Q20 of 63 Page 114

A car goes on a horizontal circular road of radius R, the speed increasing at a constant rate The friction coefficient between the road and the tyre is μ. Find the speed at which the car will skid.


The body is experiencing a force in the tangential direction as there exists some an acceleration a along this direction.


The friction force will be,



The normal reaction force will be mg as there is no motion in vertical direction.



As the path is circular the body will also experience centrifugal force in the radial direction.



Magnitude of the tangential force will be,




The car will skid when the friction will not be enough to reinforce Fa+Fc.


So, the condition for just skidding will be,








If this velocity exceeds then the car will skid.


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18

A turn of radius 20 in is banked for the vehicles going at a speed of 36 km/h. If the coefficient of static friction between the road and the tyre is 0.4, what are the possible speeds of a vehicle so that it neither slips down nor skids up?

 19

A motorcycle has to move with a constant speed on an over-bridge which is in the form of a circular arc of radius R and has a total length L. Suppose the motorcycle starts from the highest point. (a) What can its maximum velocity be for which the contact with the road is not broken at the highest point? (b) If the motorcycle goes at speed 1/√2 times the maximum found in part (a), where will it lose the contact with the road? (c) What maximum uniform speed can it maintain on the bridge if it does not lose contact anywhere on the bridge?

 21

A block of mass m is kept on a horizontal ruler. The friction coefficient between the ruler and the block is μ. The ruler is fixed at one end and the block is at a distance L from the fixed end. The ruler is rotated about the fixed end in the horizontal plane through the fixed end. (a) What can the maximum angular speed be for which the block does not slip? (b) If the angular speed of the ruler is uniformly increased from zero at an angular acceleration a, at what angular speed will the block slip?

 22

A track consists of two circular parts ABC and CDE of equal radius 100 m and joined smoothly as shown in figure (7-E1). Each part subtends a right angle at its center. A cycle weighing 100 kg together with the rider travels at a constant speed of 18 km/h on the track. (a) Find the normal contact force by the road on the cycle when it is at B and at D. (b) Find the force of friction exerted by the track on the Lyres when the cycle is at B, C and D. (c) Find the normal force between the road and the cycle just before and just after the cycle crosses C. (d) What should be the minimum friction coefficient between the road and the tyre, which will ensure that the cyclist can move with constant speed? Take g = 10 m/s2.