What is the minimum force required to lift the lid off of the container?

Question

A cylindrical container is sealed by a circular lid. The pressure in the room surrounding the container is 1.0 X 105 N/m². The pressure inside the container is 0.3 x 105 N/m². The lid has radius 0.10 m and weight 100 N. What is the minimum force required to lift the lid off of the container?

Answer 1

Does this help:

Area of Lid = A_L = πr² = π(0.1)²

"F" would be the force you apply to the lid to open the container. Note that if F is greater than the force necessary to balance the forces, then you will be able to open the lid.

W = 100N

The outside pressure P_O creates a force pushing down = P_O•A_L

The inside pressure P_I creates a force pushing up = P_I•A_L

So just set up an equation to balance all the forces:

F + P_I•A_L - W - P_O•A_L = 0

F = W + P_O•A_L - P_I•A_L

Once you solve for F, then the force to open the lid is greater than that value.