What forces are required to keep a car moving on a vertical loop?

[Larrytsai]

Point A
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- Point X (a Loop)
- - O
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If this system is frictionless, and a cart is going down from point "A" to point "X" through the loop, What is the Velocity of Point "A" = to Point "X" ?

 

[dynamicsolo]

I suspect you aren't going to get any takers on this problem until you clarify it (and show some of your own work). What exactly is the cart doing? Are you saying that it goes down a slope, around a (vertical) loop, and out to a final point? (I'm assuming the picture is to be viewed sideways.)

The question doesn't make much sense: what is "velocity of point A to point X" supposed to mean? The velocity is going to vary over this travel, so you are going to need to be more specific about what is needed...

 

[Larrytsai]

I suspect you aren't going to get any takers on this problem until you clarify it (and show some of your own work). What exactly is the cart doing? Are you saying that it goes down a slope, around a (vertical) loop, and out to a final point? (I'm assuming the picture is to be viewed sideways.)

The question doesn't make much sense: what is "velocity of point A to point X" supposed to mean? The velocity is going to vary over this travel, so you are going to need to be more specific about what is needed...

ooo sry i thought i drew it with the keyboard, its just basically a rollercoaster picture with a loop. We weren't given any numbers, we just had to explain what is the velocity compared of point A to point x where point A is higher than point X, where point x is the top of the loop.


What my response was, Point A=Point X because the law of conservation of energy states energy is neither created or destroyed only transformed. Since the whole system is frictionless, then Energy is constant.

 

[dynamicsolo]

You are correct that mechanical energy (kinetic energy + potential energy) is conserved, but that isn't the only consideration in this problem. If you started the car from rest at exactly the same height as the top of the loop, the car would slow down as it approached the top, coming to a dead stop at the very top. Would it stay on the track if that happened?

You will need to look at the forces required to keep the car moving on the vertical loop, so that it can get beyond the top of the loop. (Remember, gravity is pulling straight down on it the whole time, including when it's inside the loop.)

Make a force diagram for the car at the moment it is at the top of the loop. What forces are acting on it there? What would have to be true about how these forces are related, in order for the car not to simply fall off the track at (or before, really) that point?