Question

left piston (input) right piston (output) force 3,960 pounds area 7.8 sq. in. 50.6 sq.in. pressure what was the input force?

Explanation:

Step1: Recall Pressure Formula

Pressure \( P \) is force \( F \) over area \( A \), so \( P = \frac{F}{A} \). In a hydraulic system, pressure is equal on both pistons, so \( P_{left} = P_{right} \).

Step2: Calculate Right Piston Pressure

For the right piston, \( F_{right} = 3960 \) lb, \( A_{right} = 50.6 \) sq.in.
\( P_{right} = \frac{3960}{50.6} \approx 78.26 \) psi (pounds per square inch).

Step3: Relate to Left Piston

Since \( P_{left} = P_{right} \), and \( P_{left} = \frac{F_{left}}{A_{left}} \), solve for \( F_{left} \):
\( F_{left} = P_{left} \times A_{left} = \frac{3960}{50.6} \times 7.8 \).

Step4: Compute Input Force

Calculate \( \frac{3960 \times 7.8}{50.6} \approx \frac{30888}{50.6} \approx 610.43 \) pounds.

Answer:

Approximately 610.43 pounds (or more precisely, following the calculation: \( \frac{3960 \times 7.8}{50.6} \approx 610 \) pounds when rounded appropriately).