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conantee
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« on: December 31, 2009, 04:55:33 AM »
8. A 5-kilogram stone is dropped on a nail and drives the nail 0.025 meter into a piece of wood. If the stone is moving at 10 meters per second when it hits the nail, the average force exerted on the nail by the stone while the nail is going into the wood is most nearly
(A) 10 N
(B) 100 N
(C) 1000 N
(D) 10,000 N
(E) 100,000 N
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conantee
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« Reply #1 on: December 31, 2009, 05:02:54 AM »
Looking at the choices, we know that we need a significant answer with error less than the order of 10.

Now, in order to find force here, there is nothing to do with momentum and time here. The only source we can find average force is from work-energy conservation.

The total energy of stone, which is the kinetic energy, is converted to the work done by the average force. Hence, we got the equation

W = Fx = \frac{1}{2} mv^2 , then F =\frac{1}{2} mv^2/x

Plugging the values in, we have F = \frac{ 5 \cdot 10^2}{ 2 \cdot 0.025}= \frac{500}{0.05}=10,000 \mbox{ N}

The correction is, therefore, (D). 47 of 100 people got the right answer.
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