Question

Calculate force required to move a small piston with an area of 1.5m2 given the force of a large piston is 30N with an area of 6m2

Answer 1

To calculate the force required to move the small piston, we can utilize Pascal's principle, which states that a change in pressure applied to an enclosed fluid is transmitted undiminished to all portions of the fluid and the walls of its container.

First, we need to find the pressure exerted by the large piston. The pressure \( P \) can be calculated using the formula:

\[
P = \frac{F}{A}
\]

where:
- \( F \) is the force,
- \( A \) is the area.

For the large piston:
- Force \( F = 30 \, \text{N} \)
- Area \( A = 6 \, \text{m}^2 \)

Calculating the pressure exerted by the large piston:

\[
P = \frac{30 \, \text{N}}{6 \, \text{m}^2} = 5 \, \text{Pa} \, (\text{Pascals})
\]

Now, we can find the force required to move the small piston by using the same pressure (as pressure is equal throughout the liquid). The area of the small piston is given as 1.5 m². We can rearrange the pressure formula to find the force on the small piston:

\[
F = P \times A
\]

Now substituting the values for the small piston:

\[
F = 5 \, \text{Pa} \times 1.5 \, \text{m}^2 = 7.5 \, \text{N}
\]

Therefore, the force required to move the small piston is **7.5 N**.