Mechanical Engineering Principles

58 MECHANICAL ENGINEERING PRINCIPLES

(b) Turning moment,M is 2100 N mm and the

effective length d becomes 100 mm (see

Figure 5.2(b)).

Applying M=F×d

gives: 2100 N mm=F×100 mm

from which, force,F=

2100 N mm

100 mm

=21 N

Problem 2. A moment of 25 N m is

required to operate a lifting jack. Determine

the effective length of the handle of the jack

if the force applied to it is:

(a) 125 N (b) 0.4 kN

From above, momentM=F×d,whereF is the

force applied at right angles to the handle anddis

the effective length of the handle. Thus:

(a) 25 N m=125 N×d, from which

effective length,

d=

25 N m

125 N

=

1

5

m

=

1

5

×1000 mm=200 mm

(b) Turning momentMis 25 N m and the forceF
becomes 0.4 kN, i.e. 400 N. SinceM=F×d,
then 25 N m = 400 N×d. Thus,effective
length,

d=

25 N m

400 N

=

1

16

m

=

1

16

×1000 mm

= 62 .5mm

Now try the following exercise

Exercise 25 Further problems on the

moment of a force

1. Determine the moment of a force of 25 N
   applied to a spanner at an effective length
   of 180 mm from the centre of a nut.
   [4.5 N m]


2. A moment of 7.5 N m is required to turn a
   wheel. If a force of 37.5 N applied to the

rim of the wheel can just turn the wheel,

calculate the effective distance from the

rim to the hub of the wheel. [200 mm]

3. Calculate the force required to produce
   a moment of 27 N m on a shaft, when
   the effective distance from the centre of
   the shaft to the point of application of the
   force is 180 mm. [150 N]

5.2 Equilibrium and the principle of

moments

If more than one force is acting on an object and the

forces do not act at a single point, then the turning

effect of the forces, that is, the moment of the forces,

must be considered.

Figure 5.3 shows a beam with its support (known

as its pivot or fulcrum)atP, acting vertically

upwards, and forces F 1 andF 2 acting vertically

downwards at distancesaandb, respectively, from

the fulcrum.

F 1 F 2

Rp

ab

P

Figure 5.3

A beam is said to be inequilibriumwhen there is

no tendency for it to move. There are two conditions

for equilibrium:

(i) The sum of the forces acting vertically down-

wards must be equal to the sum of the forces

acting vertically upwards, i.e. for Figure 5.3,

Rp=F 1 +F 2

(ii) The total moment of the forces acting on a

beam must be zero; for the total moment to

be zero:

the sum of the clockwise moments about any

point must be equal to the sum of the anticlock-

wise, or counter-clockwise, moments about that

point

This statement is known as theprinciple of

moments.