Inclined Plane: 7 Important Facts You Should Know


How does an Inclined Plane make Work easier?

An inclined plane changed the world by its concept that makes work easier. Let’s see how an inclined plane – a diagonal surface that is inclined or tilted upon the horizontal surface; lift any objects easier and saves the required mechanical energy:

  • Because of its triangular shape, less force is needed to move an object in upward on an inclined plane than the force in the straight path on a horizontal surface. 
  • An object needs to move over a greater distance on an inclined plane than the horizontal surface. 
  • It helps the heavy object to overcome surface resistance and move quickly from one position to another. 
  • Therefore, as per the Work Formula, an inclined plane reduces the force by spreading the work over a longer distance, making any work easier.
How does an inclined plane make work easier
How does an inclined plane make work easier

What is Inclined Plane Examples?

An inclined plane example includes many real-life applications that allow heavy or fragile objects, including humans, to move easier. Such various inclined plane examples are listed below: 

Mountain

Some inclined planes are naturally occurring as no one created them. It just needed to be noticed. A mountain is a naturally occurring inclined plane example.

Suppose you are trekking on the mountain. Here, a mountain is an inclined plane, and you are the load that walking up the mountain, and a normal or muscular force is required to do the work. If you take the steeper trail to save the time to reach the top of the mountain, it becomes harder for you to walk as you will have required more force. Whereas, if you take a gentler slope trail than a steeper trail, it would be a longer route but much easier to move up to the mountain as it requires less force.

Inclined Plane Examples
Inclined Plane Examples – Climbing Mountain

You could observe that the difference between the height of the mountain top and mountain bottom increases as you move upward, irrespective of the route you choose. Thus, the exact amount of work will have been done once you reach the mountain top, whether you take a direct trail, steep trail, or a gentle slope trail.

Stairs

They are a basic example of an inclined plane used to reach a higher level or floor in a building or house. Instead of a climb up, walking on stairs is more accessible as it requires less energy.

Inclined Plane Examples
Inclined Plane Examples – Stairs (Image Source: Revision)

Escalator

Similarly, electronic stairs called escalators are also an example of inclined planes that propel a person up to the upper floor without exerting any energy.

Inclined Plane Examples
Inclined Plane Examples – Escalator

Wheelchair Ramp 

It is one of the essential inclined planes which make a physically disabled person’s life easier. In most public places, a flat inclined surface is attached from a higher floor to ground specially built for physically disabled people to move up or down using a wheelchair called Wheelchair Ramp. Using the ramp, the wheelchair pushes at a lower level and then lifts to higher.

The total distance needed to push the wheelchair to reach the higher floor increases, but the required force and energy decrease.

Inclined Plane Examples
Inclined Plane Examples – Wheelchair Ramp (Image Credit: robomatter)

Slides

They are one inclined plane that allows any objects to be safely lowered from height. Its one end is placed close to the ground, and the other is lifted at height. The height difference of both end’s edges makes it an inclined plane.

Suppose you are standing at the height withholding a small object in hand, and then you want to give that object to the person standing on the floor. Rather than throwing that object towards the person, if you use an inclined plane such as a slide, an object will safely descend the slide with the help of gravitational force.

Inclined Plane Examples
Inclined Plane Examples – Slides

Playground Slides

By eliminating the friction from a slide, the speed at which objects move down the slides can be increased. Hence, apart from commercial slides, playing slides is becoming the most popular form of entertainment we observe in most playgrounds.

Inclined Plane Examples
Inclined Plane Examples – Playground Slides

Roof

The roof of the houses becomes an inclined plane when it is built in the shape of a slanting slope. The roof with a slanting slope is mainly observed in hilly areas as it allows loads like rainwater, snow, or dust.

Because of this slanting slop, any waste things slide down to the ground quickly from the roof due to gravitational force.

Inclined Plane Examples
Inclined Plane Examples – Slanted Roof (Image Credit: energymodels)

Container Truck

It used to carry heavy stuff or garbage from one place to another. A similar inclined plane principle of a wheelchair ramp is used to load that heavy stuff into the truck. The tilted container-like wheelchair ramp is attached to the back of the truck.

Hence, this tilted container acts as an inclined plane which allows the loading and unloading of any objects almost effortlessly.

Inclined Plane Examples
Inclined Plane Examples – Container Truck Ramp

Letterbox

The chutes used for dropping the letter into a private letterbox are also an example of an inclined plane. The chutes offer the slanting slope connected to the letterbox openings.

