# Circular motion: Car driving along a circular hill

#### Acid92

1. The problem statement, all variables and given/known data
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

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

3. 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.

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#### 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.

#### Acid92

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

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