Page 163 - Schaum's Outline of Theory and Problems of Applied Physics

148 SIMPLE MACHINES [CHAP. 12

that passes around pulley B,soIMA 2 = 2. Pulley C merely changes the direction of the rope, and strand 5 does not
help to support the load. Hence

IMA = (IMA 1 )(IMA 2 ) = (2)(2) = 4

SOLVED PROBLEM 12.4
A woman uses a force of 80 N to raise a load of 280 N by 1.5 m with a pulley system. If she pulls a total
of6mof rope through the system, what is the efficiency of the system?
The IMA and AMA of the system are, respectively,
s in 6m
IMA = = = 4
s out 1.5m
F out 280 N
AMA = = = 3.5
F in 80 N
Hence the efficiency of the system is
AMA 3.5
Eff = = = 0.875 = 87.5%
IMA 4
SOLVED PROBLEM 12.5
How much force is needed to raise a load of 500 N with the pulley system of Prob. 12.4?

We must use the actual mechanical advantage to find F in . Hence
F out 500 N
F in = = = 143 N
AMA 3.5

SOLVED PROBLEM 12.6

A differential pulley (often called a chain hoist because a chain running over notched pulleys is used to
prevent slipping) is shown in Fig. 12-4. When the free loop of the chain is pulled as shown, strand 1 of
the chain supporting the movable pulley is shortened while strand 2 is lengthened. Because strand 1 is
shortened by more than strand 2 is lengthened, the load is raised. Pulling down on the other strand of the
free loop lowers the load. (a) Find the IMA of the differential pulley. (b) If the upper pulleys of such a

Fig. 12-4