The slanting slope helps the letter slide down into the letterbox easily and prevents the letterbox from getting jammed.

Inclined Plane Examples
Inclined Plane Examples – Letterbox Chutes

Pyramids

Have you wondered how the people during ancient times constructed the pyramid? The primary question for building pyramids, how they lift heavy blocks very high from the ground during that time.

The answer is they did not lift but drag the blocks up using inclined planes. Hence, the structure of pyramids appears as a triangle from all slides, just like an inclined plane.

Inclined Plane Examples
Inclined Plane Examples – Pyramid Ramp (Image Credit: Quora)

Funnel

It is formed by joining two types of geometric shapes, such as a cone and a cylinder. Here, the curved part of the cone acts as an inclined plane to any fluid poured into it.

The slope of the cone allows the liquid to easily slide down the cylinder with the help of gravitational force.

Inclined Plane Examples
Inclined Plane Examples – Funnel

Aircraft 

The propeller, attached at the start of the aircraft, is shaped similarly to its wings. Both parts of aircraft accelerate airflow over their curved surfaces. As a propeller spins, the speed of its blade is highest at the tip part and slowest at the bottom. During one full rotation, the blade’s tip travels much farther distance than its bottom in the same amount of time, which is why the blade angle is greatest at the bottom and the least at the tip.

If the blade angle is uniform across the propeller, there would be a variation in the thrust and pressure difference produced by a propeller from bottom to top, which leads to a negative angle of attack at the bottom and blade stop at the tip. 

Hence, the propeller blades are inclined with a higher geometric pitch at the bottom and a lower pitch at the tip, which prevents a significant air pressure difference across the blade.

Therefore, the Aircraft is one of the advanced examples of inclined planes.

Inclined Plane Examples
Inclined Plane Examples – Aircraft Propeller (Image Credit: Wikipedia)

Do you know there are so many inclined planes around you that making your life easier? List out such inclined planes examples you can find.

What is the Purpose of an Inclined plane? 

An inclined plane is one of the types of simple machines – having the purpose of reducing human efforts to make their tasks easier. 

It is a ramp or slope in which the surface is slanted, which helps move heavy objects from a lower height to higher.

Simple Machines Meaning

A basic mechanical device which is used to make work easier when any force is applied.” 

Types of Simple Machines

Simple machines are classified into six types; which can be found everywhere around us are listed below: 

  • Inclined Plane
  • Lever
  • Wedge
  • Screw
  • Wheel and Axle
  • Pulley
Simple Machine Types
Six Types of Simple Machine

What are the 3 types of Inclined Planes?

Three of the other six simple machines are based on an inclined plane are listed below: 

  • Lever : an inclined plane that supports the raised surface from a horizontal surface.
  • Wedge : a portable kind of inclined plane formed when two inclined planes joined at the edge.
  • Screw : a twisted inclined plane that is formed by wrapping around a pole or cylinder.

What Concepts, Processes are associated with Motion on an Inclined Plane?

When an object slides up or down on an inclined plane, there are following concepts or processes are associated with that object’s motion on an inclined plane which makes work done on an inclined plane easier: 

How does an Inclined Plane Effect Motion? 

The rate at which an object on an inclined plane slides depends on how inclined or titled the surface is. 

The greater the surface inclined, the faster the rate at which an object slides.

To understand the motion of an object on an inclined plane, one needs to analyse the number of forces acting on it on an inclined plane. 

Forces on an Inclined Plane

At least two forces act on an object on an inclined plane: –

  • Normal Force, which acts perpendicular direction to the surface
  • Gravitational Force, also known as the weight of an object, acts downward.

Read more about Different Types of Forces

How can the Acceleration on an Inclined Plane be Calculated?

Notice that two forces on an object on an inclined plane are in the same direction. i.e., not in the opposite direction. Therefore, one force is resolved into its perpendicular components, which easily allow adding other forces on an object. 

This process involves resolving the weight of an object (Fgrav) into two perpendicular components:

  • One directed parallel [latex]F_{\parallel }[/latex] to an inclined plane 
  • Another is directed perpendicular [latex]F_{\perp}[/latex] to an inclined plane.

