An ingot of lead is dropped with an initial velocity of 14 ft/s. When it hits the ground, its temperature has been increased by 0.25 oF. From what height was the ingot dropped (in ft)? Neglect air resistance. [h = 2.79 ft]

The ingot was dropped at a height of 2.81 feet.

Explanation:

The ingot is released from a height and accelerated by gravity, it hits the ground and stops abruptly by impact, which contributes to the temperature increase of the material. We can model this systems by means of the First Law of Thermodynamics, which is generalized form of Principle of Energy Conservation:

(Eq. 1)

Where:

, - Initial and final gravitational potential energies, measured in pound-feet per second.

, - Initial and final translational kinetic energies, measured in pound-feet per second.

- Change in internal energy of the lingot of lead, measured in pound-feet per second.

By applying definitions of gravitational potential, translational kinetic and internal energies, we expand the expression above, eliminate mass in both sides and clear the final temperature of the ingot:

If we know that , , , and , the height from which the lingot dropped is:

The ingot was dropped at a height of 2.81 feet.