Two physics KE/PE questions(and possibly more, studying for a test)

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Homework Statement



a carpenter moves his .5 kg hammer at 3m/s when it contacts a nail. The nail receives an average force of 75N as it is driven 2cm int the wood board. The carpenter notices that the nail feels warm after he hits it with the hammer. How much heat energy was transferred to the nail.

Homework Equations


W = fd

The Attempt at a Solution



work w =force Fx distsnce D
w=75nx.02m
w=1.5j

Maybe I am supposed to do Ke = .5mv^2 and get 2.25J, then 2.25- 1.5J = .75J?

Except that was wrong?
Next problem

How much work is done by accelerating a 1200kg card from rest to a speed of 12m/s while it is movin up a frictionless hill that is 18m high.

force = mass x acceleration F= 1200x12=14400n
w=force x distance w=14400x18=259200j
=259.2kj

Except my friend is getting 298080J. Not sure whos right here. Thanks everyone!

Hes doing
W = mg(18) + .5m(12)^2
 
Last edited:

Discussion

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When you calculate the work, you do need to take into account any change in potential energy. Try that for the first problem and see if it gets you a better result.
 
So for the first one, I tried

5mv^2 + mgh = W + Q
W = fd = 75N * .02m
= 1.5J
.5(.5kg)(3m/s)^2 = 2.25J
= KE
.5kg * 9.8m/s^2 * .02m = PE = .98J
2.25+ .98 = 1.5 + Q

So is Q 1.73J?