The drawing shows a hydraulic chamber with a spring (spring constant = 1380 N/m)

Question

The drawing shows a hydraulic chamber with a spring (spring constant = 1380 N/m) attached to the input piston and a rock of mass 34.0 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?

The drawing shows a hydraulic chamber with a spring (spring constant = 1380 N/m) attached to the input piston and a rock of mass 34.0 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?

Explanation / Answer

Since the piston and the plunger are at the same height
F2 =F1(A2/A1)

the force exerted on the spring

F=Kx

Kx =F1(A2/A1)

Kx =mg(A2/A1)

x =(mg/k)(A2/A1) =(34*9.8/1380)(15/65)

x=0.056m or 5.6cm

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