# Normal Force Work Problem

1. Apr 17, 2010

### Ahalp

1. The problem statement, all variables and given/known data

Can the normal force on an object ever do work on the object? Explain your answer.

The answer in the textbook is:

The normal force can do work on an object. For example, when you jump, you push down on the ground and the normal
force pushes up on you and accelerates you up, giving you kinetic energy.

3. The attempt at a solution

My initial answer before reading the textbook was, no, it can't do work.

I understand that when an object is moving on a surface, the normal force is perpendicular to the distance traveled and so it is zero.

With respect to the answer in the textbook, work is the energy transferred to an object when a force acting on it causes it to move a certain distance. Since, the normal force is a contact force, it only occurs when in contact with a surface. Wouldn't it would be zero as soon as the object loses contact or jumps. Wouldn't this mean that the normal force doesn't do work on the object..., or am i missing something?

Thanks

2. Apr 17, 2010

### rock.freak667

When jumping up, the normal force is in the same direction as the displacement. So it does work.

For an object moving horizontally on a surface, the normal force is perpendicular to the direction of the displacement, so that the work done by it is zero.

3. Apr 17, 2010

### Dickfore

If the constraining surface or line is moving itself, then the normal force can do work.

4. Apr 17, 2010

### Ahalp

Yes, but doesn't the normal force equal zero when it is not in contact with a surface. So, during the displacement, isn't the normal force 0 as the only force acting on the object is gravity. Thus, wouldn't the work done by the normal force be zero.

5. Apr 17, 2010

### jeppetrost

In the act of jumping: From you start to jump till the moment your feet loose contact, your center of mass has moved some distance. This, I guess, can be seen as work done by the normal force.

6. Apr 17, 2010

### rock.freak667

Yes but as you are pushing down, you are doing work which causes you to move upwards. As you move upwards, the normal force decreases to zero such that the upward force on you tends to zero until the only force acting is your weight. Then you move back down the Earth.

7. Apr 17, 2010

### Staff: Mentor

I'd say that your book is wrong, or at least very sloppy. It's certainly true while you are in the process of jumping the ground exerts a force on you, and that force (minus your weight) will accelerate your center of mass giving you kinetic energy. Nonetheless, no work is done on you by the normal force. The contact point--the ground--does not move, thus no work is done.

They are talking about the normal force during the act of jumping, not after you've broken contact with the ground. Think of bending your legs and forcefully straightening them.

See above.

8. Apr 17, 2010

### Staff: Mentor

Technically, no, since there is no displacement of the point of contact. No displacement = no work done.

Edit: Let me clarify. Fnet*ΔXcm = 1/2MVcm2 (the kinetic energy of the center of mass), nonetheless the normal force itself did no work on the jumper.

Last edited: Apr 17, 2010
9. Apr 17, 2010

### Ahalp

Thanks, this clarifies it a lot!

10. Feb 4, 2011

### brainpushups

The original question was "can the normal force do work?" for which the answer should be "yes," though I agree that their explanation is sloppy.

Consider the situation where the surface itself moves over some distance like the seat of a Ferris wheel, or a horse on a merry-go-round. The normal force is responsible for the displacement and does positive work on the way up and negative work on the way down.

11. Feb 4, 2011

### Staff: Mentor

You're right. There are many situations in which a normal force can do work, so the correct answer to the question should have been "yes". (But in the example given in the textbook, the normal force does no work.)