Final answer:
The problem is a physics question requiring a calculation of the temperature increase in an iron nail from the kinetic energy of hammer blows using the specific heat capacity formula.
Step-by-step explanation:
The question involves estimating the temperature rise of a 13-g iron nail from the energy transfer of 10 hammer blows, assuming the hammer's head has a mass of 1.30 kg and is moving at a velocity of 7.7 m/s before striking the nail. This problem can be approached by first calculating the kinetic energy of the hammer head before impact, then assuming all that energy is transferred into the nail as heat. The specific heat capacity of iron must be used to find the change in temperature, given by the formula ΔT = Q/(mc), where Q is the heat absorbed, m is the mass, and c is the specific heat capacity of iron.
The kinetic energy every time the hammer strikes the nail is given by KE = 1/2 m v^2, where m is mass and v is velocity. Because the hammer comes to rest, all of this energy is assumed to transfer to the nail as heat, Q. Across 10 impacts, the total energy is 10 times the kinetic energy of one impact.
With the mass m of the nail known, and the specific heat capacity c of iron, the change in temperature ΔT can be estimated. It is important to note that in a real-word setting, not all energy goes into heating the nail; some is lost to sound, vibration, and heat transfer to other materials. However, for the purpose of this physics problem, these losses are ignored in simplifying the model.