Mechanical Engineering Principles

MOTION IN A CIRCLE 189

and v 2 =

√

4 gr=

√

4 × 9. 81 × 0. 6

= 4 .852 m/s

Resolving forces in a direction along the string,
T =tension in the string=centrifugal force+
component of weight at 45°to the vertical

i.e. T=

mv 22

r

+mgcos 45°

=

0. 1 ×( 4. 852 )^2

0. 6

+ 0. 1 × 9. 81 × 0. 7071

= 3 .924 N+ 0 .6937 N

i.e.the tension in the string,T= 4 .618 N

Now try the following exercise

Exercise 82 Further problems on motion

in a vertical circle

1. A uniform disc of diameter 0.1 m rotates
   about a vertical plane at 200 rpm. The
   disc has a mass of 1.5 kg attached at
   a point on its rim and another mass of
   2.5 kg at another point on its rim, where
   the angle between the two masses is 90°.
   Determine the magnitude of the resultant
   centrifugal force that acts on the axis of
   the disc, and its position with respect to
   the 1.5 kg mass.
   [63.94 N at 59°anticlockwise]


2. If a mass of 4 kg is placed on some
   position on the disc in Problem 1, deter-
   mine the position where this mass must
   be placed to nullify the unbalanced cen-
   trifugal force. [At a radius of 36.46 mm,
   121 °clockwise to 1.5 kg mass]


3. A stone of mass 0.1 kg is whirled in a ver-
   tical circle of 1 m radius by a mass-less
   string, so that the string just remains taut.
   Determine the velocity and tension in the
   string at (a) the top of the circle,(b) the
   bottom of the circle, (c) midway between
   (a) and (b).

[(a) 3.132 m/s, 0 N

(b) 7 m/s, 5.88 N

(c) 5.42 m/s, 2.94 N]

16.5 Centrifugal clutch

A clutch is an engineering device used for transfer-

ring motion from an engine to a gearbox or other

machinery. The main purpose of the clutch is to

transfer the motion in a smooth and orderly man-

ner, so that the gears and wheels (in the case of

the motor car) will accelerate smoothly and not in a

jerky manner.

Driven

shaft

Restraining

springs

Clutch

material

Centrifugal

weight

Driving

shaft

Axis

Gap

Figure 16.7

The centrifugal clutch works on the principle that

the rotating driving shaft will cause the centrifugal

weights, shown in Figure 16.7, to move radially

outwards with increasing speed of rotation of the

driving shaft. These centrifugal weights will be

restrained by the restraining springs shown, but

when the speed of the driving shaft reaches the

required value, the clutch material will engage with

the driven shaft, through friction, and cause the

driven shaft to rotate. The driven shaft will thus

reach a high speed of rotation quite smoothly in the

required time.

Centrifugal clutches are popular when it is re-

quired to exert a high starting torque quickly and

smoothly.

A suitable clutch material is asbestos, but it is

likely that asbestos will be replaced by more modern

materials for health and safety reasons.

Now try the following exercise

Exercise 83 Short answer problems on

motion in a circle

1. The centrifugal force of a massmmoving
   at velocityvat a radiusr is given by:
   .......