Question

question 5

image of two pistons connected by a tube

	left piston (input)	right piston (output)
area	59 sq.in.	98 sq. in.
distance	3 inches

what is the output distance?

Explanation:

Step1: Recall the principle of hydraulics (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, \( A_{input} \times d_{input} = A_{output} \times d_{output} \).

Step2: Plug in the known values

We know \( A_{input} = 59 \) sq.in, \( d_{input} = 3 \) inches, and \( A_{output} = 98 \) sq.in. Let \( d_{output} \) be the output distance. Substituting into the formula: \( 59 \times 3 = 98 \times d_{output} \).

Step3: Solve for \( d_{output} \)

First, calculate the left - hand side: \( 59\times3 = 177 \). Then, we have the equation \( 177 = 98\times d_{output} \). To find \( d_{output} \), we divide both sides by 98: \( d_{output}=\frac{177}{98}\approx1.81 \) inches (or keep it as a fraction \( \frac{177}{98} \) inches).

Answer:

The output distance is approximately \( \boldsymbol{1.81} \) inches (or \( \boldsymbol{\frac{177}{98}} \) inches).