# Zero work illustrative problem

1. Sep 16, 2011

### arjose

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

A boy supports a book on his hand while standing still. Then, he walks with the book laying motionless on his hand. Is there work exerted by the boy on the book?

2. The attempt at a solution

My professor said that there is zero work done on the book because of the perpendicularity of the displacement of the book and the force applied by the boy on the book. But, I ask, if the book moved from rest, doesn't it mean it accelerated? If it accelerated, doesn't it mean that a net force along the x-axis acted on it? If so, then doesn't it mean that there IS work? Please help.

2. Sep 16, 2011

### vela

Staff Emeritus
Yes, you're right. There was work done on the book to get it to move horizontally.

Once the book is moving, if it's moving at constant velocity, there's no work being done on it by the boy because the force exerted by his hand is perpendicular to the displacement.

3. Sep 16, 2011

### arjose

Given that the book is moving at constant velocity, does it matter if the force exerted by his hand is counteracted by the weight of the book? I mean is there even work to be computed if net vertical force on the book is zero?

4. Sep 16, 2011

### mstud

The net vertical force is zero. What do you think about the horizontal direction?
Which forces are acting on the book then (2 forces)?

When he starts walking there is acceleration, and some work is involved.

Is there work done thereafter? The answer depends on the sizes of 2 forces in the horizontal direction, which determine whether he then walks with constant acceleration (sum of acting forces zero) or has acceleration (sum of acting forces other than zero)

5. Sep 16, 2011

### PeterO

Strictly speaking there is a little bit of work done on the book starting it moving when the boy walks off, then a bit more stopping it again when the boy stops.
What you professor is referring to is that the Force supporting the book, perhaps 10N if the book has a mass of 1 kg, does no work as the boy carried the book 5m across a room. Some people would be inclined to think that since work if force x distance, then 50 J of work was done in the above situation. That reasoning is incorrect.

6. Sep 16, 2011

### vela

Staff Emeritus
Yes, you can calculate the work done by the force the boy exerts and the work done by gravity separately. In this case, they both turn out to be 0 J so it's not very interesting.

You will likely do a problem where, say, a force is exerted on an object, causing it to move across the ground with constant velocity. The net force on the object is 0 N, but you'll be asked to calculate the work done by the applied force and the work done by friction separately. You'll find that neither is 0 J, but they cancel so that the total work done is 0 J.

7. Sep 17, 2011

### arjose

Those underlined got me confused again. How is the object moving at just a constant velocity if net forces cause acceleration? I'm thinking a force moved it from rest. If so, then there was acceleration, which also means a nonuniform velocity.

8. Sep 17, 2011

### vela

Staff Emeritus
I didn't say there was a net force exerted on the object, just a force, like someone pushing a box across the floor. Other forces, like friction from the floor, act on the object as well, which result in a net force of 0 N.

9. Sep 18, 2011

### arjose

Ah. Now i get it. Thanks, vela.