Calculating Velocity for a Loop the Loop

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Homework Help Overview

The discussion revolves around calculating the minimal velocity required at point A to reach point B in a loop-the-loop scenario, specifically focusing on the dynamics involved without friction.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants explore energy conservation arguments and question the required speed at point B, as well as the forces acting at that point. There is a debate on the necessary velocity to reach the top of the loop versus completing the loop.

Discussion Status

The discussion is active, with participants providing insights into the forces involved and questioning the assumptions about the required speed. Some guidance has been offered regarding the need for sufficient speed to maintain contact with the track.

Contextual Notes

There is a mention of the absence of friction and the specific requirement to only reach the top of the loop rather than complete it, which influences the calculations and assumptions being discussed.

motti
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Hi,

i need to calculate the minimal velocity at point A to reach point B
Not asked to complete full loop, There is no friction.

I guess (mv^2)/2 = mg*2r >>> v = sqrt(4gr), my friend say v = sqrt(5gr)

Thanks.
 

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You have used an energy argument. With this argument, what would be the speed at B? What is the corresponding required centripetal force at B? What is the actual centripetal force at B?
 
Probably zero..
i know that its 5gr if i want to "loop the loop" - but i only want to reach the top..
 
The point is that you need that speed to reach the top. Otherwise the acceleration due to gravity is too large and the normal force from the track would have to be negative (with positive direction defined as being towards the loop center) in order to keep the car on track. So unless the car is somehow fixed to the track (as in some roller coasters that at points have "negative gs") you will need the extra speed in order to actually reach B.
 

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