A cylindrical space capsule lands in the ocean. This capsule is \(2.34 \mathrm{~m}\) long, \(1.10 \mathrm{~m}\) in diameter, and weighted at onc end so that it floats with its long central axis vertical and \(0.820 \mathrm{~m}\) of its length above the water surface. The mass density of sea water is \(1025 \mathrm{~kg} / \mathrm{m}^{3}\).

(a) What is the magnitude of the buoyant force exerted on the capsule?

(b) Suppose the capsule springs a leak and sinks. What is the magnitude of the buoyant force exerted on it once it sinks?

(c) Why does the capsule sink if the magnitude of the buoyant force is greater after it has sunk than when it was floating?