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

[ThomasMagnus]

Roller Coaster--Circular Motion

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

 

[Doc Al]

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?

 

[ThomasMagnus]

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 f_g and f_n and they are in the same direction (downwards)

Since the centripetal force is the sum of these then: F_c=F_g+F_N

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 :) )

 

[Doc Al]

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

True. But realize that while f_g is fixed (it's your weight), f_n is not. f_n depends on the speed.

Since the centripetal force is the sum of these then: F_c=F_g+F_N

OK. Note that F_n and F_c 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.)

F_n 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.

 

[ThomasMagnus]

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?

 

[ThomasMagnus]

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)?

 

[Doc Al]

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!

 

[ThomasMagnus]

Great.

Thank you very much for your help!