Inclined Plane Formula 

The equation of parallel components is:

[latex]F_{\parallel } = mgsin\theta[/latex] ………… (1)

The equation of perpendicular components is:

[latex]F_{\perp} = mgcos\theta[/latex] ……………… (2)

The perpendicular component of gravitational force balances the normal force as it is directed opposite to the normal force, whereas the parallel component of gravitational force remains unbalanced. 

Here, the net force on an inclined plane is the unbalanced parallel component of gravitational force that accelerates an object on an inclined plane. 

Use of Inclined Plane
Forces on an Inclined Plane

The net force on an inclined plane is given by, 

[latex]F_{net} = mgsin\theta[/latex] …………………. (3)

If no friction exists between an inclined plane and an object, then that plane is said to be the ‘ideal inclined plane’

For ideal inclined plane, 

The work done on load-lifting by an inclined plane, which is output work (Wout) is equal to the work done by the applied force, which is input work (Win).

Wout = Win ………………………….. (4)

As per Newton’s Second Law of Motion,

[latex]a = \frac{F_{net}}{m}[/latex]

An object’s acceleration is the parallel component of gravitational force divided by its mass(m) for an ideal inclined plane. 

We yield the equation of acceleration on inclined plane as follows:

[latex]a = gsin\theta[/latex] …………….. (5)

An object will be sliding down with acceleration of [latex]gsin\theta[/latex] on a frictionless surface of an inclined plane.

How to determine Inclined Plane Friction?

When a frictional force (denoted by ffric) come into the picture in the inclined plane, it is related to the normal force (fN) by 

[latex]f_{fric} = \mu f_{N}[/latex] …………….(6)

Where [latex]\mu[/latex] is a coefficient of friction.

How to find the angle of an Inclined Plane with Friction?

To determine the friction force by an inclined plane, we first have to find the normal force. Notice that two forces on an inclined plane are in opposite directions. Therefore, an object’s motion slides down, and the friction force is parallel to the slope of a plane, whereas the normal force between an object and an inclined plane is perpendicular to its slope. 

The equation of perpendicular component of normal force is

[latex]F_{\perp} = mgcos\theta[/latex]

As per equation (6), the frictional force on an inclined plane is 

[latex]f_{fric} = \mu mgcos\theta[/latex] ……………………… (7)

How many different ways to Calculate Friction on a Sliding Object down an Inclined Plane?

To determine the friction force between two objects, we can accept that an object can slide down at a constant motion on an inclined plane – if the net force is zero.

Use of Inclined Plane
Forces on Inclined Plane

The diagram shows that frictional force and the parallel gravitational force components act on an object in the opposite direction. 

Note that when both forces on an object have equal magnitude, its acceleration is zero. 

[latex]f_{net} = 0[/latex]

[latex]f_{fric} + f_{grav}= 0[/latex]

[latex]\mu mgcos\theta – mgsin\theta= 0[/latex]

Note [latex]mgsin\theta[/latex] is negative as gravitational force is in the opposite direction. 

[latex]\mu = \frac{mgsin\theta}{mgcos\theta}[/latex]

[latex]\mu = tan\theta[/latex]

Here, [latex]\theta[/latex] is the angle of friction, also called the angle of repose at which an object can remain stationary without sliding down on an inclined plane due to friction.

What is the Mechanical Advantage of Inclined Plane?

  • The mechanical advantage provides the amount of force needed to move any objects on an inclined plane.
  • MA is based on an inclined plane’s slope and height. The lesser the slope, the smaller the force required and the greater its mechanical advantage.

Mechanical advantage (MA) is defined as “the ratio of the output force exerted on an object by inclined plane to the input force applied on an object.”

Use of Inclined Plane
Mechanical Advantage of an Inclined Plane

Mechanical Advantage of an Inclined Plane Formula

For an inclined plane, the output force on an object is a gravitational force. i.e., its weight Fw, whereas the input force is parallel to the plane Fi

The mechanical advantage is given by 

[latex]MA = \frac{F_{w}}{F_{i}}[/latex] ……………………..(8)

How is Mechanical Advantage Calculated?

Let’s calculate the mechanical advantage in terms of frictionless surface.

Coming back to the equation (4),

The output work is equal to the product of output force and vertical displacement or height or rise of an inclined plane.

[latex]W_{out} = F_{w} \ast Rise[/latex] …………………(A)

The input work is equal to the product of input force and diagonal length of an inclined plane.

