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 14 and 31 kg. If A and B are hA = 4.2 and hB = 1.3 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?

vB

vB

vB

vB

Explanation / Answer

1) for heavier box

mass of heavier box = 31 kg

so after sliding down the height of ( hA-hB)

work done by gravity = change of KE

mg (hA-hB) = 1/2 m v2

9.81 *( 4.2 -1.3) = 1/2 * v2

v = 7.54 m/s

2) for lighter box

mass of heavier box = 14 kg

so after sliding down the height of ( hA-hB)

work done by gravity = change of KE

m'g (hA-hB) = 1/2 m' v2

9.81 *( 4.2 -1.3) = 1/2 * v2

v = 7.54 m/s

for both boxes the velocity at B will be same

3) KE ratio

=KEheavier / Klighter

= {1/2 *(31) * 56.89 } / 1/2 *(14) * 56.89

=31/14

=2.21    answer

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