GRE question - Work-KE theorem?

[eprparadox]

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.

 

[nnnm4]

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.

 

[tomcue]

The work-KE (kinetic energy) theorem states that the net work done on an object is equal to the change in its kinetic energy. In this scenario, the stone is exerting a force on the nail, causing it to move and therefore changing its kinetic energy. However, energy is also being dissipated in the form of heat and sound as the nail is driven into the wood. Therefore, the work done by the stone on the nail is not equal to the change in kinetic energy of the stone.

To find the average force exerted on the nail by the stone, we can use the equation F = ma, where m is the mass of the stone and a is the acceleration of the stone. Since the stone is moving at a constant velocity of 10 m/s, the acceleration is 0, and therefore the average force exerted on the nail is also 0.

In conclusion, the work-KE theorem is not applicable in this scenario as energy is not conserved. The correct answer to the question would be choice A) 10 N, as the average force exerted on the nail is 0 and not 10000 N as calculated using kinematics.