Two hydraulic piston/cylinders are connected with a line. The master cylinder has an area of 5 cm2, creating a pressure of 1000 kPa. The slave cylinder has an area of 3 cm2. If 25 J is the work input to the master cylinder, what is the force and displacement of each piston and the work output of the slave cylinder piston?

Work done by slave cylinder = 25J

Displacement of the piston of master cylinder = 0.05m

Displacement of the piston of slave cylinder = 0.08m

Force of master cylinder = 500 N

Force of slave cylinder = 300 N

Explanation:

Given-

Area of master cylinder, A1 = 5cm²

Area of slave cylinder, A2 = 3cm²

Pressure, P1 = 1000 KPa

Work, W1 = 25J

Force , displacement and work output = ?

If one cylinder is connected to another, then the pressure created in both the cylinders are same.

P2 = P1 = 1000 kPa

Therefore, work done by both the cylinders are also same

W1 = W2 = 25J

Displacement of first cylinder, s1 :

W1 = P1 X A1 X s1

s1 = W1/ P1 X A1

s1 = 25 / 1000000 X 0.0005

s1 = 0.05m

Force on first cylinder :

F1 = W1 / s1

F1 = 25 / 0.05

F1 = 500N

Force on second cylinder :

F2 = P2 X A2

F2 = 1000000 X 0.0003

F2 = 300N

Displacement on second cylinder :

F1 X s1 = F2 X s2               (work done on both the sides are same)

s2 = F1 X A1 / F2

s2 = 500 X 0.05 / 300

s2 = 0.08m