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Two blocks of ice, one four times as heavy as the other, are at rest on a frozen lake. A person pushes each block the same distance d. Ignore friction and assume that an equal force F is exerted on each block. Which of the following statements is true about the kinetic energy of the heavier block after the push?

It is smaller than the kinetic energy of the lighter block.

It is equal to the kinetic energy of the lighter block.
It is larger than the kinetic energy of the lighter block.
It cannot be determined without knowing the force and the mass of each block.
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Let's do a comparison with some example values and then I'll explain the theory. Let's say that the first block is 10kg and the second block is 40kg (4 times heavier). Say that the force is 100N. Since F = ma, we know that:

For the first block:

F = ma
100N = 10kg * a
a1 = 10m/s2

For the second block:

F = ma
100N = 40kg * a
a2 = 2.5m/s2

Now say that the distance is 10m. We can find the final velocity of each block via:

Vf2 = V02 + 2a(d)

This is just one of the kinematic equations that you should know from previous chapters. So the final velocities are (assume each block starts from zero):

Block 1 = 14.14m/s
Block 2 = 7.07m/s

There is a pattern here, I'll explain at the end if you don't see it already.

Now that we have the final velocities, we can solve for the kinetic energy of each block, using the equation KE = 1/2mv2:

Block 1:

KE = 1/2mv2
KE = 1/2(10)(14.14)2
KE = 1,000J

Block 2:

KE = 1/2mv2
KE = 1/2(40)(7.07)2
KE = 1,000J

So the answer is B. It is equal to the kinetic energy of the lighter block.
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