# Centripetal Acceleration at top of Loop

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1. Dec 7, 2014

### Sylvia

1. The problem statement, all variables and given/known data
A roller coaster is on a track that forms a circular loop in the vertical plane. If the car is to just maintain contact at the top of the loop, what is the minimum value for its centripetal acceleration at this point?
A) 2g downward
B) g downward
C) 2g upward
D) g upward
E) 0.5 downward

2. Relevant equations
fcp = m(v^2 / r)

3. The attempt at a solution
I thought since normal force and weight are pointing in the same direction, the Fcp would be mg + mg = 2mg. But the correct answer is g downward. Please explain.

2. Dec 7, 2014

### Staff: Mentor

In the case discussed here, there is no normal force. Centripetal acceleration is purely coming from gravity.

3. Dec 7, 2014

### Sylvia

I dont understand why there's no normal force. It says it "just maintains contact" which means the cart and rail are in contact, meaning that there should be a normal force, right? Thank you for replying.

4. Dec 7, 2014

### Staff: Mentor

They are "just in contact" - they are directly at the border between "separating" and "contact with a contact force" - therefore, zero force but still some sort of contact.