Conservation of energy and vertical circular motion

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Homework Help Overview

The discussion revolves around the conservation of energy in the context of vertical circular motion, specifically focusing on the energy required for a block to complete a loop while considering frictional forces.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the relationship between kinetic energy and the forces acting on the block, particularly questioning how energy relates to force in the context of circular motion and friction. There are discussions about the displacement related to friction and the role of centripetal acceleration in maintaining contact with the track.

Discussion Status

Participants are actively engaging with the problem, raising questions about the need for calculus and the specifics of energy and force relationships. Some guidance has been provided regarding the calculations needed for friction and centripetal acceleration, but multiple interpretations and uncertainties remain evident.

Contextual Notes

There is mention of assumptions regarding the average frictional force and the need to consider the distance traveled by the block in relation to the work done against friction. The discussion also highlights the complexity of calculating forces in non-linear paths.

tubworld
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Thanx! Appreciate that!
 
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Realize that the block must have a certain amount of kinetic energy (at point B) to make it around the loop if there was no friction. (Hint: How fast must it be going at the very top to stay in contact with the track?) Then realize that the block uses up additional energy doing work against friction. (How much? Consider the definition of work.)
 
I agree that it's to have sufficient energy to overcome resistance to continue the loop at its highest pt, but what has energy got to do with force? I only remember that force * displacement of force = energy. But in this case. the frictional force doesn't travel on a st line, making it hard to calculate the ans. I can't possibly take the diameter as the displacement right? Neither can I take the perimeter of half a circle as the displacement? I am seriously lost here. The second equation seems really hard to form, especially involving the circular motion.
 
tubworld said:
I agree that it's to have sufficient energy to overcome resistance to continue the loop at its highest pt, but what has energy got to do with force? I only remember that force * displacement of force = energy.
You just answered your own question. Work = Force x Displacement (parallel to the force).

But in this case. the frictional force doesn't travel on a st line, making it hard to calculate the ans. I can't possibly take the diameter as the displacement right? Neither can I take the perimeter of half a circle as the displacement?
The problem tells you the average frictional force is F. So all you need is the distance the block travels in getting up to the top. (Yes... it's half the circumference. It's that simple.)
 
Ohh... ... I see... but now that i have this value, where does the centripetal acceleration come to place? i don't seem to have any use for it in this question...
 
You'll need to use centripetal acceleration to figure out the minimum speed the block must have to maintain contact with the track as it reaches the very top. (That minimum speed is not zero!) Apply Newton's 2nd law.
 
Just one question that is bugging me though, is there a need for calculus in this question?
 
No calculus is needed to solve this problem.
 
thanx!
i got it solved! appreciate that!
 

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