# Diameter of football player's Piston

## Homework Statement

A 54.0kg cheerleader uses an oil-filled hydraulic lift to hold four 120kg football players at a height of 1.30m . If her piston is 19.0cm in diameter, what is the diameter of the football players' piston?

## Homework Equations

I think the only equation needed is (F1/A1)=(F2/A2). I didn't think that density or the height being raised was relevant in this problem

## The Attempt at a Solution

So first I rearranged the formula so that ((F2A1)/F1)= A2.

I know that the force is the weight of the cheerleaders(54 kg) and the four football players( 480). The value g cancels out, so I'm left with ....

(480pi(r1)^2)/54= pi(r2)^2

so by subbing in for r1 ( .095m) I get...

.252=pi(r2)^2

I then rearrange the formula to solve for r2

r2=sqrt(.252/pi)=r1=.283

then to get the diameter I multiply by two to get .566m or 56.6 cm

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Simon Bridge
Homework Helper
Welcome to PF;
It depends on how she is holding who up with the lift ... and what the relationship is between her piston and the player's piston. You need to be explicit about the setup.

You seem to be saying that the pressure on the player's piston is the same as the pressure on the cheerleaders. Why?

Notice that the pi's cancel out in the first equation you have them in?
The ratio of the radii is also the ratio of the diameters too.