Page 167 - Schaum's Outline of Theory and Problems of Applied Physics

152 SIMPLE MACHINES [CHAP. 12

The IMA of the vise is
2π L (2π)(200 mm)
IMA = = = 251
p 5mm
and its AMA is

AMA = (Eff)(IMA) = (0.4)(251) = 100.4
The output force is therefore
F out = (AMA)(F in ) = (100.4)(40 N) = 4016 N

SOLVED PROBLEM 12.11
A screw jack has a pitch of 5 mm and a handle 60 cm long. If a force of 50 N is needed to raise a load of
700 kg, find the efficiency of the jack.
The IMA and AMA of the jack are, respectively,
2π L (2π)(60 cm)
IMA = = = 754
p 0.5cm
2
mg (700 kg)(9.8 m/s )
F out
AMA = = = = 137
F in F in 50 N
The efficiency of the jack is
AMA 137
Eff = = = 0.18 = 18%
IMA 754

TORQUETRANSMISSION
Belt and gear drives make possible the transmission of torques from one shaft to another (Fig. 12-10). The actual
mechanical advantage of any such system is
τ out output torque
AMA = =
τ in input torque
The ideal mechanical advantage of a pulley system equals the ratio between the radius of the driven pulley r out
and that of the driving pulley r in , which is the same as the ratio of their diameters:

r out d out
IMA = =
r in d in

t out

r
t in in
r out

Fig. 12-10

In the case of a gear drive, since the number of teeth on a gear is proportional to its radius,
N out number of teeth on driven gear
IMA = =
N in number of teeth on driving gear