# Homework Help: Decelerating box on a truck and work

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1. May 21, 2015

### physicsisgreat

1. The problem statement, all variables and given/known data
A truck is moving at constant velocity v0 with a box of mass m on it. Suddenly it starts decelerating until its velocity becomes zero. Between the box and the truck the is a force of friction and the deceleration of the truck is sufficiently slow to allow the box not to start moving or rotating relative to the truck.
What is the work done by all the forces applied to the box?

2. Relevant equations
ΔK = W

3. The attempt at a solution
It seems to me rather obvious that the work is simply
W = ΔK = - 1/2 m v2
but my teacher said it is 0 and I really can't see why.

2. May 21, 2015

### mrnike992

If the only forces acting on the box are the force of gravity and force friction, you must consider if these forces do any work, ie does the box move due to these forces?

3. May 21, 2015

### physicsisgreat

I understand that this is the crucial point, but my reasoning is: if no horizontal force would be applied on the box, the box would feel no acceleration. But the box is decelerating, so some force is applied on it, and the only force acting on it is friction.

"The principle of work and kinetic energy (also known as the work-energy principle) states that the work done by all forces acting on a particle (the work of the resultant force) equals the change in the kinetic energy of the particle." (from Wikipedia)
so it seems to me that, as the kinetic energy has changed, some work has to be done!

I trust you are right, but why is my reasoning wrong? :D

Last edited: May 21, 2015
4. May 21, 2015

### mrnike992

Work is only net force x distance. And we need to keep in mind that this is kinetic energy within a system. We aren't adding that the planet is hurtling through space at approximately 30,000 m/s, etc. The box never moved in the truck. Therefore there is no change in kinetic energy. The box is not decelerating.

5. May 21, 2015

### Staff: Mentor

I'd say that you are correct and your teacher is wrong.

6. May 21, 2015

### TSny

I concur with Doc Al. The net work done by all the forces acting on the box is ΔKbox, as you said.

7. May 21, 2015

### mrnike992

I'm sure you both (Doc Al and TSny) are much more qualified to answer this than I am, but it does say
If this is all relative to the truck, there is no change in kinetic energy if it is at rest and does not begin moving.

8. May 21, 2015

### Staff: Mentor

The box does not move with respect to the truck, but it surely moves with respect to the ground and accelerates. (Which is the most likely inertial frame to use; the frame of the truck is not an inertial frame.)

9. May 21, 2015

### mrnike992

Well yes, it moves with respect to the ground, and with respect to the sun, and a whole bunch of things. But the problem specifically mentions the frame of reference of the truck. Why can the truck not be an inertial frame??

10. May 21, 2015

### Staff: Mentor

Only to describe the motion of the box. Try this: Say there were zero friction on the box. (Assume the truck bed is long enough so that the box doesn't fall off.) What would be the work done on the box in that case?

It's accelerating.

11. May 21, 2015

### TSny

The first sentence of the problem mentions the initial speed of the truck. This is apparently from the point of view of the reference frame of the earth. The second sentence mentions that the truck decelerates to rest. Again, this is from the frame of the earth. So, it is natural to assume that the rest of the problem relates to the frame of the earth.

But, you have a point. If you look at it in the noninertial frame of the truck then none of the forces do any work.

The truck is a noninertial frame because it is accelerating relative to the inertial frame of the earth.

12. May 21, 2015

### physicsisgreat

This is fun :D
I also would add the following to see if you agree again with me.
Imagine you are inside a car which is accelerating and a friend of yours is still outside the car. From the frame of the earth his energy is constant and the total force acting on him/her is 0, so W = 0 too. Since the laws of physics have to be true regardless of the reference frame, even from your frame you will have ΔK = W. For you he/she is accelerating thus gaining kinetic energy – the force which is doing the corresponding work is in this case the apparent force due to the non-inertial nature of your frame of reference.
Am I right? May I go to my teacher and tell him he is a very very bad boy? :D

13. May 21, 2015

### TSny

Well, Newton's laws are generally valid only in inertial frames. The work-energy theorem is a consequence of Newton's 2nd law. So, you would not expect the work-energy theorem to be valid in a noninertial frame.

14. May 22, 2015

### physicsisgreat

I'm not sure I can quite agree with you on this. As long as you correctly take into account the fictitious forces acting on a non-inertial frame, it doesn't come to my mind any example of non-validity of Newton's laws: what am I missing?

15. May 22, 2015

### TSny

You are correct. If you want to include fictitious forces, you can then use Newton's laws in a non-inertial frame.