The radius of the bump on a road is r. What force does the road exert on a car of mass m when the car passes the highest point on the bump ? Calculate the maximum speed with which the car can pass the highest point before losing contact wtih the road ?

Explanation

The forces acting on the car are the normal force exerted by the bump acting vertically upwards at the highest point and the weight of the car mg acting vertically downwards. The resultant of these two forces gives the centripetal force.
`mg - N = (mv^(2))/r`
`N = mg - (mv^(2))/r`

The force exerted by the road on the car at the highest point `=mg - (mv^(2))/r`
When the car just loses contact with the road the normal force exerted by the road on the car is zero (i.e, N= 0)
`0= mg -(mv^(2))/r`
`(mv^(2))/r = mg`
`v^(2) = rg`
`v = sqrt(rg)`
So the maximum speed with which the car can pass the highest point is `v_("max") = sqrt(rg)`