Question

A car drives over the top of a perfectly spherical hill of radius 1.99 m. What is the maximum speed the car can have without flying off the road at the top of the hill (loosing contact with the road)? Express your answer in m/s.

Answer 1

Suppose, mass of the car = m

So, weight of the car, W = m*g (in the downward direction)

Suppose, N = Normal reaction of the ground on the car (in the upward direction)

Now,

Net force pointing toward the circle,

Fnet = W - N

The maximum value of Fnet will occur when, N = 0

Means,

Fnet = W - 0 = m*g - 0 = m*g

Now, for a circular motion -

Fnet = m*v^2 / r

therefore,

m*g = m*v^2 / r

=> v^2 = r*g

given that -

r = 1.99 m

So, v^2 = 1.99*9.8

=> v = sqrt(1.99*9.8) = 4.42 m/s (Answer)