# Work done down an inclined plane

1. May 21, 2013

### Dongorgon

1. The problem statement, all variables and given/known data
A toy car of mass 20kg moves down a slope of length 35m, which is inclined at arcsin(2/7) to the horizontal. The height of the car initially is 10m, and a constant frictional force of 100N acts against the car through motion. Calculate the work done, power and efficiency of the system:

3. The attempt at a solution
My initial issue here is calculating the work done by the car travelling down the entirety of the slope. I'm not sure whether the work done is just the friction force x distance which would give 3500J, or whether you need to take into account the horizontal component of the cars weight when descending the slope, resolving horizontally?
Any advice here would be greatly appreciated! Thanks.

2. May 21, 2013

### cepheid

Staff Emeritus
Dongorgon,

It doesn't make sense to speak of the work done "by" the car. Work is force * distance, so work is done BY forces ON objects as those forces move those objects over distances. If you want to compute the total work done ON the car, you have to take into account the work done by all forces acting on the car. So you have to account for the work done by gravity as well as the work done by friction. Another way to look at it: the total (net) work done on the car will be the work done by the net force. I hope this helps.

3. May 21, 2013

### HallsofIvy

Staff Emeritus
You need to take into account both gravity and friction. The work done by friction is the force, 100N, times the distance traveled, 35m. The work done by gravity can be calculated by the decrease in potential energy, mg= (20)(9.81) times the vertical distance, (2/7)35= 10 m, the car has gone. Becareful- one is work done increasing the speed of the car, the other is work done decreasing the speed of the car.

(There is no "horizontal component of weight". Weight is a force vector pointing vertically.)

4. May 21, 2013

### haruspex

Given the question about efficiency, I suspect they want the work done by gravity.
Dongorgon, have you quoted the problem exactly as given?