A person drives a car along a circular track on a level ground .
(1). Derive an expression for the maximum safe speed of the car
(2). Why do we give banking to curved road!
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on a level road the only force that helps the car move in a circular path is the friction force.
let mu be coefficient of friction. Normal force on the car exerted by the ground is N = m g.
Friction = f = mu N = mu m g.
A centripetal force is needed to keep the car moving in a circular path. it is equal to m v^2/r.
so mv^2/r < mu m g
v^2 < mu r g.
Banking of curved roads is done to increase centripetal force. The slope provides a component of normal reaction force also to supply centripetal force. So vehicles can go with higher speeds at the curves.
let mu be coefficient of friction. Normal force on the car exerted by the ground is N = m g.
Friction = f = mu N = mu m g.
A centripetal force is needed to keep the car moving in a circular path. it is equal to m v^2/r.
so mv^2/r < mu m g
v^2 < mu r g.
Banking of curved roads is done to increase centripetal force. The slope provides a component of normal reaction force also to supply centripetal force. So vehicles can go with higher speeds at the curves.
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2) banking provide more centripetal force to vehicle negotiating the curve
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