A car passes over a convex bridge. The centre of gravity of the car follows an arc of a circle of radius 30 m. Assuming that the car has a mass of 1000 kg, find the force that the car will exert at the highest point on the bridge, if the velocity of the car is 15 m`cdot s^(-1)`. At what speed will the car lose contact with the road?

Explanation

Mass of the car, m = 1000 kg,
velocity, v = 15 m`cdot s^(-1)`
and radius of the circular path , r = 30 m
The weight of the car = mg and the necessary centripetal force = `(mv^(2))/(r )`.
Let at the highest point on the convex bridge, the effective normal force by the road be F. Then
F = mg - `(mv^(2))/(r)= m(g - (v^(2))/(r)) = 10^(3)(9.8 - (15^(2))/(30))`
= 2.3`xx 10^(-3)` N
[` because g = 9.8 m cdot s^(-2) , v = 15 m cdot s^(-1) and r = 30 m` ]
When F = 0, the car loses contact with the road, In that situation, if the speed of the car is u, then
mg - 0 = `(m u^(2))/(r ) " " or, " " u^(2) =`gr
`therefore " "u = sqrt(9.8 xx 30 ) = 17.1 m cdot s^(-1)`.