A hydraulic press has one piston of diameter 2.0cm and the other pisto

1.	A hydraulic press has one piston of diameter 2.0cm and the other piston of diameter 8.0cm what force must be applied to the smaller piston to obtain a force of 1600 N at the larger piston.
Answer» We know that P₁ = \(\frac{F_1}{A_1}\) then P₂ = P₁ _{\(\frac{F_2}{A_2}=\frac{F_1}{A_1}\)} _{\(F_2 = A_2\times\frac{F_1}{A_1}\)} _{\(F_2=\pi r_2^2 \times \frac{F_1}{\pi r_1^2}\)} _{\(F_2=F_1(\frac{r_2}{r_1})^2\)} \(F_2 = 1600\times(\frac{0.04}{0.01})^2\) \(F_2 = 1600\times16\) F₂ = 25600 N

A hydraulic press has one piston of diameter 2.0cm and the other piston of diameter 8.0cm what force must be applied to the smaller piston to obtain a force of 1600 N at the larger piston.

Answer»

We know that

P₁ = \(\frac{F_1}{A_1}\)

then P₂ = P₁

_{\(\frac{F_2}{A_2}=\frac{F_1}{A_1}\)}

_{\(F_2 = A_2\times\frac{F_1}{A_1}\)}

_{\(F_2=\pi r_2^2 \times \frac{F_1}{\pi r_1^2}\)}

_{\(F_2=F_1(\frac{r_2}{r_1})^2\)}

\(F_2 = 1600\times(\frac{0.04}{0.01})^2\)

\(F_2 = 1600\times16\)

F₂ = 25600 N

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A hydraulic press has one piston of diameter 2.0cm and the other piston of diameter 8.0cm what force must be applied to the smaller piston to obtain a force of 1600 N at the larger piston.

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