Calculating Velocity for a Loop the Loop

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To calculate the minimal velocity at point A to reach point B in a loop-the-loop scenario without friction, the correct formula is v = sqrt(5gr), which accounts for the necessary centripetal force at the top of the loop. While the initial calculation suggested v = sqrt(4gr), this does not provide enough speed to counteract gravity and maintain contact with the track. The discussion emphasizes that without sufficient velocity, the normal force would become negative, indicating that the car would not stay on the track. The centripetal force required at point B must be positive to ensure the vehicle remains on the path. Thus, achieving the correct speed is crucial for successfully navigating the loop.
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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