Why Is the Minimum Speed Where the Seat Exerts No Force?

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SUMMARY

The minimum speed at which a roller coaster seat exerts no force on a rider occurs at the top of the loop, where the rider is on the verge of losing contact with the seat. At this point, the gravitational force (Fg) and the normal force (Fn) act downwards, contributing to the required centripetal force (Fc). If the speed is too low, the normal force becomes zero, leading to a loss of contact. Understanding this concept is crucial for analyzing forces in circular motion.

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Roller Coaster--Circular Motion

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I have a few questions about the way this question was done. The instructor said: "The minimum speed will be at the point where the seat doesn't have to exert any force on you".

This doesn't make sense to me. Why will the minimum speed be at this point?

Thanks
 
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ThomasMagnus said:
Why will the minimum speed be at this point?
That defines the point where you just start to lose contact with the seat--in other words, it's the point where you start to fall out of the seat.

You do realize that the faster you go, the more you are pushed against the seat and thus the greater the normal force?
 


Doc Al said:
You do realize that the faster you go, the more you are pushed against the seat and thus the greater the normal force?

This is where I am mixed up.

At the top of the loop, the forces acting on the the person will be fg and fn and they are in the same direction (downwards)

Since the centripetal force is the sum of these then: Fc=Fg+FN

If both forces are acting downwards, what is pushing you into your seat? Why won't you fall out?

Thanks (I'm new at this :) )
 


ThomasMagnus said:
At the top of the loop, the forces acting on the the person will be fg and fn and they are in the same direction (downwards)
True. But realize that while fg is fixed (it's your weight), fn is not. fn depends on the speed.

Since the centripetal force is the sum of these then: Fc=Fg+FN
OK. Note that Fn and Fc will change with the speed.

If both forces are acting downwards, what is pushing you into your seat? Why won't you fall out?
Realize that you are moving fast. Without the seat there, you'd go shooting off into the air. You need forces pushing you down, not up. (You can think of it as your inertia pushing you into the seat.)

Fn is a measure of how hard the seat has to push down on you to keep you from going straight. If you go too slow, the seat won't have to push you at all--you'll start falling.
 


Thank you, I think I am catching on.

Why would you need forces acting down if the car is upside down? Wouldn't you need them upwards to keep you in the seat?
 


Would it be because on the way up the loop, your body is going to want to travel in a straight vertical path according to Newton's first law, and thus the seat is going to have to correct that (ie push down)?
 


ThomasMagnus said:
Would it be because on the way up the loop, your body is going to want to travel in a straight vertical path according to Newton's first law, and thus the seat is going to have to correct that (ie push down)?
Exactly!
 


Great.

Thank you very much for your help! :smile:
 

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