Serway & Jewett — Fluid Mechanics: Problem 36

Review. Assume a certain liquid, with density \(1230 \text{ kg/m}^3\), exerts no friction force on spherical objects. A ball of mass \(2.10 \text{ kg}\) and radius \(9.00 \text{ cm}\) is dropped from rest into a deep tank of this liquid from a height of \(3.30 \text{ m}\) above the surface. (a) Find the speed at which the ball enters the liquid. (b) Evaluate the magnitudes of the two forces that are exerted on the ball as it moves through the liquid. (c) Explain why the ball moves down only a limited distance into the liquid and calculate this distance. (d) With what speed will the ball pop up out of the liquid? (e) How does the time interval \(\Delta t_{\text{down}}\), during which the ball moves from the surface down to its lowest point, compare with the time interval \(\Delta t_{\text{up}}\) for the return trip between the same two points? (f) What If? Now modify the model to suppose the liquid exerts a small friction force on the ball, opposite in direction to its motion. In this case, how do the time intervals \(\Delta t_{\text{down}}\) and \(\Delta t_{\text{up}}\) compare? Explain your answer with a conceptual argument rather than a numerical calculation.