A cylinder of density ? c , length l, and cross-section area A floats in a liqui
ID: 1390813 • Letter: A
Question
A cylinder of density ?c, length l, and cross-section area A floats in a liquid of density ?f with its axis perpendicular to the surface. Length h of the cylinder is submerged when the cylinder floats at rest.
a) Find the expression for h
b)Suppose the cylinder is distance y above its equilibrium position. Find an expression for (Fnet)y , the y-component of the net force on the cylinder. Use what you know to cancel terms and write this expression as simply as possible. Assume that y-axis points upward.
c) You should recognize your result of part b as a version of Hooke's law. What is the "spring constant" k?
d) If you push a floating object down and release it, it bobs up and down. So it is like a spring in the sense that it oscillates if displaced from equilibrium. Use your "spring constant" and what you know about simple harmonic motion to find the cylinder's oscillation period.
Explanation / Answer
d) If you push a floating object down and release it, it bobs up and down. So it is like a spring in the sense that it oscillates if displaced from equilibrium. Use your "spring constant" and what you know about simple harmonic motion to find the cylinder's oscillation period.