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. (a) If atmospheric pressure is p0, how much force must the bodybuilder exert on each shell?
p = F/A
Area of hemisphere A = 2πr2 = πD2/2
The Attempt at a Solution
So I just took the force pushing on a hemisphere from pressure p0 negative the force pushing out on the the hemisphere from pressure p to get the force needed to pull away. F = (p0 - p)πD2/2.
This answer is not correct apparently, the correct answer is F = (p0 - p)πD2/4. What I'm thinking is that the pulling force required is the x-component of force F but I can't figure how to get that. Also, what direction does F have? If I were to use p = F/A to calculate the force on a sphere what direction would F have? Or is F a scalar? Then how should I get the x-component of scalar?