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

Question

The drawing shows two boxes resting on frictionless ramps. Onebox is relatively light and sits on a steep ramp. The other box isheavier and rests on a ramp that is less steep. The boxes arereleased from rest at A and allowed to slide down the ramps. Thetwo boxes have masses of 12 and 38 kg. If A and B are5.5 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 theheavier box to that of the lighter box at B?

Explanation / Answer

a) mA is lighter for energy conservation" (1/2)mAvB2 =mAg(hA - hB) vB = [2g(hA - hB)] =[2*9.8m/s2 (5.5m - 0.5m)] = 9.90m/s b) mB is lighter for energy conservation" (1/2)mB uB2 =mBg(hA - hB) uB = [2g(hA - hB)] =[2*9.8m/s2 (5.5m - 0.5m)] = 9.90m/s c) KEA/KEB = (1/2)mA vB2 /(1/2)mB uB2 = mA/ mB =12/38 = 6/19 mB is lighter for energy conservation" (1/2)mB uB2 =mBg(hA - hB) uB = [2g(hA - hB)] =[2*9.8m/s2 (5.5m - 0.5m)] = 9.90m/s c) KEA/KEB = (1/2)mA vB2 /(1/2)mB uB2 = mA/ mB =12/38 = 6/19

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