A hydraulic jack has pistons 2.0 cm and 25 cm across…

Contributed by StemPy Lab

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

A hydraulic jack has pistons $2.0\ \text{cm}$ and $25\ \text{cm}$ across. What force on the small piston holds up a $2000\ \text{kg}$ van? How far must the small piston move in all to raise the van by $10\ \text{cm}$ ? ( $g = 9.8\ \text{m/s}^2$ .)

Need a reminder? The key ideaShow

Pressure is force per unit area, $p = \dfrac{F}{A}$ , in pascal. Below the surface of a liquid, $p = p_0 + \rho gh$ ; the gauge pressure is $\rho gh$ . Pascal's law: a change of pressure in an enclosed fluid reaches every part of it, so a hydraulic machine gives $F_2 = F_1\dfrac{A_2}{A_1}$ .

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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