Conservative Force Problem

  • Thread starter mrshappy0
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  • #1
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Homework Statement


A mass is placed at the top of a frictionless incline track. The bottom of the track goes into a loop. At what minimum height does the block with mass m have to be released above the ground in order to reach point b (the top of the loop).


Homework Equations




mg(hmin)=mvb2/2 +mg2R.

The Attempt at a Solution



The above formula shows that the minimum height has to be 2R because vb=0. I understand that Ugravity= mgh. But I don't understand why mv^2/2 was added on the right side. I am sitting here study my textbook and can't make sense of it.
 

Answers and Replies

  • #2
Doc Al
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The above formula shows that the minimum height has to be 2R because vb=0.
How fast must the block be moving at the top of the loop in order to maintain contact? (vb = 0 won't work.)
 
  • #3
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That is from the answer key of a past exam. Maybe I stated it incorrectly. It seems right. If the block is just barely reaching that point that means that it is also stopping there which would make the velocity zero.
 
  • #4
Doc Al
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That is from the answer key of a past exam. Maybe I stated it incorrectly. It seems right. If the block is just barely reaching that point that means that it is also stopping there which would make the velocity zero.
There's a minimum speed required at the top (greater than zero) otherwise the block will leave the track before ever reaching the top.

There's nothing wrong with that formula: it's just energy conservation. But if the answer key says that vb = 0, that's incorrect.
 
  • #5
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Okay, well more importantly is that equation an example of the Mechanical Energy= Kinetic Energy+ potential energy?
 
  • #6
Doc Al
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Okay, well more importantly is that equation an example of the Mechanical Energy= Kinetic Energy+ potential energy?
Sure. But if you actually wanted to solve for the minimum height, you'd need to input a minimum value for the kinetic energy term. (You'd solve for that term by applying Newton's 2nd law at the top of the loop.)
 

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