Mechanical Engineering Principles

SIMPLE MACHINES 199

Dividing both numerator and denominator by Fl
gives:

Fl

aFl+b

=

1

a+

b

Fl

When the load is large,Flis large and

b

Fl

is small

compared with a. The force ratio then becomes

approximately equal to

1

a

and is called thelimiting

force ratio,i.e

limiting ratio=

1

a

Thelimiting efficiencyof a simple machine is
defined as the ratio of the limiting force ratio to the
movement ratio, i.e.

Limiting efficiency

=

1

a×movement ratio

×100%

whereais the constant for the law of the machine:

Fe=aFl+ b

Due to friction and inertia, the limiting efficiency of
simple machines is usually well below 100%.

Problem 1. A simple machine raises a load

of 160 kg through a distance of 1.6 m. The

effort applied to the machine is 200 N and

moves through a distance of 16 m. Takingg

as 9.8 m/s^2 , determine the force ratio,

movement ratio and efficiency of the

machine.

From equation (18.1),

force ratio=

load

effort

=

160 kg

200 N

=

160 × 9 .8N

200 N

= 7. 84

From equation (18.2),

movement ratio=

distance moved by the effort

distance moved by the load

=

16 m

1 .6m

= 10

From equation (18.3),

efficiency=

force ratio

movement ratio

×100%

=

7. 84

10

× 100 = 78 .4%

Problem 2. For the simple machine of

Problem 1, determine: (a) the distance

moved by the effort to move the load

through a distance of 0.9 m, (b) the effort

which would be required to raise a load of

200 kg, assuming the same efficiency, (c) the

efficiency if, due to lubrication, the effort to

raise the 160 kg load is reduced to 180 N.

(a) Since the movement ratio is 10, then from

equation (18.2),

distance moved by the effort

= 10 ×distance moved by the load

= 10 × 0. 9 =9m

(b) Since the force ratio is 7.84, then from equa-

tion (18.1),

effort=

load

7. 84

=

200 × 9. 8

7. 84

=250 N

(c) The new force ratio is given by

load

effort

=

160 × 9. 8

180

= 8. 711

Hencethe new efficiency after lubrication

=

8. 711

10

× 100 = 87 .11%

Problem 3. In a test on a simple machine,

the effort/load graph was a straight line of

the formFe=aFl+b. Two values lying on

the graph were atFe=10 N,Fl=30 N,

and atFe=74 N,Fl=350 N. The

movement ratio of the machine was 17.

Determine: (a) the limiting force ratio,

(b) the limiting efficiency of the machine.

(a) The equationFe=aFl+bis of the form

y=mx+c,wheremis the gradient of the

graph. The slope of the line passing through