# Physics: Temperature increase in the nail after 10 hammer blows

a nail driven into a board inc in temp. if we assume that 60% of the kinetic energy delivered by a 1,8 kg hammer w/ a speed of 7.5 m/s is transformed into heat that flows into the nail and does not flow out, what is the temp inc of an 8 g aluminum nail after it is struck ten times?

### Kinetic energy in a single

Kinetic energy in a single blow of hammer
$E = \frac{1}{2}mv^2 = \frac{1}{2}(1.8)(7.5)^2$

$E = 50.625 ~ \text{Joules}$

Kinetic energy for 10 hammer blows
$E_{10} = 10(50.625) = 506.25 ~ \text{Joules}$

Sixty percent of E10 is transferred into the nail in the form of heat energy. Energy in the nail after 10 blows is...
$E_n = 0.60(506.25) = 303.75 ~ \text{Joules}$

I don't have the information about specific heat capacity of aluminum. If you have that information, you can calculate the temperature increase of the nail using the following:
$\Delta T = \dfrac{E_n}{\text{heat capacity of aluminum} \times \text{mass of nail}}$