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

In summary, a small block is released from rest at the point P, which is at a height of (35)/8R. The Kinetic Energy at point B is given by the potential energy initial and potential energy final. The tangential speed at C is found by using the -F normal-mg=-m((v^2)/R).
  • #1
physics10189
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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

 
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  • #2
Yes energy conservation is the right idea. Where did you get stuck?
 
  • #3
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?
 
  • #4
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!
 
  • #5
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.
 
  • #6
so if I want to find the tangential speed do I use the -F normal-mg=-m((v^2)/R)?
 
  • #7
Since the ball is rolling on the surface of loop, its velocity is always along the tangent at any point, to the surface.
 
  • #8
physics10189 said:
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.
 

1. What is kinetic energy?

Kinetic energy is the energy that an object possesses due to its motion. It is dependent on the mass and velocity of the object.

2. How is kinetic energy related to rollercoasters?

In a rollercoaster, kinetic energy is generated as the cart moves down a slope. As the cart gains speed, its kinetic energy increases.

3. How does the height of a rollercoaster affect its kinetic energy?

The height of a rollercoaster determines how much potential energy it has. As the cart moves down a slope, this potential energy is converted into kinetic energy, increasing the speed of the cart.

4. How does the speed of a rollercoaster affect its kinetic energy?

The speed of a rollercoaster is directly proportional to its kinetic energy. The faster the cart moves, the more kinetic energy it possesses.

5. Can kinetic energy be converted into other forms of energy on a rollercoaster?

Yes, kinetic energy can be converted into other forms of energy, such as potential energy, heat, and sound, as the cart moves along the track and experiences different forces.

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