Question

A force exerted on a hydraulic cylinder with a diameter of 16.0 cm produces a pressure increase of 275 kPa. Calculate the force exerted on the cylinder.

Answer 1

5527.5 N

Step-by-step explanation:

The pressure can be calculated as

`P=(F)/(A)`

Where F is the force exerted and A is the area. Solving for F, we get:

`F=PA`

Then, we can calculate the area as the area of the base of the cylinder. This area is equal to:

`A=\pi r^2`

Where r is the radius. In this case, the diameter is 16.0 cm, so the radius is

r = diameter/2

r = 16.0 cm / 2

r = 8.0 cm

r = 0.08 m

Then, replacing the radius, we get:

`\begin{gathered} A=(3.14)(0.08\text{ m\rparen}^2 \\ A=0.0201\text{ m}^2 \end{gathered}`

Therefore, replacing P = 275 kPa = 275000 Pa and A = 0.0201 m², we get that the force exerted is equal to

`\begin{gathered} F=(275000Pa)(0.0201\text{ m}^2) \\ F=5527.5\text{ N} \end{gathered}`

So, the answer is 5527.5 N