Mechanical Engineering Principles

200 MECHANICAL ENGINEERING PRINCIPLES

points (x 1 ,y 1 )and(x 2 ,y 2 ) of the graph

y=mx+cis given by:

m=

y 2 −y 1

x 2 −x 1

Thus forFe=aFl+b, the slopeais given by:

a=

74 − 10

350 − 30

=

64

320

= 0. 2

Thelimiting force ratiois

1

a

,thatis

1

0. 2

= 5

(b) Thelimiting efficiency

=

1

a×movement ratio

× 100

=

1

0. 2 × 17

× 100 = 29 .4%

Now try the following exercise

Exercise 89 Further problems on force

ratio, movement ratio and

efficiency

1. A simple machine raises a load of 825 N
   through a distance of 0.3 m. The effort
   is 250 N and moves through a distance
   of 3.3 m. Determine: (a) the force ratio,
   (b) the movement ratio, (c) the efficiency
   of the machine at this load.

[(a) 3.3 (b) 11 (c) 30%]

2. The efficiency of a simple machine is
   50%. If a load of 1.2 kN is raised by an
   effort of 300 N, determine the movement
   ratio. [8]


3. An effort of 10 N applied to a simple
   machine moves a load of 40 N through
   a distance of 100 mm, the efficiency at
   this load being 80%. Calculate: (a) the
   movement ratio, (b) the distance moved
   by the effort. [(a) 5 (b) 500 mm]


4. The effort required to raise a load using
   a simple machine, for various values of
   load is as shown:

LoadFl(N) 2050 4120 7410 8240 10300

EffortFe(N) 252 340 465 505 580

If the movement ratio for the machine is

30, determine (a) the law of the machine,

(b) the limiting force ratio, (c) the limit-

ing efficiency.

[(a)Fe= 0. 04 Fl+170 (b) 25

(c) 83.3%]

5. For the data given in question 4, deter-
   mine the values of force ratio and effi-
   ciency for each value of the load. Hence
   plot graphs of effort, force ratio and
   efficiency to a base of load. From the
   graphs, determine the effort required to
   raise a load of 6 kN and the efficiency at
   this load. [410 N, 49%]

18.3 Pulleys

Apulley system is a simple machine. A single-

pulley system, shown in Figure 18.1(a), changes the

line of action of the effort, but does not change the

magnitude of the force. A two-pulley system, shown

in Figure 18.1(b), changes both the line of action

and the magnitude of the force.

Effort

Load

(a)

Figure 18.1(a)

Theoretically, each of the ropes marked (i) and

(ii) share the load equally, thus the theoretical effort

is only half of the load, i.e. the theoretical force

ratio is 2. In practice the actual force ratio is less

than 2 due to losses. A three-pulley system is shown

in Figure 18.1(c). Each of the ropes marked (i),

(ii) and (iii) carry one-third of the load, thus the

theoretical force ratio is 3. In general, for a mul-

tiple pulley system having a total ofnpulleys, the

theoretical force ratio isn. Since the theoretical effi-

ciency of a pulley system (neglecting losses) is 100