How much work is done by the engine to get the car up the hill?

[aurao2003]

Homework Statement

Hi

I have a slight problem. Please comment on the question and solution.

A car of mass 2 Tonnes arrives at a foot of a hill, traveling at a speed of 10m/s and reaches the top of the hill with a speed of 5m/s. The hill is 500m long and rises 1 in 125. If there is a retarding force of 100N, calculate the amount of work done by the engine in getting the car up the hill.

Homework Equations

Solution 1: Energy conservation.
I surmised the following:
Initial KE - Work done= PE gained + Final KE (Is this correct?)

The Attempt at a Solution

Initial KE= 0.5 X 2000 X 100 = 100KJ
Work done=?
PE Gained= 2000 x 10 x 1/125 = 160J
Final KE = .5 X 2000 X 25 = 25KJ

Work Done = (100-160-25)KJ= -85KJ

 

[Delphi51]

Initial KE - Work done= PE gained + Final KE

I would put a + sign before work done rather than a minus sign.

The assumption that the height of the hill is 1/125 m does not seem right. One part in 125 x 500 = 4, suggesting the height is 4 meters.

 

[willem2]

I think the retarding force of 100 N is friction, and the engine has to do work to overcome that as well.