# Work on Inclined Plane: All Answers & Explanations

• Dark Visitor
In summary, the box slides down an incline at a constant speed and does not do any work due to the normal force, weight, and friction.
Dark Visitor
There are multiple questions all related to the same problem. I want to make sure I get them all correct, so any help would be much appreciated. I need this by tonight.

A box slides at a constant speed down a rough inclined plane whose angle is 30 degrees above the horizontal. There are no ropes or outside agents pushing or pulling on it.

1. The work done by the normal force is:
* positive
* negative
* zero
* not enough information

2. The work done by friction is:
* positive
* negative
* zero
* not enough information

3. The work done by the weight is:
* positive
* negative
* zero
* not enough information

4. The total work (or net work) done on the box is:
* positive
* negative
* zero
* not enough information

My thoughts are that the work done by the normal force is positive, the work done by weight is negative, and the work done by friction is negative, which leaves total work to be negative. Please tell me if I am wrong, and where I am wrong.

What do you base your thoughts on? Remember that the work done by a constant force is the product of three things

W = F d cosθ

F is the magnitude of the force (always positive or zero)
d is the magnitude of the displacement (always positive or zero)
cosθ is the cosine of the angle between the force and displacement vectors (sometimes positive, sometimes negative, sometimes zero)

Moral: The algebraic sign of the work is the algebraic sign of the cosine.

I drew a picture of a box, like the problem stated, with it on an incline, and drew my forces (weight, normal, friction) on it.

I know that W = F*d, and for this problem, W = F*d*cos30, but we don't have any numbers to apply here. So how would I apply that?

Look at your diagram and then at the first question. What is the cosine of the angle between the normal force and the displacement?

30 degrees? Because the normal force is perpendicular to the plane the box is sliding on.

Or would it be 90 + 30 degrees = 120 degrees?

In what direction is the displacement vector?

Perpendicular to the plane the box is on, which is up, which made me think positive.

Does the box move move in a direction perpendicular to the plane that it is on? Try again.

No, the box moves straight down the plane. But normal always points perpendicular to the plane the object is on.

Yes, normal is perpendicular to the plane. My question is what is the angle between the normal force (that we know is perpendicular to the plane) and the displacement of the box?

Last edited:
If I am thinking this right, I say 90 degrees? But I feel confused...

It is 90 degrees, you are correct. So the direction of motion is perpendicular to the normal force. What is the cosine of 90 degrees?

Zero. So the normal force does no work?

Yup. Whenever a force acts in a direction perpendicular to the displacement, the work done of the force is zero. Try to remember that.

One down three to go.

Okay, I will try my best.

Well, I still think weight is negative, and friction is negative. Are either of those right?

Remember that the cosine of an angle is positive when the angle is less than 90 degrees, zero when the angle is 90 degrees and negative when the angle is greater than 90 degrees. Use this information and your diagram and you should be OK. I have to sign off for today. Good luck.

## 1. What is an inclined plane and how does it work?

An inclined plane is a simple machine that is a flat surface set at an angle, rather than a horizontal or vertical plane. It works by reducing the amount of force needed to move an object to a higher or lower position by spreading the force over a longer distance.

## 2. How does the angle of the inclined plane affect the amount of work required?

The angle of the inclined plane affects the amount of work required in two ways. Firstly, the steeper the angle, the shorter the distance the object needs to be moved, so less work is required. Secondly, the steeper the angle, the greater the component of the force acting against gravity, so more work is required.

## 3. What is the formula for calculating work on an inclined plane?

The formula for calculating work on an inclined plane is W = Fd cosθ, where W is work, F is the force applied, d is the distance moved, and θ is the angle of the inclined plane.

## 4. How does friction affect the work done on an inclined plane?

Friction can make the work done on an inclined plane greater than the theoretical amount calculated without accounting for friction. This is because some of the force applied is used to overcome friction, rather than moving the object along the inclined plane.

## 5. What are some real-life examples of using inclined planes to do work?

Inclined planes are used in many everyday objects and activities to make work easier. Some examples include ramps for wheelchairs or strollers, slides, conveyor belts, and roads on hills. They are also used in more complex machines, such as escalators, cranes, and aircraft wings.

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