The drawing shows two boxes resting on frictionless ramps. One box is relatively

Question

The drawing shows two boxes resting on frictionless ramps. One box is relatively light and sits on a steep ramp. The other box is heavier and rests on a ramp that is less steep. The boxes are released from rest at A and allowed to slide down the ramps. The two boxes have masses of 11 and 47 kg. If A and B are 5.0 and 0.5 m, respectively, above the ground, determine the speed of (a) the lighter box and (b) the heavier box when each reaches B. (c) What is the ratio of the kinetic energy of the heavier box to that of the lighter box at B?

Explanation / Answer

speed = sqrt(2gh), so speed at B = sqrt(2 x 9.8 x 5-0.5)=9.39m/s for both boxes (since velocity doesnt depend on mass) ratio of kinetic energies = ratio of potential energies = (m1gh)/(m2gh) = m1/m2 = 47/11 = 4.2727 Ans

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