Reaction force at the top of a rollercoaster loop

[dainckp]

I understand that in a rollercoaster loop, two forces combine to make the centripetal force required to keep the cart moving in a circular path - the cart's weight, and the reaction force of the track against the cart (except in the special case where the cart's weight alone is sufficient for the centripetal force)

What I don't understand is, why is there a reaction force at all? If the rails are pushing back on the cart, by Newton's Third Law the cart must be in the first place exerting an equal and opposite force on the rails, but I can't see where such a force would come from. The cart's velocity is perpendicular to the rail, and the acceleration is directed towards the centre of the loop, and I was taught there is no such thing as an outward centrifugal force, so why does the cart push on the rails in the first place?

A reaction force yes, but a reaction to what?

 

[russ_watters]

Welcome to PF!

The force is from (or, rather, causes) part of the acceleration: f=ma. Gravity causes the rest.

 

[CWatters]

If the rails are pushing back on the cart, by Newton's Third Law the cart must be in the first place exerting an equal and opposite force on the rails, but I can't see where such a force would come from.

The cart wants to go in a straight line but the rails force the cart to move in a curve. eg The rails apply a force on the cart.

 

[A.T.]

If the rails are pushing back on the cart, by Newton's Third Law the cart must be in the first place...

No, not "in the first place". The two equal and opposite forces act simultaneously, and are on the same footing. There is no cause-effect relationship between them, contrary to what the unfortunate naming "action & reaction" suggests.

 

[PJC01]

Thank you for your question. As you mentioned, according to Newton's Third Law, for every action there is an equal and opposite reaction. In the case of a rollercoaster loop, the reaction force at the top of the loop is a result of the cart's weight and its velocity as it moves through the loop.

When the cart is at the top of the loop, its weight is acting downwards towards the ground. At the same time, the cart's velocity is directed tangent to the loop, meaning it is moving horizontally. These two forces combine to create a resultant force that is directed towards the center of the loop, which is necessary for the cart to maintain its circular motion.

The reaction force of the track against the cart is the equal and opposite force to this resultant force. It is necessary for the track to exert this reaction force in order to keep the cart moving in its circular path. Without this reaction force, the cart would not be able to maintain its speed and direction and would fly off the track.

So, in summary, the reaction force at the top of the rollercoaster loop is a result of the cart's weight and its velocity, and it is necessary for the cart to maintain its circular motion. I hope this helps to clarify any confusion. Let me know if you have any further questions.