# Circular motion: Car driving along a circular hill

## Homework Statement

A car of mass m is travelling along a circular hill of radius r with a constant speed v, write an expression for the force "on the car from the hill" when the car is at the top of the hill

## Homework Equations

F (weight) = mg
F (centripetal) = mv^2 /r

## The Attempt at a Solution

I think the force on the car from the hill is the normal to the car which at the top of the hill seems to me to be mg. The actual answer is F = mg - (mv^2)/r, I cant seem to figure out how theyve come to this.

Doc Al
Mentor
I think the force on the car from the hill is the normal to the car which at the top of the hill seems to me to be mg. The actual answer is F = mg - (mv^2)/r, I cant seem to figure out how theyve come to this.
The normal force at the top of the hill would equal mg if there were no acceleration. But there is acceleration, so apply Newton's 2nd law to figure out the normal force.

The normal force at the top of the hill would equal mg if there were no acceleration. But there is acceleration, so apply Newton's 2nd law to figure out the normal force.

Ah right, I forgot that there would be a centripetal acceleration even when the car is at the top of the hill, thanks!

mg - normal = ma = m(v^2 /r)
normal = mg =(mv^2)/r