How Do You Calculate Kinetic Energy and Acceleration on a Loop-the-Loop Track?

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The discussion focuses on calculating kinetic energy and acceleration for a block sliding on a loop-the-loop track. The block starts from rest at a height of 52.0 m and has a mass of 1.3 kg. Key points include the conservation of mechanical energy, where potential energy at the starting point is converted to kinetic energy at point A. The participants discuss deriving the kinetic energy at point A and the necessary centripetal acceleration to maintain motion through the loop. Ultimately, they conclude that the minimum height for the block to complete the loop can be determined by equating mechanical energy at both points.
  • #31
Can you show me how to set up the equations that I need?
 
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  • #32
bulldog23 said:
Can you show me how to set up the equations that I need?

You should be able to do this if you made it this far. You already set them up in parts a and b. What is the mechanical energy at P? What is the mechanical energy at A? Then, set these two quantities equal to each other, since you know they are equal, and you should be able to solve for h. As I said, you already did this in part a and b, but there you were just solving for something else. In simplest form then, the equation you want is:

ME_P=ME_A

Again, you should be able to find ME_P and ME_A, since you were able to do this in a) and b).
 
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  • #33
So I do 1/2mv_1^2+mgy_1=1/2mv_2^2+mgy_2? And then I am solving for y_1 right?
 
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  • #34
or do I just set mgh=204 and solve for h?
 
  • #35
bulldog23 said:
So I do 1/2mv_1^2+mgy_1=1/2mv_2^2+mgy_2? And then I am solving for y_1 right?

This is correct.
 

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