Non-uniform circular motion, [stunt Car inside a ring]

[Krishan93]

Homework Statement

[PLAIN]http://img695.imageshack.us/img695/3864/unled1dxu.jpg

Homework Equations

F=(mv^2)/r

The Attempt at a Solution

NetForce=0
N-W=0

===
A free body diagram of the car at the bottom would just incorporate a downwards W force and an upwards N force together equalling 0, wouldn't it?

 

[Doc Al]

A free body diagram of the car at the bottom would just incorporate a downwards W force and an upwards N force together equalling 0, wouldn't it?

Those are the correct forces, but why would they add to 0? The car is accelerating!

 

[Krishan93]

Those are the correct forces, but why would they add to 0? The car is accelerating!

Accelerating as in change of direction?
I would think that the bottom of the loop is the maximum speed of the car, past that half the car begins to decelerate, no?

 

[Doc Al]

Accelerating as in change of direction?

Yes. It's executing circular motion, so what kind of acceleration must exist?

I would think that the bottom of the loop is the maximum speed of the car, past that half the car begins to decelerate, no?

You are told that the speed is constant.

 

[Krishan93]

Yes. It's executing circular motion, so what kind of acceleration must exist?

You are told that the speed is constant.

I think I got it. Knowing constant velocity did help.
Given the top of the loop circumstances, the only forces acting upon the car are N and W, together they equal the centripetal force.
Keeping the same velocity at the bottom, the N and W act against each other, but the centripetal force still has to equal that of when it was at the top in order to maintain circular motion.
Apparently N takes on a greater value to compensate I guess and I get an answer of 20.1

How's my reasoning? Is this the same reasoning with planes flying in a circular loop as well?

 

[Doc Al]

I think I got it. Knowing constant velocity did help.
Given the top of the loop circumstances, the only forces acting upon the car are N and W, together they equal the centripetal force.
Keeping the same velocity at the bottom, the N and W act against each other, but the centripetal force still has to equal that of when it was at the top in order to maintain circular motion.
Apparently N takes on a greater value to compensate I guess and I get an answer of 20.1

Good!

How's my reasoning? Is this the same reasoning with planes flying in a circular loop as well?

Similar considerations apply to anything moving in a vertical circle. (Of course, the speed of the plane will not necessarily be constant.)