Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

A block of mass 'm' sides on a frictionless table. it is constrained to move inside a ring of radius 'R' which is fixed to the table. At t=0, the block is moving along the inside of the ring with velocity 'Vo'. The coefficient of friction between the block and the ring is 'u'.Find the speed and position of the block as the function of 't'.

A block of mass 'm' sides on a frictionless table. it is constrained to move inside a ring of radius 'R' which is fixed to the table. At t=0, the block is moving along the inside of the ring with velocity 'Vo'. The coefficient of friction between the block and the ring is 'u'.Find the speed and position of the block as the function of 't'.

Grade:12

2 Answers

vikas askiitian expert
509 Points
10 years ago

friction acting on the block at any time is f ...

f = k(normal reaction)                           (k is cofficient of friction)

normal reaction (N)= mv2/R                            (mass is in contact with ring)

 

f = ma = uN

a = -kv2/R                                     (-ve sign coz ,  friction produces retardation)

now , a  = dv/dt

dv/dt = -k v2/R

dv/v2 = -kdt/R    

integrating both sides

(-1/v) = -kt/R + C          ...........1                  ( C is constant of integration)

now at t=0 , v = vo  (given) so

 C = -1/vo            ,  after plugging value eq 1 becomes

-1/v = -kt/R - 1/vo

v = [Rvo/(R+vokt)]

Aiswarya Ram Gupta
35 Points
10 years ago

thnx...

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

ASK QUESTION

Get your questions answered by the expert for free