Question

a 55.0 kg cheerleader uses an oil-filled hydraulic lift to hold four 130 kg football players at a height of 0.800 m . the diameter of the cheerleader's piston is 19.0 cm . what is the diameter of the football players' piston if the football players are held to a height 0.800 m above the cheerleader?

Answer 1

The diameter of the football player's piston is 0.55 m

Given that the mass of the cheerleader(m) is 55 kg, mass of football player to be hold (M) is 130 kg, height of the players (h) is 1.30 m, radius of the piston corresponding to the diameter (r) is 0.09 m, Diameter of football player's piston (R), P1 is Pressure on the cheerleader's side, P2 is Pressure on the football player's side

Using Pascal's law,

This law states that if there is a change at a point of a body immersed in a fluid then that change will spread thoroughly to each and every point of the body.

The formula of hydraulic system is,

P1= P2

F1/A1 = F2/A2

mg/πr^2 = 4Mg/πR^2

m/r^2=4M/R^2

R^2=4M×r^2/m

By plugging the values, we get.,

R^2=(4×130×0.09^2)/55

R^2=4.21/55=0.076

R=√0.076 = 0.275 m

Hence, diameter of football player's piston is 0.55 m

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