Question

In a hydraulic press, a force of 200 N is applied to master piston of area of 25cm-2. If the press is designed to produce a force of 5000N, determine

a:the area of the slave piston
b:the radius of the slave piston

Answer 1

`625\ \text{cm}^2`

`14.1\ \text{cm}`

Step-by-step explanation:

`F_1` = Force applied to master piston = 200 N

`F_2` = Force applied to slave piston = 5000 N

`A_1` = Area of master piston =
`25\ \text{cm}^2`

`A_2` = Area of slave piston

r = Radius of slave piston

From Pascal's law we have

`(F_1)/(A_1)=(F_2)/(A_2)\\\Rightarrow A_2=(F_2)/(F_1)A_1\\\Rightarrow A_2=(5000)/(200)* 25\\\Rightarrow A_2=625\ \text{cm}^2`

The area of the slave piston is
`625\ \text{cm}^2`

Area of the slave piston is given by

`A_2=\pi r^2\\\Rightarrow r=\sqrt{(A_2)/(\pi)}\\\Rightarrow r=\sqrt{(625)/(\pi)}\\\Rightarrow r=14.1\ \text{cm}`

The radius of the slave piston is
`14.1\ \text{cm}`.