Faling to loop the loop in a rollercoaster. How does this happen?

[shahir_elmadr]

Homework Statement

At the top of the loop, we are in an upside down position, with our head being pointed towards the centre of the circle. As long as the ride is fast enough, it's impossible for us to fall out. But what happens if the ride slows down? if the rollercoaster slows down, the centripetal force is smaller. Which means the contact force from the seat will be smaller, right? if the velocity decreases further, the contact force at the top decreases to zero, since centripetal force is the sum of weight + contact/reaction force. If the rollercoaster slows down even further and the weight becomes greater than the required centripetal force, we are supposed to fall down.

Homework Equations

Why do we fall down if the weight becomes greater than the centripetal force? What is the physics behind this motion?

The Attempt at a Solution

 

[tiny-tim]

welcome to pf!

hi shahir_elmadr! welcome to pf!

apply good ol' Newton's second law …

F_total = ma ​

to keep moving in a circle, you must have the appropriate centripetal acceleration

(this is geometry, not physics )

if the net force isn't enough to give you that acceleration (this is physics), you can't stay in the circle

 

[shahir_elmadr]

Thanks for the help, man. But I guess I failed to explain my question clearly. I am saying that if the velocity decreases so much that, at the top of the loop, the weight becomes greater than the 'required centripetal force', the person on the roller coaster is going to fall head-on vertically downwards.
Centripetal force at the top of the loop = weight + contact force
If velocity decreases and keeps decreasing, the centripetal force also decreases, and the contact force decreases until it becomes zero. If the velocity doesn't decrease any further, the coaster will 'just' make the loop. But if it does, then it's supposed to fall downwards. I just don't understand why?

 

[tiny-tim]

hi shahir_elmadr!

… if the velocity decreases so much that, at the top of the loop, the weight becomes greater than the 'required centripetal force', the person on the roller coaster is going to fall head-on vertically downwards.

no, he'll follow a parabola just like any projectile …

he'll leave the rails at the angle at which the reaction force is zero, and gracefully follow a parabola until he crashes into the opposite side of the loop

(and if he actually reaches the top, he'll stay on even if the reaction force there is zero)