CIRCULAR MOTION

3.5 A Centrifuge

A centrifuge works on the principle of centrifugal force.

The centrifuge consists of two steel tubes suspended from the ends of a horizontal bar which can be rotated at high speed in a horizontal plane by an electric motor.

The tubes are filled with the liquid and the bar is set into rotation.

Due to rotational motion, the tubes get tied and finally become horizontal.

Due to heavy mass, the heavier particles experience more centrifugal force than that of the liquid particles.Therefore, is then stopped so that the tubes becomes vertical.

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Ex.9 Two balls of equal masses are attached to a string at distance 1 m and 2 m from one end as shownin fig. The string with masses is then moved in a horizontal circle with constant speed. Find the ratioof the tension T1 and T2 ?

Sol. Let the balls of the two circles are r1 and r2. The linear speed of the two masses are v1 = r1, v2 = r2where is the angular speed of the circular motion.

The tension in the strings are such that

222

2 22

mvT m rr

= =

221

1 2 11

mvT T m rr

= =

T1 = m2r1 +T2 = m2 (r1 + r2)

1 1 2

2 2

T r rT r

+=

=

1 2 32 2+

=

4 . CONICAL PENDULUM

(This the best example of uniform circular motion)A conical pendulum consists of a body attached to a string, suchthat it can revolve in a horizontal circle with uniform speed. Thestring traces out a cone in the space.

The force acting on the bob are (a) Tension T (b) weight mgThe horizontal component T sin of the tension T provides the cen-tripetal force and the vertical component Tcos balances the weightto bob

T sin = 2mv

r and T cos = mg

From these equations

T1 T2mm

2m

1mO

r2

r1

O T1 T2 T2

Tcos

Tsin

mg

P

S

h

r Omv

r

2

l

T