Question

left piston (input) right piston (output) volume area 2.7 sq. in. 60 sq.in. distance 41 in what was the input distance?

Explanation:

Step1: Recall Pascal's Principle (Volume Conservation)

In a hydraulic system, the volume of fluid displaced by the input piston equals the volume displaced by the output piston. The formula for volume is \( V = A \times d \), where \( A \) is the area and \( d \) is the distance. So, \( V_{input} = V_{output} \), which means \( A_{left} \times d_{left} = A_{right} \times d_{right} \).

Step2: Solve for \( d_{left} \)

We know \( A_{left} = 2.7 \) sq. in., \( A_{right} = 60 \) sq. in., and \( d_{right} = 41 \) in. Rearranging the formula \( d_{left} = \frac{A_{right} \times d_{right}}{A_{left}} \).

Substitute the values: \( d_{left} = \frac{60 \times 41}{2.7} \).

First, calculate \( 60 \times 41 = 2460 \). Then, divide by 2.7: \( \frac{2460}{2.7} \approx 911.11 \) (rounded to two decimal places).

Answer:

The input distance is approximately \( \frac{2460}{2.7} \approx 911.11 \) inches (or more precisely, \( \frac{8200}{9} \approx 911.11 \) inches).