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Math Help - Work done on a hill

  1. #1
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    Work done on a hill

    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, travelling 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.

    Solution 1: Energy conservation.
    I surmised the following:
    Initial KE - Work done= PE gained + Final KE (Is this correct?)
    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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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by gbenguse78 View Post
    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, travelling 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.

    Solution 1: Energy conservation.
    I surmised the following:
    Initial KE - Work done= PE gained + Final KE (Is this correct?)
    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
    The PE gained is m \times g \times h where $$ h is the change in height

    The work done by the retarding force is the force times the distance the car moves in the direction of the force.

    CB
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  3. #3
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    Hi
    A very belated reply to all your help. As a husband, worker and A levels student you can call me superman. Apologies for the delay in responding. Thanks once again
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