In a lecture demonstration, a professor pulls apart two hemispherical, steel she

Question

In a lecture demonstration, a professor pulls apart two hemispherical, steel shells (diameter D) with ease using their attached handles. She then places them together, pumps out the air to an absolute pressure of p, and hands them to a bodybuilder in the back row to pull apart.

Part A

If atmospheric pressure is p0, how much force must the bodybuilder exert on each shell?

Express your answer in terms of the given quantities.

Part B

Evaluate your answer for the case p=0.025atm, D=10.0cm.

Express your answer using two significant figures. in Newtons

Explanation / Answer

The force required to apply is equal to the force needed to overcome the pressure difference.

The force due to pressure difference is equal to pressure difference times the surface area. But the force applied by he body builder is only in horizontal direction. Hence, the required force is half of pressure difference times the surface area. Also we are pulling on both sides so there is another factor of half.

F = (1/4)*(P0-P)*4*pi*(r^2) = (p0-p)*pi*(D^2)/4

For p=0.025 atm = 0.025*1.01325 bar, D = 10 cm = 0.1 m

=> F = 775.91 N

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