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 30 kg. If A and B are 4.0 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

velocity on reaching B does not depend on mass of the bodies

velocity at B is v = sqrt(2*g*h) = sqrt(2*9.8*(4-0.5)) = 8.28 m/sec

A) velcoity if light body is 8.28 m/sec

B) velocity of heavier mass is 8.28 m/sec

Kinetic energy of heavier body is K1 = 0.5*m1*v1^2

Kinetic energy of lighter body is K2 = 0.5*m2*v2^2

since v1 =v2 ,then

K1/K2 = (0.5*m1*v1^2)/(0.5*m2*v2^2) = m1/m2 = 30/11 = 2.78

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