Mechanical Equivalent of Heat

Formulas Used

1. Suppose that a 0.990 kg hammer strikes the head of an iron nail at 69 cm/s. If the mass of the nail is 5.0 grams, how much will the temperature of the nail increase, assuming that all heat from impact is transferred to the nail? (The specific heat capacity of iron is 450 J/kg-K.)
2. A man is grilling on his 38.1 meter high balcony when the wind blows an aluminum serving tray at 19.89 °C out of his hand, sending it crashing to the ground. If all of the heat generated by this process is transferred to the tray, what will the tray’s final temperature be? (The specific heat capacity of aluminum is 890 J/kg-K.)
3. From what height would a ball of ice have to fall in order to raise its temperature from -13.72 °C to -8.01 °C upon impact? (The specific heat capacity of ice is 2100 J/kg-K.)
4. An old copper penny is thrown against a wall at 38 m/s, subsequently rebounding from the wall at 16 m/s. By how much does its temperature increase, assuming that all kinetic energy lost in the collision is retained by the penny as heat? (The specific heat capacity of copper is 390 J/kg-K.)
5. At what speed would one need to fire a lead projectile in order for its temperature to rise from 22.1 °C to 35.4 °C upon impact with a stationary object? (The specific heat capacity of lead is 130 J/kg-K.)
6. A worker drives an iron stake with a mass of 820 grams into the ground with ten swings of a sledgehammer. If the worker swings the hammer at 3.02 m/s, what would the mass of the sledgehammer need to be in order to raise the stake’s temperature by 0.638 °C? (The specific heat capacity of iron is 450 J/kg-K.)