Question

The drawing shows a hydraulic chamber with a spring (spring constant = 1600 N/m) attached to the input piston and a rock of mass 40.0 kg resting on the output plunger. The piston and plunger are nearly at the same height, and each has a negligible mass. By how much is the spring compressed from its unstrained position?

Answer 1

Answer:

$\Delta x=245\ mm$

Explanation:

Given:

• spring constant of the spring attached to the input piston, $k=1600\ N.m^{-1}$

• mass subjected to the output plunger, $m=40\ kg$

Now, the force due to the mass:

$F=m.g$

$F=40\times 9.8$

$F=392\ N$

Compression in Spring:

$\Delta x=\frac{F}{k}$

$\Delta x=\frac{392}{1600}$

$\Delta x=0.245\ m$

or

$\Delta x=245\ mm$