Expert Answer to "Piston 1 in Figure has a diameter of..."

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Reggie

Answered question

2021-01-08

Piston 1 in Figure has a diameter of 0.25 in. Piston 2 haves a diameter of 1.2 in. In the absence of friction, determine the force, necessary to support the 500 lb weight.

Answer & Explanation

Tasneem Almond

Skilled2021-01-09Added 91 answers

First,use Pascal’s principle, $\frac{F_{1}}{A_{1}} = \frac{F_{2}}{A_{2}}$ to find the force piston 1 will exert on the handle when a 500-lb force pushes downward on piston2.
$F_{1} = (\frac{A_{1}}{A_{2}}) F_{2} = (\frac{\frac{π d_{1}^{2}}{4}}{\frac{π d_{2}^{2}}{4}}) F_{2} = (\frac{d_{1}^{2}}{d_{2}^{2}}) F_{2}$
Now, consider an axis perpendicular to the page, passing through the left end of the jack handle
$(+ 21.7 l b) (2.0 \in) - F (12 \in) = 0$ , or $F = 3.62 l b$
Free Body Diagram:

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