Derive an expression for maximum safety speed with which a vehicle should move?
Friday, February 24, 2023
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Question: Derive an expression for maximum safety speed with which a vehicle should move?
The maximum safety speed with which a vehicle should move is the speed at which the vehicle can navigate a curve or turn without skidding off the road. This speed is determined by the centripetal force required to keep the vehicle on the road and the maximum frictional force available between the tires and the road surface.
The expression for maximum safety speed can be derived by equating the centripetal force to the maximum frictional force. The centripetal force is given by:
Fc = mv^2 / r
where m is the mass of the vehicle, v is the velocity of the vehicle, and r is the radius of the curve or turn. The maximum frictional force is given by:
Ff = μN
where μ is the coefficient of friction between the tires and the road surface, and N is the normal force acting on the tires.
Equating Fc and Ff, we get:
mv^2 / r = μN
Solving for v, we get:
v = √(μgr)
where g is the acceleration due to gravity. This expression represents the maximum safety speed with which a vehicle can navigate a curve or turn without skidding off the road, given the radius of the curve and the coefficient of friction between the tires and the road surface.
It is important for drivers to understand and adhere to this expression for maximum safety speed, as driving at speeds higher than this limit can lead to loss of control of the vehicle and potentially dangerous accidents.
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