A cart is going around a circular loop, as shown in the figure. The cart moves with the smallest speed necessary to stay in contact with the loop to complete a circular path at point 1. What is the speed of the cart at point 2?

The speed of this cart at point 2 is given as √5GR
This is the distance that is covered by an object over a defined or a specific amount of time.
g = gravitational speed
m = mass of cart
r = radius
at 1 speed = v1
centripetal force = f1
f1 = mv1²/R
m1 = mg
mv1²/R = mg
cross multiply
v1² = gr
v1 = √gr
H = 2R
mgH + mv1²/2 = mv2²/2
2GH + v1² = v2²
2g(2R) + (√gR)² = v2²
4gr + GR = V2²
5GR = v2²
√5GR = v2
Therefore at point 2, the speed of the cart is given as √5GR
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