Minimum speed of an object required to go round a circular loop.

[supersingh]

hey, how would you find the minimum speed of an object required to make it go around a circular loop?

 

[LURCH]

If at all possible, put the object at the top of the loop and let it roll down. Measure its speed as it reaches the bottom of the loop, and that is the speed with which it will need to enter the loop, but you must then add whatever speed you expect to lose to friction, plus whatever safety margin you want.

BTW; if this is for a roller coaster, you're definitely going to want an eliptical loop that is NOT circular. Is that a workable solution for your application?

 

[cesiumfrog]

if this is for a roller coaster, you're definitely going to want an eliptical loop that is NOT circular.

Why?

 

[Loren Booda]

Due to friction? Neglecting friction, in theory, the potential energy at the top of the circular loop at most equals kinetic energy at the bottom of the loop.

 

[LURCH]

A loop that is elongated vertically requires roughly the same velocities as a circular loop, but you can load fewer g's onto the car as it climbs, and more at the top where the turn is sharper. That way, you get the g-forces you need to keep the thing stuck to the rails at the top of the loop, without putting so many g's at the start as to break the necks of the human passengers.

Of course, if they paid in advance...

 

[cesiumfrog]

Oh, so you don't actually mean elliptical, but egg shaped.

 

[LURCH]

Either one's good, but yes; egg-shaped is even better than elliptical.

 

[stewartcs]

hey, how would you find the minimum speed of an object required to make it go around a circular loop?

If you are referring to the minimum velocity required to maintain contact within a loop (at the top most portion), then the you can find it typically with v = SQRT(g*r).

where,

v = velocity
g = gravitational accel.
r = radius of loop