Centripetal acceleration of a car in a loop

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star56
A car travel in a loop when the car reach the top of the loop it's upside down. The radius of the loop stay the same but the velocity changes. I need to find the minimum velocity at the top of the loop without the car falling of the loop. Why does the centripetal acceleration of the car at the top of the loop have to equal to 9.80m/s^2????
 

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Originally posted by star56
A car travel in a loop when the car reach the top of the loop it's upside down. The radius of the loop stay the same but the velocity changes. I need to find the minimum velocity at the top of the loop without the car falling of the loop. Why does the centripetal acceleration of the car at the top of the loop have to equal to 9.80m/s^2????
In general, the centripetal acceleration at the top of the look doesn't have to equal g. But if you add the condition that it has the minimum velocity to avoid falling off the loop, the normal force is zero. (If the velocity is above the minimum, then there can be a nonzero normal force: mv2/r = mg + N.) That means that only gravity is acting on the car, so the centripetal acceleration is equal to the acceleration of gravity.
 

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