A 5-g coin is dropped from a 300-m building. If it reaches a terminal velocity of 45 m/s, and the rest of the energy is converted to heating the coin, what is the change in temperature (in °C) of the coin? (The specific heat of copper is 387 J/kg⋅°C.)
A) 9
B) 2
C) 5
D) 21
E) 0.5

Question

Quizplus · Accepted Answer

The energy converted to heat is the difference between the potential energy lost and the kinetic energy gained at terminal velocity. The potential energy (PE) lost is given by $PE = mgh$, where $m = 0.005$ kg (mass of the coin), $g = 9.8$ m/s$^2$ (acceleration due to gravity), and $h = 300$ m (height). So, $PE = 0.005 \times 9.8 \times 300 = 14.7$ J. The kinetic energy (KE) at terminal velocity is given by $KE = \frac{1}{2}mv^2$, where $v = 45$ m/s is the terminal velocity. So, $KE = \frac{1}{2} \times 0.005 \times 45^2 = 5.0625$ J. The energy converted to heat is $14.7 - 5.0625 = 9.6375$ J. The change in temperature ($\Delta T$) is given by $\Delta T = \frac{Q}{mc}$, where $Q$ is the heat energy, $m$ is the mass, and $c$ is the specific heat capacity. Thus, $\Delta T = \frac{9.6375}{0.005 \times 387} \approx 5$ °C.

A 5-G Coin Is Dropped from a 300-M Building