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PhysicsW.E.P.Vertical circular motionMedium2 minQB

PhysicsMediuminteger

Passage / Comprehension

A small slider of mass m is released from rest at A and slides along a vertical-plane track. The track is smooth from A to D and rough from D onward, with kinetic friction coefficient $μ_{k} = \frac{1}{3}$ . The track geometry is shown below.

Source diagram for Phase II Advanced shared passage group 1

The maximum normal force $N_{Max}$ exerted by the track on the slider during its motion, is $β mg$ . Find the value of $β$ , where $β$ is the least integer.

Answer:

Solution:

On the smooth track the speed at C follows from the drop of 3R.

$\frac{1}{2} m v_{C}^{2} = m g (3 R) \Rightarrow v_{C}^{2} = 6 g R$

At C the normal force supplies centripetal force in addition to balancing weight.

$N_{C} - m g = \frac{m v _{C}^{2}}{R} = 6 m g$

$N_{m a x} = N_{C} = 7 m g \Rightarrow β = 7$

Stream:JEESubject:PhysicsTopic:W.E.P.Subtopic:Vertical circular motion

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