Question

An airtight box has a removable lid of area 1.24e-2 m2 and negligible weight. The box is taken up a mountain where the air pressure outside the box is 8.57e4 Pa. The inside of the box is completely evacuated. What is the magnitude of the force required to pull the lid off the box?

Answer 1

The force required to pull the lid off the airtight box at mountain pressure is approximately 1061.88 Newtons, calculated using the formula F = P × A, where P is the outside pressure and A is the lid area.

Step-by-step explanation:

The question asks for the magnitude of the force required to remove the lid from an airtight box on a mountain where external air pressure is 8.57×104 Pa, given that the inside of the box is fully evacuated and has a lid of area 1.24×10-2 m2. The formula for force (F) due to pressure (P) on a surface area (A) is F = P × A, where P is the pressure and A is the area over which the pressure acts.

Since the lid weight is negligible and the box is evacuated, the external pressure is the only pressure acting on the lid. Thus, the force required to lift the lid can be directly calculated by multiplying the external pressure by the area of the lid.

Applying the formula:

F = 8.57×104 Pa × 1.24×10-2 m2 = 1061.88 N

Therefore, a force of approximately 1061.88 Newtons is needed to pull the lid off the box.