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

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Homework Help Overview

The problem involves a block sliding along a loop-the-loop track, focusing on calculating kinetic energy and acceleration at specific points. The context includes concepts from mechanics, particularly energy conservation and circular motion.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss energy conservation principles, questioning how to relate potential and kinetic energy at different points on the track. There are attempts to derive relationships between energy and velocity, as well as considerations of centripetal acceleration.

Discussion Status

Participants are actively engaging with the problem, exploring various approaches to calculate kinetic energy and acceleration. Some have reached partial conclusions regarding energy conservation, while others are still clarifying their understanding of the relationships involved.

Contextual Notes

There is an emphasis on showing work to receive help, and participants are navigating through the implications of mechanical energy being constant throughout the motion. Some are uncertain about specific values, such as velocity at different points, which affects their calculations.

  • #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).
 
Last edited:
  • #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?
 
Last edited:
  • #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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