Engineering Mechanics

(^204) „„„„„ A Textbook of Engineering Mechanics
EXERCISE 11.2

1. In a differential pulley block, diameters of the concentric pulleys are 300 mm and 250 mm
   respectively. It was found that an effort of 20 N just lifts a load of 200 N. Calculate (i)
   Efficiency of the machine; (ii) Effort lost in friction and (iii) Frictional load.
   [Ans. 83.3%; 3.33 N; 40 N]


2. In a Weston’s differential pulley block, the difference in the number of teeth of the two
   pulleys is 3. If the efficiency of the machine is 60% and an effort of 100 N just lifts a load
   of 1 kN, find the number of teeth of the two pulleys. [Ans. 22 and 25]
   Hint :
   Given: T 1 = T 2 + 3

M.A. =

1000

100

W

p

=

12 2

12 2 2

22(3)26

V.R.

–(3)– 3

TT T

TT T T

++

== =

+

∴ Efficiency,

(^22)
M.A. 10 30
0.6
V.R.^2626
3
T T
== =

• 
  
  
  
  • ∴ 2 T 2 + 6 =
    30
    0.6
    or T 2 = 22 and T 1 = 22 + 3 = 25
  
  
  
  

3. A geared pulley block has the following dimensions :
   No. of cogs on the effort wheel = 100
   No. of cogs on the load wheel = 20
   No. of teeth on the pinion = 10
   No. of teeth on the spur wheel = 60
   If the machine has an efficiency of 60%, find the effort required to lift a load of 900 N.
   [Ans. 50 N]


4. In a worm and worm wheel, the number of teeth in the worm wheel is 25. The effort
   handle is 300 mm long and the load drum is 150 mm diameter. Find the efficiency of the
   machine, if an effort of 30 N can lift a load of 345 N and the worm is double threaded.
   [Ans. 23%]


5. A worm geared pulley block has its effort wheel of 250 mm diameter. The worm is double
   threaded and the worm wheel has 50 teeth. The load drum is of 100 mm diameter. Determine
   the effort required to lift a load of 5 kN, if efficiency of the machine is 40%.
   [Ans. 100 N]


6. A single purchase crab has 300 mm long handle, 120 mm diameter drum and diameter of
   the lifting rope is 10 mm. Number of teeth on the pinion are 25 and that on the wheel 130.
   Calculate the velocity ratio of the crab. If an effort of 20 N lifts a load of 300 N, what is the
   mechanical advantage and efficiency of the crab? [Ans. 24; 15; 62.5%]
   Hint : Effective diameter of the effort wheel
   = 120 + 10 = 130 mm
   ∴ Effective radius, r = 65 mm