The hydraulic system shown in figure 1 is used to lift heavy equipment. A person
ID: 2243154 • Letter: T
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
a) Maximum weight = 500* A2/A1 = 500 * (2/0.5)^2 =500*16 =8000 N
b) Since volume remains constant
Height raised by slave = A1* h1 /A2 =(0.5/2)^2 *1 = 1/16 = 0.0625 m
c) work done by person on master cylinder = F1* h1 = 500 J
D) work done by slave cylinder on equipment = 500 J due to conservation of energy
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