Page 169 - Schaum's Outline of Theory and Problems of Applied Physics

154 SIMPLE MACHINES [CHAP. 12

SOLVED PROBLEM 12.13
An engine develops 6 kW at 4000 rev/min. What gear ratio is needed if an output torque of 60 N·mis
required?
Since
rad/s

ω = (4000 rev/min) 0.105 = 420 rad/s
rev/min
the engine itself develops a torque of
P 6000 W
τ = = = 14.3N·m
ω 420 rad/s
Hence the required gear ratio is
N out τ out 60 N·m
= = = 4.2
N in τ in 14.3N·m

Multiple-Choice Questions

12.1. A machine can increase which one or more of the following?
(a) work (c) force
(b) speed (d) torque
12.2. A machine has an IMA of 6.0 and an AMA of 5.0. The work input needed by the machine to raise a 40-kg load by
3.0mis
(a) 0.98 kJ (c) 1.4 kJ
(b) 1.2 kJ (d) 5.9 kJ

12.3. A person uses a force of 300 N to pry up one end of a 120-kg box with a lever 2.4 m long. The distance from the end
of the box to the fulcrum is
(a) 40 cm (c) 81 cm
(b) 49 cm (d) 171 cm
12.4. The smallest number of pulleys needed for an IMA of 5 is

(a) 3 (c) 5
(b) 4 (d) 6

12.5. A force of 50 N is needed to raise a 240-N load with a pulley system. The load goes up 1 m for every5mof rope
pulled through the pulleys. The efficiency of the system is
(a) 48% (c) 96%
(b) 50% (d) 104%
12.6. Two sets of spur gears, each set 96 percent efficient, drive a worm gear that is 80 percent efficient. The overall
efficiency of the system is
(a) 74% (c) 80%
(b) 77% (d) 96%

12.7. A screw jack has a pitch of 4.0 mm and a handle 50 cm long. Its efficiency is 20 percent. The force that must be
applied to the handle in order to lift a load of 400 kg is
(a)1 N (c)5 N
(b) 2.5 N (d)25 N