(^192) „„„„„ A Textbook of Engineering Mechanics
and
1500
M.A.
W
PP

We also know that efficiency,
1500
M.A. 60
0.8
V.R. 25
P
P

or
60
75 N
0.8
P== Ans.
Example 11.7. In a differential pulley block, a load of 1800 N is raised by an effort of 100 N.
The number of teeth on the larger and smaller blocks are 12 and 11 respectively. Find the velocity
ratio, mechanical advantage and efficiency of the machine.
Solution. Given: Load (W) = 1800 N; Effort applied (P) = 180 N; Number of teeth on the
larger block (T 1 ) = 12 and number of keeth on the smaller block (T 2 ) = 11.
Velocity ratio
We know that velocity ratio
1
12
2 212
V.R. 24
–12–11
T
TT
×
== =^ Ans.
Mechanical advantage
We know that mechanical advantage
1800
M.A. 18
100
W
P
== = Ans.
Efficiency of the machine
We also know that efficiency of the machine,
M.A. 18
0.75 75%
V.R. 24
η= = = = Ans.
EXERCISE 11.1

1. In a simple wheel and axle, radii of effort wheel and axle is 240 mm and 40 mm respectively.
   Find the efficiency of the machine, if a load of 600 N can be lifted by an effort of 120 N.
   [Ans. 83.3%]


2. In a simple wheel and axle, the diameter of the wheel is 150 mm and that of the axle is 30
   mm. If efficiency of the machine is 60%, determine the effort required to lift a load of 500 N.
   [Ans. 166-7 N]


3. A differential wheel and axle, having velocity ratio as 12, is used to lift a load of 300 N. If
   the coefficient of friction for the pulley spindle is 0.2, find the effort required to lift the
   load. [Ans. 31.25 N]
   Hint : Efficiency = 1 – 0.2 = 0.8


4. In a differential wheel and axle, having a velocity ratio of 24, a load of 200 N can be lifted
   by and effort of 15N and a load of 250 N can be lifted by an effort of 18 N. Find (a) Effort
   required to lift a load 375 N; (b) Effort wasted in friction and (c) Maximum efficiency of
   the machine. [Ans. 25.5 N; 7.58 N; 69.4%]