Centripetal acceleration of a car in a loop

[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?

 

[Ambitwistor]

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.

 

[M98Ranger]

The minimum velocity at the top of the loop can be found using the equation for centripetal acceleration, which is a = v^2/r, where v is the velocity and r is the radius of the loop. In order for the car to not fall off the loop, the centripetal acceleration at the top of the loop must be equal to or greater than the force of gravity pulling the car downwards, which is 9.80m/s^2.

This is because at the top of the loop, the car is at the highest point and is momentarily at rest before it starts to descend. In order for the car to stay on the loop, the centripetal acceleration must be strong enough to counteract the force of gravity pulling the car downwards. This is known as the minimum required centripetal acceleration.

If the centripetal acceleration is less than 9.80m/s^2, the force of gravity will be greater and the car will not be able to maintain its circular motion, causing it to fall off the loop. Therefore, the centripetal acceleration at the top of the loop must be equal to or greater than 9.80m/s^2 to ensure that the car stays on the loop without falling off.

In conclusion, the minimum velocity at the top of the loop can be calculated using the equation for centripetal acceleration, and it must be equal to or greater than 9.80m/s^2 to prevent the car from falling off the loop. This highlights the importance of understanding centripetal acceleration and its role in circular motion.