(^208) „„„„„ A Textbook of Engineering Mechanics
A little consideration will show, that for x displacement of the weight, the effort will move
through a distance to nx, where n is the number of pulleys in both the blocks. Thus velocity ratio
V.R.
nx
n
x

Now M.A.
W
P
= ...as usual
and efficeincy,
M.A.
V.R.
η= ...as usual
Example 11.18. A weight of 1 kN is lifted by an effort of 125 N by second system of pulleys,
having 5 pulleys in each block.
Calculate the amount of effort wasted in friction and the frictional load.
Solution. Given: Weight lifted (W) = 1 kN = 1000 N ; Effort (P) = 125 N and no. of
pulleys (n) = 2 × 5 = 10.
Amount of effort wasted in friction
We know that velocity ratio
V.R. = n = 10
and amount of effort wasted in friction,
(effort )
1000

• 125 – 25 N
  V.R. 10

W

FP== =^ Ans.

Amount of frictional load

We also know that amount of frictional load,

F(load) = (P × V.R.) – W = (125 × 10) – 1000 = 240 N Ans.

11.14. THIRD SYSTEM OF PULLEYS

In Fig. 11.13, is shown a third system of pulleys. In

this system, like the first system of pulleys, the pulleys are

arranged in such a way that there are as many strings as

there are pulleys. One end of each string is fixed to a block

B –B, to which the load is attached. The other end of each

string, passing round the upper periphery of the pulley, is

fastened to the next lower pulley as shown in 11.13.

The velocity ratio, of the system, may be obtained

by considering a unit motion of the load. In this case, let the

weight W be raised by x metres. Since the llad is supported

on all the strings, therefore all the strings will be slackened

by x metres.

Now consider the pulley 1, which is fixed to the

ceiling. The slackness of string s 1 equal to x metres will

have to be taken up by the pulley 2, which should come

down through a distance of 2x metres. But as the string s 2

also slacks by x metres, therefore the string s 1 will be pulled

through a distance of (2x – x) = x metre. Now consider the

pulley 2. As the string s 1 has been pulled through a distance

x metres, therefore the string s 2 will be pulled through a Fig. 11.13. Third system of pulleys.