In the figure, a frictionless roller coaster car of mass m = 672 kg tops the first hill with speed v0 = 19.4 m/s at height h = 34.7 m. How much work does the gravitational force do on the car from that point to (a) point A, (b) point B, and (c) point C? If the gravitational potential energy of the car-Earth system is taken to be zero at C, what is its value when the car is at (d) B and (e) A?

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  1. (a) W(grav) = 0 since there is no change in height between the initial point and point A.
    (b) W(grav) – mgh –mg(h/2) = mgh/2
    (c) W(grav) mgh -0 = mgh
    (d) mgh/2
    (e) mgh

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