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

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SUMMARY

The discussion centers on calculating the work done by a car engine to ascend a hill, given specific parameters. The car, weighing 2 tonnes, starts at a speed of 10 m/s and finishes at 5 m/s after traveling 500 meters up a hill with a gradient of 1 in 125. The initial kinetic energy (KE) is calculated as 100 kJ, while the potential energy (PE) gained is 160 J, and the final KE is 25 kJ. The participant concludes that the work done by the engine is -85 kJ, indicating a misunderstanding of the height calculation and the impact of a 100 N retarding force, which is likely due to friction.

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aurao2003
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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
 
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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.
 
I think the retarding force of 100 N is friction, and the engine has to do work to overcome that as well.
 

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