# Work done by friction (rolling resistance)

1. Jan 20, 2016

### Rumplestiltskin

1. The problem statement, all variables and given/known data
The carriage and its passengers start at rest at A. At B, the bottom of the ride, the maximum speed of the carriage is 20ms-1. The vertical distance between A and B is 110m. The length of the track between A and B is 510m. The mass of the carriage and the passengers is 4000kg.

By considering the energy changes from A to B, determine the average frictional force acting on the carriage.

2. Relevant equations
3. The attempt at a solution

GPE at A = mgh = 4000 * 9.81 * 110 = 4316400 J
KE at B = 0.5 * 4000 * 202 = 800000 J
4316400 - 800000 = 3516400 J work done.
W = Fx. 3516400 = F * 510
F = 6900 N?

2. Jan 20, 2016

### haruspex

Your arithmetic looks fine, but sadly the question is wrong. You do not have enough information to determine the average force.
Average force is $\Delta p/\Delta t$, where p is momentum and t is time. This comes out the same as $\Delta E/\Delta s$ when the force is constant, but in not general.
See section 3 of https://www.physicsforums.com/insights/frequently-made-errors-mechanics-forces/ for a fuller discussion.

3. Jan 20, 2016

### Rumplestiltskin

Will be sure to tell my teacher. :P I guess this should suffice though. Thanks.