Procedure
This demonstration includes a cart on a roller coaster track that has an added mass. The added mass is a cup of water. The objective is to see whether the water will spill or not when it passes through the loop. This is one of the various practical experiments you can try on a roller coaster.
The Physics Behind It
There are three forces acting upon the cart during its motion through the loop without spilling the water . They include Normal force(FN),Gravitational force(mg), and centripetal acceleration(ac). Each force listed goes in the same direction which is downward at the interval when the cart is upside down.
Therefore...
Fnet=m.a
The net force is equal to mass times acceleration.
FN + mg = m.V2/R
This is FN plus mg which is equal to m times ac=m . V2/R
ac= m.V2/R
The formula of centripetal acceleration.
Weff=FN =mV2/R-mg.
Thus, the effective weight (Weff) is equal to FN which is equal to mV2/R minus mg.
For Vmin, FN = 0
V2min=gr
Vmin=√(gr)
V≥√(gr)
Materials
This link includes the materials and instructions on how to assemble the track.