how can i estimate the temperature rise?

Question

the problem asks: the 1.20 kg head of a hammer has a speed of 8m/s just before it strikes a nail and is brought to rest. Estimate the temperature rise of a 14 g iron nail generated by 10 such hammer blows done in quick succession. Assume the nail absorbs all the energy.

I'm not asking for anyone to solve this problem for me, all i ask for is for someone to explain the steps i need to take in order to find the temperature rise...


thank you for alll of your help!

Answer 1

The kinetic energy K = mv^2/2 of the hammer head is transformed into heat Q=K and absorbed by the nail.

The absorbed heat Q causes the internal energy E of the nail
to increase by amount Q after each blow:
E1 - E0 = Q
E2 - E1 = Q
...............
E10 - E9 = Q, or

E10 - E0 = 10 Q

On the other hand the change in the internal energy
of the nail is given by the equation:

E10 - E0 =
(mass of the nail) *
(specific heat ot nail material) *
(temperature increase)

Since your nail is made of iron, you'll need
the specific heat of iron too.

Answer 2

First detemine the amount of kinetic energy in the hammer swing. Now that you now the amount of energy per swing multiply it by 10 for the number of swings. With this total amount of energy, assuming it is all transferred to the nail in the form of heat. Use the specific heat of iron to determine how much of a temperature rise you will get in 14 g with the energy you just calculated.

Answer 3

Using kinetic energy = 1/2 m v^2, you can calculate the energy imparted to the nail by one hit. Multiply it by 12 hits to get the total energy absorbed. Set that equal to the heat capacity times the temperature change (if you do not have it for iron, can get estimate by using specific heat of water of 1 cal/gm/C and multiply by 1200 gm. Solve for temperature change.