Consider a \(0.10-\mathrm{kg}\) pendulum swinging at a maximum speed of \(0.80 \mathrm{~m} / \mathrm{s}\) inside a box that contains \(1.0 \times 10^{23}\) nitrogen molecules. The mass of a nitrogen molecule is \(4.7 \times 10^{-26} \mathrm{~kg}\), and at room temperature a typical nitrogen molecule moves at \(500 \mathrm{~m} / \mathrm{s}\). What are

(a) the mechanical energy of the pendulum,

(b) the average kinetic energy of one nitrogen molecule, and

(c) the sum of the average kinetic energies of all the nitrogen molecules?