Mechanical Engineering Principles

206 MECHANICAL ENGINEERING PRINCIPLES

then,

movement ratio=

force ratio

efficiency

× 100

=

3

100

× 100 = 3

This result shows that to raise the load by, say,
100 mm, the effort has to move 300 mm.

Problem 10. A second-order lever,AB,is

in a horizontal position. The fulcrum is at

pointC.Aneffortof60NappliedatBjust

moves a load at pointD,whenBDis 0.5 m

andBCis 1.25 m. Calculate the load and the

force ratio of the lever.

A second-order lever system is shown in
Figure 18.7(b). Taking moments about the fulcrum
as the load is just moving, gives:

anticlockwise moment=clockwise moment

i.e. 60 N× 1 .25 m=load× 0 .75 m

Thus, load=

60 × 1. 25

0. 75

=100 N

From equation (1),

force ratio=

load

effort

=

100

60

= 1. 67

Alternatively,

force ratio=

distance of effort from fulcrum

distance of load from fulcrum

=

1. 25

0. 75

= 1. 67

Now try the following exercises

Exercise 93 Further problems on levers

1. In a second-order lever system, the force
   ratio is 2.5. If the load is at a distance of
   0.5 m from the fulcrum, find the distance
   that the effort acts from the fulcrum if
   losses are negligible. [1.25 m]


2. A leverABis 2 m long and the fulcrum is
   at a point 0.5 m fromB. Find the effort to

be applied atAto raise a load of 0.75 kN

atBwhen losses are negligible. [250 N]

3. The load on a third-order lever system is
   at a distance of 750 mm from the fulcrum
   and the effort required to just move the
   load is 1 kN when applied at a distance
   of 250 mm from the fulcrum. Determine
   the value of the load and the force ratio
   if losses are negligible. [333.3 N, 1/3]

Exercise 94 Short answer questions on

simple machines

1. State what is meant by a simple machine.


2. Define force ratio.


3. Define movement ratio.


4. Define the efficiency of a simple
   machine in terms of the force and
   movement ratios.


5. State briefly why the efficiency of a
   simple machine cannot reach 100%.


6. With reference to the law of a simple
   machine, state briefly what is meant by
   the term ‘limiting force ratio’.


7. Define limiting efficiency.


8. Explain why a four-pulley system has a
   force ratio of 4 when losses are ignored.


9. Give the movement ratio for a screw-
   jack in terms of the effective radius of
   the effort and the screw lead.


10. Explain the action of an idler gear.


11. Define the movement ratio for a two-
    gear system in terms of the teeth on the
    wheels.


12. Show that the action of an idler wheel
    does not affect the movement ratio of a
    gear system.


13. State the relationship between the speed
    of the first gear and the speed of the last
    gear in a compound train of four gears,
    in terms of the teeth on the wheels.


14. Define the force ratio of a first-order
    lever system in terms of the distances
    of the load and effort from the fulcrum.