# In the figure, a spring of spring constant 2.90 x 104 N/m is between a rigid beam and the output...

## Question:

In the figure, a spring of spring constant 2.90 x 104 N/m is between a rigid beam and the output piston of a hydraulic lever. An empty container with negligible mass sits on the input piston. The input piston has area Ai, and the output piston has area 18.0Ai. Initially the spring is at its rest length. How many kilograms of sand must be (slowly) poured into the container to compress the spring by 7.00 cm?

## Hydraulic Ram

A hydraulic Ram is a device that is used for lifting heavier weights by applying small forces. It works on the principle of Pascal's law, according to which the pressure difference on the same level is zero when the fluid is at rest.

We know that the pressure at both the end would be same, therefore

{eq}\displaystyle P_{1} = P_{2} \\ \frac{mg}{A_{i}} = \frac{Kx}{18A_{i}} {/eq}

Where

• m is mass of the sand which is poured into the container
• K is spring constant
• x is the compression of the spring = 7 cm = 0.07 m

Now putting all the values

{eq}\displaystyle \frac{mg}{A_{i}} = \frac{Kx}{18A_{i}} \\ \dfrac{m*9.81}{A_{i}} = \dfrac{2.9*10^{4}*7*10^{-2}}{18A_{i}} \\ m = 11.496 \ kg {/eq}