Physics problem: nail driven in board?

A nail driven into a board increases in temperature.


If 60.0% of the kinetic energy delivered by a 1.80 kg hammer with a speed of 7.80 m/s is transformed into heat that flows into the nail and does not flow out, what is the increase in temperature of an 8.00 g aluminum nail after it is struck 10.0 times? (answer in degrees C please)Physics problem: nail driven in board?
use this formula





60/100 * 1/2 * 1.8 * 7.8^2 * 10 = 8 * Cp * delta T


you should know the Cp of Al to find the delta T in J/gK, i will not do it for you.Physics problem: nail driven in board?
Kinetic energy of hammer = 1/2 mv虏 = 1/2 (1.8)(7.8虏)





60 % of kinetic energy is delivered per hammer strike.





Energy delivered per strike = 60% of [1/2 (1.8)(7.8虏)]





= 0.6 X [1/2 (1.8)(7.8虏)]





= (0.3)[(1.8)(7.8虏)]





There are 10 strikes so total energy delivered is





10 X (0.3)[(1.8)(7.8虏)]





= 3[(1.8)(7.8虏)]





= 328.536 Joules.





Equate this to energey absorbed by nail mc螖T





Where m = mass of nail = 0.008 kg





c = specific heat capacity of aluminium





螖T = temperature rise








mc螖T = 328.536





螖T = 328.536 / mc








螖T = (328.536) / (0.008c)





Just plug in the value for c and you have your answer.