#1 Bowling balls can be made from a variety of substances and are required to ha

Question

#1 Bowling balls can be made from a variety of substances and are required to have a circumference of roughly 27.4 inches. The construction of the ball typically consists of a high density core surrounded by a lower density shell. Suppose a bowling ball floats in water with half of its volume submerged. If the specific gravity of the shell is 0.350 and the specific gravity of the core is 0.560, calculate the thickness of the shell.

*I thought it would be 1.44 or 0.44 but it's wrong*

#2 A stainless steel tank contains 2% fat milk (SG = 1.030). A pressure gauge at the bottom of the tank monitors the gauge pressure of the vessel, and from that reading, the height of milk within the tank can be determined If the tank was actually pressurized such that the top surface of the milk was at a pressure of 124.0 kPa, what was the actual height of milk in the tank?

*it's not 2.25 m*

Explanation / Answer

radius of core is r1 and outer radius of ball is r2.

then 2pi*r2 = 27.4

r2 = 4.36 inch = 4.36 x0.0254 m = 0.111 m

Weight of ball = (volume1 x density1 + volume2 x denity2 )g

W = [(4pi*r1^3 x (0.560x1000)/3) + (4pi (r2^3 - r1^3) x(0.350*1000)/3)g

W = [(4pi*r1^3 *70) + (4pi*r2^3*117)]g

Buyoncy force Fb = volume of water displaced x density of water x g

Fb = (2pi*r2^3 / 3) x 1000 x g

W = Fb

[(4pi*r1^3 *70) + (4pi*r2^3*117)]g = (2pi*r2^3 / 3) x 1000 x g

140r1^3 + 0.318 = 0.456

r1 = 0.0995 m = 3.92 inch

thickness = r2 - r1 = 4.36 - 3.92 = 0.443 inch Or 0.011 m

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