Atoy car of mass m can travel at a fixed speed. it moves in a circle on a horizontal table . the string is attached to a block of mass m that hangs by a string from the table with which the toy car is attached . the coefficient of friction is k. find the ratio of maximum radius to the minimum radius.

The tension in the string 'Mg' is constant here..now at a low speed the centrifugal force is less..so it cannot balance out the Mg force..hence the toy car has a tendency to move towards the centre..and hence friction (for minimum and maximum values of radius this friction can be considered to be on the verge of being kinetic friction..that is the maximum amount of static friction) acts in the outwards from the centre in direction of the centrifugal force to balance the 'Mg' force..in another case for a high speed case the centifugal force is larger than the tension in the string 'Mg' ..so now the tendency of the toy car is to move outward from the circle which now is balanced by the frictional force acting inwards in the direction of the tension in the string.corresponds to the minimum radii.so write down the two dynamic equations from the free body diagrams..to obtain the ratio of radius.

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