[latex]W_{in} = F_{i} \ast Length[/latex] ………………………(B)

Substituting the equations (A) and (B) into the equation (4), we get

[latex]F_{w} \ast Rise = F_{i} \ast Length[/latex]

[latex]\frac{F_{w}}{F_{i}} = \frac{Length}{Rise}[/latex]

As per the equation (8),

[latex]MA = \frac{F_{w}}{F_{i}} = \frac{Length}{Rise}[/latex] …………….(C)

From the diagram, the mechanical advantage can be expressed by the angle [latex]\theta[/latex] of an inclined plane, 

[latex]sin\theta = \frac{Rise}{Length}[/latex]

Finally, the mechanical advantage (MA) on an inclined plane is solved as,

[latex]MA = \frac{F_{w}}{F_{i}} = \frac{1}{sin\theta }[/latex] ……………………….(D)

The lesser the tilted or inclined angle of the plane, the more tremendous its mechanical advantage.

How do you find an Inclined Planes Actual Mechanical Advantage?

An inclined plane’s mechanical advantage (MA) without any friction is said to be ‘Ideal Mechanical Advantage (IMA)’.

When an inclined plane has any friction, its mechanical advantage is said to be ‘Actual Mechanical Advantage (AMA)’.

The actual mechanical advantage (AMA) is given by,

[latex]AMA = \frac{F_{w}}{F_{i}+F_{fric}}[/latex]

Where Ffric is a frictional force acting on an object. 

What is the Efficiency of an Inclined Plane?

The efficiency of an inclined plane is the percent of input work by applied force to output work by force exerted by an inclined plane. 

The efficiency of an inclined plane is calculated as: 

Efficiency = Output work / Input work ×100%

Since some of the quantity of input work is used to overcome friction, it is greater than the output work, which leads to less 100% efficiency of an inclined plane. Thus, the closer an inclined plane’s efficiency is to 100%, the better it can overcome friction.

How to increase the Efficiency of an Inclined Plane?

Coming back to the equation (D) of mechanical advantage on an inclined plane

To increase the efficiency of an inclined plane, we must reduce the friction by decreasing the coefficient of friction [latex]\mu[/latex] or increasing the angle of friction [latex]\theta[/latex].

The efficiency is practically increased by using rollers in conjunction with an inclined plane or a wedge instead of an inclined plane.


FREQUENTLY ASKED QUESTIONS (FAQs)

What will happen if the slope of an inclined plane is too steep?

Ans: If the slope of an inclined plane is too steep, then it takes more effort to move an object on an inclined plane as follows:

  • the lesser the distance an object has to travel
  • the larger the force will have required to move an object on a plane
  • the lesser mechanical advantage of an inclined plane

A force applied by an inclined plane to an object is the?

Ans: Two forces applied by an inclined plane to on an object is given below:

  • Gravitational Force
  • Normal Force

Is an inclined plane wrapped around a central cylinder a lever?

Ans: A Level is an inclined plane that supports the raised surface from a horizontal surface.

A twisted inclined plane that is formed by wrapping around the cylinder is called a Screw. 

You tilt an inclined plane with an object on top of it until it reaches the angle where it starts to slip. Does the mass of the object or gravity have an effect on what this angle is?

Ans: When the angle is greater than the angle of friction, the objects start to slide down on an inclined plane.

Since this angle of friction is derived from the gravitational force on an object having mass m, the gravity or its mass affects this angle of friction.

Does a body move on an inclined plane when no gravity is present but friction is exercises Newtonian mechanics forces friction physics?

Ans: The friction force that pushes an object on an inclined plane depends on the normal force between an object and an inclined plane. The perpendicular components of force of gravity provide the normal force. 

Therefore, if no gravity is present, there will be no normal force and no friction force on an object. Hence, the body does not move on an inclined plane in the absence of gravity. 


Manish Naik

Hello, I'm Manish Naik completed my MSc Physics with Solid-State Electronics as a specialization. I have three years of experience in Article Writing on Physics subject. Writing, which aimed to provide accurate information to all readers, from beginners and experts. In my leisure time, I love to spend my time in nature or visiting historical places. I am honoured to be part of LambdaGeeks. Looking forward to connecting you through LinkedIn - https://www.linkedin.com/in/manish-ashok-naik/ Also, for Maharashtra travel guide and heritage conservation articles, visit my website Wandering Maharashtra - https://wanderingmaharashtra.com/travel-blogs/

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