Two blocks of ice are at rest on a smooth frozen lake. One block is 3 times the

Question

Two blocks of ice are at rest on a smooth frozen lake. One block is 3 times the mass of the other block. A man pushes each block the same distance, d meters with an equal force. Compared to the speed of the heavier block, how fast does the light block move?

1. The velocity of the lighter block is one-third as fast as the velocity of the heavier block.

2. The velocity of the lighter block is half as fast as the velocity of the heavier block.

3. The velocity of the lighter block is the same as the velocity of the heavier block.

4. The velocity of the lighter block is the square root of three times faster than the velocity of the heavier block.

5. It cannot be determined without knowing the speed and the mass of each block.

What is right?

Explanation / Answer

mlighter = mass of lighter block = m

vlighter = speed gained by ligheter block

mheavy = mass of heavier block = 3m

vheavy = speed gained by heavy block

F = force applied

d = distance moved

consider the motion of the lighter block

F d = (0.5) mlighter (vlighter2)                        eq-1

consider the motion of the heavy block

F d = (0.5) mheavy (vheavy2)                        eq-2

using eq-1 and eq-2

(0.5) mlighter (vlighter2) = (0.5) mheavy (vheavy2)

m (vlighter2) = 3m (vheavy2)

vlighter = sqrt(3) vheavy

The velocity of the lighter block is the square root of three times faster than the velocity of the heavier block.

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