# Loop Question

1. Mar 28, 2005

### NickCherryJiggz

Question: A small object of mass m slides without friction around a loop-the-loop aparatus. It starts from rest at point A, at height h above the bottom of the loop.......What is the minimum value of h (in terms of R [the radius of the loop] such that the object moves around the loop without falling off at the loop's highest point, B.

The solution to this question is probably a very simple one...I'm familar with similar problems concerning potential/kinetic energy, but one point confuses me...I'm not sure what the requirement is for the block to not fall off.

2. Mar 28, 2005

### xanthym

The object would not fall off if, at the highest point z=(2*R), the centripetal force required to remain in circular motion is greater than or equal to the object's weight. That is:
mv2/R = mg ::: (minimum requirement at highest point)
::: ⇒ v2 = {g*R} ::: Eq #1
By conservation of energy, if the object begins from rest at height z=h, then at height z=(2*R):
m*g*h = m*g*(2*R) + (1/2)*m*v2
Using Eq #1 above for (v2), we get:
m*g*h = m*g*(2*R) + (1/2)*m*{g*R}
::: ⇒ h = (5/2)*R

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Last edited: Mar 28, 2005