Motion, Forces and Energy - Pressure

A rectangular block of wood has a weight of $600\ N$ and dimensions $2\ m \times 0.5\ m \times 0.1\ m$. Calculate the maximum pressure it can exert on the ground.

$P_{max} = \frac{F}{A_{min}}$ $A_{min} = 0.5\ m \times 0.1\ m = 0.05\ m^2$ $P = \frac{600\ N}{0.05\ m^2} = 12,000\ Pa$

To exert maximum pressure, the block must be placed on its smallest surface area. We identify the two smallest dimensions to calculate the minimum area.

Calculate the pressure exerted by water at the bottom of a swimming pool that is $3\ m$ deep. (Density of water $\rho = 1000\ kg/m^3$, $g = 9.8\ m/s^2$)

$P = \rho g h$ $P = 1000\ kg/m^3 \times 9.8\ m/s^2 \times 3\ m$ $P = 29,400\ Pa$

The pressure in a fluid depends on the density, gravity, and the height of the fluid column. This value represents the pressure due to the water alone (gauge pressure).

A hydraulic jack has an input piston with an area of $0.02\ m^2$ and an output piston with an area of $0.5\ m^2$. If a force of $150\ N$ is applied to the input piston, what is the weight of the load that can be lifted?

$P_1 = P_2 \Rightarrow \frac{F_1}{A_1} = \frac{F_2}{A_2}$ $\frac{150\ N}{0.02\ m^2} = \frac{F_2}{0.5\ m^2}$ $F_2 = \frac{150 \times 0.5}{0.02} = 3750\ N$

According to Pascal's Principle, the pressure is transmitted equally throughout the hydraulic fluid. Because the output area is larger, the output force is magnified.