AP Physics 2 Exam Question

A rectangular container has a length of 0.5 m, a width of 0.3 m, and a height of 0.4 m. The container is filled with water to a height of 0.2 m. Calculate:

a) The pressure at the bottom of the container. b) The force exerted by the water on the bottom of the container. c) The total force exerted by the water on the container walls.

Answer with Step-by-Step Explanation

a) To calculate the pressure at the bottom of the container, we can use the equation:

Where:

• $P$ is the pressure
• $\rho$ is the density of water ($1000 \, \text{kg/m}^3$)
• $g$ is the acceleration due to gravity ($9.8 \, \text{m/s}^2$)
• $h$ is the height of the water column ($0.2 \, \text{m}$)

Substituting the values into the equation, we have:

Therefore, the pressure at the bottom of the container is $1960 \, \text{N/m}^2$.

b) The force exerted by the water on the bottom of the container can be calculated using the formula:

Where:

• $F$ is the force exerted by the water
• $P$ is the pressure at the bottom of the container ($1960 \, \text{N/m}^2$)
• $A$ is the area of the bottom of the container ($0.5 \, \text{m} \times 0.3 \, \text{m}$)

Substituting the values into the equation, we have:

Therefore, the force exerted by the water on the bottom of the container is $294 \, \text{N}$.

c) The total force exerted by the water on the container walls can be calculated by subtracting the force exerted on the bottom from the weight of the water:

The volume of water is:

Substituting the values:

Since the force exerted on the bottom is $294 \, \text{N}$, the total force exerted by the water on the container walls is 0 N.