Diameter of Football Players' Piston: Calculating

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To calculate the diameter of the football players' piston, the relationship between force and area in a hydraulic system is applied using the equation F1/A1 = F2/A2. The cheerleader's weight (55 kg) and the combined weight of the football players (440 kg) are factored into the calculations. The area of the cheerleader's piston is determined using the formula A = πr², with a diameter of 16 cm. The volume displaced by both pistons must be equal, leading to the equation area_cheerleader * height_cheer = area_footballers * height_footballers. The challenge lies in incorporating the height into the equation to solve for the unknown area of the football players' piston.
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Homework Statement



A 55 kg cheerleader uses an oil-filled hydraulic lift to hold four 110 kg football players at a height of 1.0m. If her piston is 16 cm in diameter, what is the diameter of the football players' piston?

Homework Equations



F1/A1=F2/A2
A=pi*r^2
F=mg

The Attempt at a Solution



(55)(9.8)/pi(0.08)^2=(440)(9.8)/pi(r^2)

After I did this, I realized that I need to work the height into the equation, but I'm not sure where it would fit in.
 
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The simplest way is to think of the volume displaced - since the hydraulic fluid is in incompressible that must be the same for the cheerleader and the footballers.
In addition the force exerted by the cheerleader and footballers is known.

area_cheerleader * height_cheer = area_footballers * height_footballers
55g / area_chearleader = 110g/area_footballer

The unknowns are area_footballer and height_cheerleader.
 

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