Making a study guide for my final. Please show all work so that I may easily fol

Question

Making a study guide for my final. Please show all work so that I may easily follow. Thank you!

A sturdy rubber band with a rectangular cross section is cut to form a long piece of rubber with dimensions 60.00
cm by 0.3000 cm by 0.1500 cm. The rubber used has a Young's modulus Y = 5.500 x 10^6 N/m^2 , a bulk modulus B = 1.000 x 10^6 N/m^2, and a density p = 940.0 kg/m3 .

A ball is made from this same rubber. The volume of the ball is 7.979 x 10^-4 m^3, and the radius of the ball is 5.754 x 10^-2 m. It has a mass of .7500 kg.

Q: If the ball is put into a swimming pool, what percentage of its volume will be submerged underwater when it has settled to its equilibrium depth?

Explanation / Answer

At equilibrium sum of all the forces should be zero.
now force due to gravity on the ball = mg = .75 * g
force due to buoyancy = water * g * Vsubmerged = weight of water displaced = Vsubmerged *1000*g

At equilibrium

1000g * Vsubmerged = .75 * g

Vsubmerged = 7.5*10-5 m3

% Vsubmerged = (Vsubmerged / vol. of ball) *100 = 9.399 %

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