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A small bead of mass m is given an initi...

A small bead of mass m is given an initial velocity of magnitude `v_(0)` on a horizontal circular wire. If the coefficient of kinetic friction is `mu_(k)`, determine the distance travelled before the collar comes to rest.

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A small bead of mass m is given an ittial velocity of magnitude v_(0) on a horizontal circular wire. If the coefficient of kinetic friction is mu_(k) , the determine the distance travelled before the collar comes to rest ( Given that radius of circular wire is R).

A small collar of mass m is given an intial velocity of magnitude v_(0) on the horizontal circular track fabricated from a slender rod. If the coefficient of kinetic friction is mu_(K) , determine the distance travelled before the collar comes to rest. (Recognize that the friction force depends on the net normal force).

Knowledge Check

  • A small hoop of mass m is given an initial velocity of magnitude v_(0) on the horizontal circular ring of radius 'r' . If the coefficient of kinetic friction is mu_(k) the tangential acceleration of the hoop immediately after is release is ( assume the horizontal ring to be fixed and not in contact with any supporting surface )

    A
    `mu_(k)g`
    B
    `mu_(k)(v_(0)^(2))/(r)`
    C
    `mu_(k)sqrt(g^(2)+(v^(2))/(r))`
    D
    `mu_(k)sqrt(g^(2)+(v_(0))/(r^(2)))`

  • A block of mass m is given an initial downward velocity v_(0) and left on inclined place ( coefficient of friction =0.6). The block will

    A
    continue of move down the plane with constant velocity `v_(0)`
    B
    accelerate downward
    C
    decelerate and come to rest
    D
    first accelerate downward then decelerate

  • A ring of mass m sliding on a smooth surface with velocity v_(0) enters rough surface with coefficient of kinetic friction mu_(k) , then

    A
    the linear distance moved by centre of mass before the ring starts pure rolling is `(3v_(0)^(2))/(8 mu_(k)g)`
    B
    the gain in kinetic energy is `(mv_(0)^(2))/(8)`
    C
    the loss in kinetic energy is `(mv_(0)^(2))/(4)`
    D
    the work done by friction force is `-(3mv_(0)^(2))/(8)`

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    A block is projected along a rough horizontal road with a speed of 10 m/s. If the coefficient of kinetic friction is 0.10, how far will it travel before coming to rest?

    A block of mass m moving with a velocity v_(0) on a rough horizontal surface from x=0 coefficient of friction is given by mu=mu_(0)=ax . Find the kinetic energy of the block as function of x before it comes to rest.

    A collar having a mass M and negligible size slides over the surface of a horizontal circular rod for which the coefficient of kinetic friction is mu_(k) If the colar is given a speed v_(1) and then released at theta=0^(@) , determine how far d it slides on the rod before coming to rest. Given, M=0.75kg, r=100mm, mu_(k)=0.3,g=9.81m//s^(2),v_(1)=4m//s .

    A small mass slides down an inclined plane of inclination theta the horizontal the coefficient of friction is m = mu_(0)x , where x is the distance by the mass before it stops is .

    A particle of mass m is given a velocity u on a rough horizontal surface of friction coefficient mu . The average power imparted by friction until it stops is

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