Physics

A crate of mass 10 kg is pulled up a rough incline with an initial speed of 1.5 m/s. The pulling force is 100 N, parallel to the incline; which makes an angle of 20o with the horizontal. The coefficient of friction is 0.40, and the crate is pulled 5.0 m. Has the mechanical energy of the system increased or decreased? Show your work.

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  1. potential energy m g h went up. h is 5 sin 20 so change in PE = 10 *9.81 *1.71 = 168 Joules
    what happened to kinetic energy .5 m v^2 ?
    force up slope = 100 - mu *m*g* cos 20
    force up slope = 100 - .4 *10*9.81* .94 = 100-36.9 = 63.1 Newtons
    acceleration up slope = 63.1/10 = 6.31 m/s^2
    v = 1.5 + a t
    x = 0 + 1.5 t + .5 (6.31) * t^2 = 5 meters
    3.16 t^2 + 1.5 t -5 = 0 , solve quadratic, plus root = 1.04 seconds
    so v = 1.5 + 6.31(1.04) = 11.6 m/s at top
    so BOTH potential energy and Kinetic energy INCREASE

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    Damon

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