Driving an RC car in a vertical loop, What formula to use?

[FreeForAll]

I once drove my RC car in a vertical loop in a concrete drain pipe.

If you know the diameter of the pipe, and the weight of the vehicle, what is the formula used to determine the minimum speed required for it to complete the loop?

 

[CWatters]

At the top you want the force of gravity Mg to be less than the centripetal force needed to move in a circle radius r at velocity V. So...

Mg < MV²/r

Mass M cancels

Rearrange it to find V.

 

[FreeForAll]

Wow I never would have thought that mass is irrelevant, but it makes sense. I thought it would have been way more complicated than that, taking into account the amount of time "at the top" and mass.

Would this formula be for a simple planetary orbit of constant speed and radius? Mg = MV2/r

 

[CWatters]

No because gm is only valid at the surface of a planet. You would need to use GmM/r² instead. There is also the complication that both planets orbit about their common centre of mass (eg the moon does not orbit about the centre of the earth).

In case you haven't studied this: m and M are the masses of the two bodies. G isn't the same as g. "Big G" is the gravitational constant whereas "little g" is the gravitational acceleration on earth.