Roller Coaster Loop-the-Loop: Solving for Kinetic Energy at Point B

[physics10189]

Homework Statement

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I am stuck with this question about a roller coaster going into the loop-the-loop situation.
So here is the question, friction between the coaster and the track is negligible.
Consider a loop the loop systems where the radius of the loop is R. A small block (of negligible size) is released from rest at the point P, which is at a height of (35)/8R.
So the question is the Kinetic Energy at B is given by...
point B is located at the right side of the circle or the loop. When I mean on the right side let us assume that the loop is a unit circle and point be is located at 0 degree.
I appriecate for your guys help.

Homework Equations

I think it could be the PE=KE

The Attempt at a Solution

 

[Sourabh N]

Yes energy conservation is the right idea. Where did you get stuck?

 

[physics10189]

Even if I do the energy conservation. mgh=.5mv^2 How do I use this to get the kinetic energy at point B where B is not at the top or bottom postion but instead it is on the right side?

 

[physics10189]

Ok never mind I actually got it. Kinetic engergy = Potential energy initial- Potential energy final.
Since I got that... What is the tangential speed at C...Let us assume that we have a unit circle and point C is at the 90 degree...so it is the top of the loop.
First please explain what is the tangential speed. Thank you!

 

[Sourabh N]

Tangential speed is the component of speed along the tangent. And the ball will never reach the topmost point, as it would violate the energy conservation equation you wrote in your last post.

 

[physics10189]

so if I want to find the tangential speed do I use the -F normal-mg=-m((v^2)/R)?

 

[Sourabh N]

Since the ball is rolling on the surface of loop, its velocity is always along the tangent at any point, to the surface.

 

[LowlyPion]

so if I want to find the tangential speed do I use the -F normal-mg=-m((v^2)/R)?

When you determined the 1/2*m*v² from the m*g*Δh, the v is your tangential velocity.

The force relationship speaks to the radial forces and is useful in determining if the ball contacts the loop.