Question

A car drives over the top of a hill that has a radius of 50 m.

What maximum speed can the car have without flying off the road at the top of the hill?

Answer 1

To solve this problem it is necessary to apply the concepts related to the centripetal force, the force of gravity that produces the weight and the balance of these two. So that the car does not lose contact with the floor, the force of the weight must be equal to the centripetal force therefore

$\sum F = 0$

$F_c -F_w = 0$

$F_c = F_w$

$mg = \frac{mv^2}{R}$

Here,

m = mass

v =Velocity

R = Radius

Rearranging to find the velocity

$v = \sqrt{gR}$

Replacing,

$v = \sqrt{(9.8)(50)}$

$v = 22.136m/s$

Therefore the maximum speed that can the car have without flying off the road at the top of the hill is 22.136m/s