GRE question - Work-KE theorem?

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The discussion revolves around calculating the average force exerted on a nail by a 5-kilogram stone dropped at 10 meters per second, which drives the nail 0.025 meters into wood. The work-energy theorem is relevant here, as it relates the work done on the nail to the change in kinetic energy of the stone. While the initial assumption was that acceleration is constant, the key point is that the question seeks the average force, which can be treated as constant for the purpose of calculation. The correct answer is identified as choice D, which is 10,000 N, despite concerns about energy dissipation during the process. The clarification emphasizes that average force can be determined without assuming constant acceleration.
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Homework Statement


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) 10000 N
E) 100000 N


Homework Equations


W = delta K


The Attempt at a Solution


I've used kinematics to find the answer to this problem (choice D), but that assumes that the acceleration is constant, which I don't think we can do.

Is there a way to apply the work-KE theorem? I know energy cannot be conserved because there is energy dissipated while the nail is driven into the wood.

Thanks for any help.
 
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I get the answer you do (D). You don't assume that acceleration is constant, you're finding the AVERAGE force, so it's effectively asking for a constant force.
 

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