A mass $m$ travels a vertical distance $\Delta h$ in a uniform gravitational field and gains gravitational potential energy $\Delta E_P$. The acceleration of free fall is $g$. Use the idea of work done to show that $\Delta E_P = mg\,\Delta h$.
A $0.60\,\text{kg}$ mass is tied to a string that is wound around the wheel of a generator, as shown in Fig. 4.1. The mass is kept still above the floor. When it is released, the mass first speeds up and then drops at a steady speed, turning the wheel. The generator produces a current in a resistor. Air resistance is negligible. State the main energy change when the mass is falling at a steady speed. ........ energy to ........ energy.
While moving at a steady speed, the mass in (b) descends through a vertical distance of $1.4\,\text{m}$ in $4.0\,\text{s}$. This produces a current of $90\,\text{mA}$ in the resistor. The resistance of the resistor is $47\,\Omega$. Calculate the rate of work done by the falling mass.
Calculate the power dissipated in the resistor.
Calculate the efficiency of the generator.