A water polo ball (which looks like a waterproof yellow volleyball ) is a hollow

Question

A water polo ball (which looks like a waterproof yellow volleyball ) is a hollow sphere of outer radius 12.5 cm and mass 750.grams. The ball starts by floating on the surface of a swimming pool. (Assume that the density of the pool's water is 1.000 g/cm3.) While floating, what fraction of the ball's volume is underwater? show your work completely. Express your final answer either as a decimal value (to 3 sig.figs.). Suppose that a polo player starts pushing downwards on the floating ball, gradually increasing his force. What is the magnitude of the athlete's downward force when the ball has exactly 25% of its volume submerged below the surface? Show your work completely.

Explanation / Answer

a) to float

F bouyancy - m g = 0

f bouyancy = dwater Vsubmerged g

so 1000*V submerged - .75 =0
V submerge = .75/1000
percentage = (.75/1000)/(4/3*pi*12.5E-2^3)=0.0917 = 9.17 %

b)

so now F bouyancy - mg - F = 0

d V g - m g - F = 0

1000*(.25*4/3*pi*12.5E-2^3)*9.81 - .75*9.81 - F = 0

F=12.7 N

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