1. Expression for the maximum safe speed for a vehicle onwithout skidding off : Consider a car of mass m taking a turn of radius r along a level
road. If u is the coefficient of static friction
between the car tyres and the road surface,
the limiting force of friction is
Fs=ųsmg,
where N= mg is the normal reaction.The forces on the car, as seen from aninertial frame of reference are shown in
Then, the maximum safe speed Vmax with which the car can take the turn without skiddingoff is set by
maximum centripetal force = limiting force of static friction.
mv²max/r = ųsmg
Vmax= √(rųsg)
This is the required expression.
The above expression shows that the maximum safe speed depends critically upon friction
which changes with circumstances, e.g, the nature of the surfaces and presence of oil or
water on the road. If the friction is not sufficient to provide the necessary centripetal torcer
the vehicle is likely to skid off the road.
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