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 10 and 37 kg. If A and B are hA = 4.4 and hB = 1.7 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

Because we are neglecting friction heavy and light objects will fall at the same rate.

To solve this problem we can equate potential energy to kinetic energy and solve for speed:

so mgh = .5mv^2

The masses kill each other (see the first sentence) and solving for v we get: v = sqrt[2gh]. In this case the hight is 4.4 - 1.7 = 2.7 so v = sqrt[2(9.8)(2.7)] = 7.27 m/s. This is the answer to 'a' and 'b'.

For question 'c' the kinetic energy is .5mv^2 so the ratio of the kinetic energies is just the ratio of the masses: 37/10 = 3.7

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