Calculating Velocity for a Loop the Loop

[motti]

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.

 

[Orodruin]

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?

 

[motti]

Probably zero..
i know that its 5gr if i want to "loop the loop" - but i only want to reach the top..

 

[Orodruin]

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.

 

[HalfLostAndSearching]

Hello,

Calculating the velocity required for a loop the loop can be done using the conservation of energy principle, where the kinetic energy at the beginning of the loop is equal to the potential energy at the top of the loop. In this case, since there is no friction, all of the initial kinetic energy will be converted to potential energy at the top of the loop.

The formula you have used, (mv^2)/2 = mg*2r, is correct. This can be simplified to v = sqrt(4gr), where m is the mass of the object, v is the velocity, g is the acceleration due to gravity, and r is the radius of the loop. This formula assumes that the object starts at the bottom of the loop and reaches the top of the loop without losing any energy to friction.

Your friend's formula, v = sqrt(5gr), may be taking into account the additional potential energy at the top of the loop due to the height difference between point A and point B. This formula would be accurate if the object were starting at point A and completing the full loop, with a radius of r/2.

In summary, both formulas are correct depending on the specific scenario. If the object is starting at the bottom of the loop and reaching the top, the correct formula is v = sqrt(4gr). If the object is starting at point A and completing the full loop, the correct formula is v = sqrt(5gr). I hope this helps clarify the situation. Best of luck with your calculations!