free fall.

Solution:

Given:
Initial height, $h = 50 \, \text{m}$

Acceleration due to gravity, $g = 9.8 \, \text{m/s}^2$

During free fall, the acceleration is equal to the acceleration due to gravity.

Therefore, the acceleration of the ball during free fall is $a = g$ .

Hence, the acceleration of the ball during free fall is $a = 9.8 \, \text{m/s}^2$ .

Problem 2:

An object is thrown vertically upwards with an initial velocity of 20 m/s. Find the acceleration during its upward motion.

Solution:

Given:
Initial velocity, $u = 20 \, \text{m/s}$ (upwards)

Acceleration due to gravity, $g = 9.8 \, \text{m/s}^2$

During the upward motion, the acceleration is equal to the acceleration due to gravity but in the opposite direction.

Therefore, the acceleration during the upward motion is $a = -g$ .

Hence, the acceleration during the upward motion is $a = -9.8 \, \text{m/s}^2$ .

Problem 3:

A stone is thrown vertically downwards with an initial velocity of 15 m/s. Determine the acceleration during its downward motion.

Solution:

Given:
Initial velocity, $u = 15 \, \text{m/s}$ (downwards)

Acceleration due to gravity, $g = 9.8 \, \text{m/s}^2$

During the downward motion, the acceleration is equal to the acceleration due to gravity and in the same direction.

Therefore, the acceleration during the downward motion is $a = g$ .

Hence, the acceleration during the downward motion is $a = 9.8 \, \text{m/s}^2$ .

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