Question

A 57.0 kg cheerleader uses an oil-filled hydraulic lift to hold four 120 kg football players at a height of 1.10 m. If her piston is 19.0 cm in diameter, what is the diameter of the football players' piston?

Answer 1

Answer:

The diameter of the piston of the players equals 55.136 cm.

Explanation:

from the principle of transmission of pressure in a hydraulic lift  we have

$\frac{F_{1}}{A_{1}}=\frac{F_{2}}{A_{1}}$

Since the force in the question is the weight of the individuals thus upon putting the values in the above equation we get

$\frac{57.0\times 9.81}{\frac{\pi \times (19.0)^{2}}{4}}=\frac{4\times 120\times 9.81}{\frac{\pi \times D_{2}^{2}}{4}}$

Solving for $D_{2}$ we get

$D_{2}^{2}=\frac{4\times 120}{57}\times 19^{2}\\\\\therefore D_{2}=\sqrt{\frac{4\times 120}{57}}\times 19\\\\D_{2}=55.136cm$