The hydraulic system shown in figure 1 is used to lift heavy equipment. A person

Question

The hydraulic system shown in figure 1 is used to lift heavy equipment. A person exerts a force on the

narrow piston and a heavy instrument is lifted by the large piston. The thin side is a cylinder with a

diameter of 50 cm. The large side is a cylinder with a diameter of 2 meters. Suppose a person pushes on

the master cylinder (thin side) with a force of 500 N. (a) What is the maximum weight that could be lifted

by the slave cylinder (large side)? (b) If the person exerts this force and pushes the master cylinder down

1 m, how high will the slave cylinder lift the equipment? (c) How much work does the person do on the

master cylinder? (d) How much work does the slave cylinder do on the equipment?

The hydraulic system shown in figure 1 is used to lift heavy equipment. A person exerts a force on the narrow piston and a heavy instrument is lifted by the large piston. The thin side is a cylinder with a diameter of 50 cm. The large side is a cylinder with a diameter of 2 meters. Suppose a person pushes on the master cylinder (thin side) with a force of 500 N. (a) What is the maximum weight that could be lifted by the slave cylinder (large side)? (b) If the person exerts this force and pushes the master cylinder down 1 m, how high will the slave cylinder lift the equipment? (c) How much work does the person do on the master cylinder? (d) How much work does the slave cylinder do on the equipment?

Explanation / Answer

using pascal law ,

F1 /A1 = F2 /A2

or,

a) F2= F1*A2/A1

= 500* 3.14 * 2*2*4 / 3.14*.05*.05*4

= 800000 N

b) equating the volume ,

3.14 * .05 *.05 * 1 = 3.14* 2*2* h

= .000625 m

c) work done on master cylinder = force * displacement = 500 *1 = 500 N - m

work done on slave cylinder = 800000*.000625 = 500 N-m

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