c) A spring is mounted vertically at the bottom of an empty swimming pool. A blo

Question

c) A spring is mounted vertically at the bottom of an empty swimming pool. A block of mass M = 596 kg is attached to the spring, and it compresses the spring from its equilibrium position by distance xo. Now the swimming pool is filled with fresh water, and the block is submerged. You find the the spring is now extended distance x = 1.61xo from its equilibrium position. Find the density of the block.
3kg/m3

d) Suppose now that the block in question c is made of a wood of density ? = 517 with a large cavity in the middle. What percentage of the volume of the block is empty? You can assume that the air inside the cavity had negligible mass.
NOTE: You cannot solve this problem until you solve part c!
4%

Explanation / Answer

c) without water, -M g + k x0=0 with water F bouyancy - M g - k x = 0 1000*V*g - M g - 1.61 M g = 0 1000*V = 2.61 M M/V = 1000/2.61=383.14 d) V = 596/383.14=1.56 m^3 d = (m air + m wood)/ (V air + v wood) 383.14 = ( 0 + 517 * V wood)/1.56 Vwood=1.1561 Vwood/V = 1.1561/1.56=.741= 74.1 %

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