Question

A container is filled with gas at a pressure of $4.0 \times 10^{5} \mathrm{Pa}\( The container is a cube, \)0.10 \mathrm{m}$ on a side, with one side facing south. What is the magnitude and direction of the force on the south side of the container due to the gas inside?

Short answer

Answer: The magnitude of the force is 4000 N, and the direction is towards the north.

Step-by-step solution

Calculate the area of the south side of the container

The container is a cube, with each side measuring \(0.10 \ \text{m}\). Therefore, the area of the south side of the container can be calculated by squaring its length: \(A = (0.10 \ \text{m})^2 = 0.01 \ \text{m}^2\)

Use the pressure and area to calculate the force

Recall that the formula for pressure is \(P = \frac{F}{A}\). Rearrange this formula to solve for force: \(F = P \times A\). Using the given pressure of \(4.0 \times 10^{5} \ \text{Pa}\) and the calculated area of the south side, the force on the south side is: \(F = (4.0 \times 10^{5} \ \text{Pa})(0.01 \ \text{m}^2) = 4000 \ \text{N}\)

Determine the direction of the force

The force will be exerted by the gas inside the container, as it pushes against the south side. As a result, the force will act in the opposite direction (north) since the gas is exerting pressure on the inside of the south side.

Present final answer

The magnitude of the force on the south side of the container due to the gas inside is 4000 N, and the direction of the force is towards the north.