# Need help on work-energy principle

1. Mar 28, 2004

### viper_ace

Need help on work-energy principle!!

How do work relate to energy?

If a car which have kinetic energy of 10,000 Joules. A collide with a wall but the wall doesn't move so does the car do the work on the wall? But in the the book they state that energy spend = workdone.

only the wall that do work on the car in this case because the car chasee would collide backward

2. Mar 28, 2004

### kurious

The wall does work on the car. Work done = force x distance moved.
The best way to look at this problem is to consider all the mass of the car to be located at one point in space -at the centre of mass .Then work done = force wall exerts on car x the distance from the centre of mass to the wall.The force depends on the mass of the car and how long the car takes to slow down because force = mass x (initial speed - final speed)/ time taken to slow down.

3. Mar 28, 2004

### Staff: Mentor

no displacement = no work

Since the wall doesn't move (displacement = zero) it does no work on the car.

The wall certainly exerts a force on the car, which does change the KE of the center of mass. One can integrate Newton's 2nd law to find that:
Force X Displacement of center of mass = Î”KE (of center of mass)

Here's a similar situation: You jump up into the air. Does the ground do work on you? No! There is no displacement at the point of application of the force, so no work is done. This makes sense: The ground is not an energy source. The energy for your jump comes from converting chemical potential energy (in your muscles) to KE.

4. Mar 29, 2004

### Michael D. Sewell

I actually tried this experiment once. From my reference frame the wall appeared to move. It also appeared to have a significant "impact" on the appearance of my car.

5. Mar 29, 2004

### turin

In the rest frame of the wall, after impact, the car loses 10 kJ of (kinetic) energy. Does the wall gain 10 kJ of energy from the car?

In the rest frame of the car, the wall is moving. After impact, in the same frame, the car is moving with (almost) KE = 10 kJ. Does the wall lose energy, transferring 10 kJ to the car?

This issue is probably best understood by assuming a wall that is a gazillion times more massive than the car, but can still be affected by work and impulse.

Last edited: Mar 29, 2004
6. Mar 30, 2004

### Staff: Mentor

I would say that the 10 kJ goes to deformation of the car and increase of thermal energy in car and wall. Not into increase of KE of wall.
Yes, energy is frame dependent. The (massive) wall loses energy--I would say 20 kJ: 10 kJ goes into deformation/thermal energy and 10 kJ goes into the KE of the car.
Right.

7. Mar 30, 2004

### Aeonic333

work

Work is equal to (F)(d), so since the wall does not move the car does no work on the wall. If you consider Newton's Third Law (every action has an equal and opposite reaction) then the wall exerts a force back on the car. Depending on whether this is an elastic (like a ball bouncing off rubber) or inelastic (like throwing a piece of gum at a wall) the wall will transfer that energy back to the truck in a different way. Keep in mind though, that not all of the original 10,000 J has to be transfered back to the truck; some of this energy could be spent elsewhere, such as heating up the wall.

8. Mar 31, 2004

### Michael D. Sewell

The collision was more inelastic.

I didn't check the wall to see how hot it was. lol.

My local body shop did a lot of "work" on the car.
-Mike

9. Mar 31, 2004

### Staff: Mentor

In my comments I assume that when the car slams into the wall we have pretty close to a perfectly inelastic collision.

10. Mar 31, 2004

### Michael D. Sewell

Doc Al,
Don't try this at home! Your assumption is correct. I wasn't disagreeing with you at all, I was just having some fun at my own expense. Many students have trouble with the concept of work. Your explanation is a good one.
-Mike