The question
Name: ______________________ Date: ____________ A coin on a floating block (8 points)
Diagram
Two floating blocks
Two rectangular wooden blocks, each of mass M, float upright in water of density ρ with their flat bottoms horizontal. Block 1 has bottom area A. Block 2 has bottom area 2A. A coin of mass m is placed at the center of the top of each block. Both blocks still float, with their tops above the water, and come to rest.
(a) When the coin is added, each block sinks an additional distance Δd lower in the water. Is Δd greater for block 1, greater for block 2, or the same for both? Justify your answer without using equations. [2 points]
(b) Starting with Newton's second law, derive an expression for Δd for a block of bottom area A. Express your answer in terms of m, ρ, A and physical constants, as appropriate. [4 points]
(c) Explain how your expression from part (b) supports or does not support your claim in part (a). [2 points]