Question

A loop-the-loop cart runs down an incline into a vertical circular track of radius 3 m and then describes a complete circle. Find the minimum height above the top of the circular track from which the cart must be released.

Answer 1

Data : r = 3 m 

To just loop-the-loop, the cart must have a speed V₁ = \(\sqrt{rg}\) at the top of the loop.

If h is the minimum height above the top of the loop from which the cart must be released, by the principle of conservation of energy, we have, mgh = \(\frac{1}{2}mv^2_1\) = \(\frac{1}{2}mgr\)

∴ h = \(\frac{r}2\) = \(\frac{3}2\) = 1.5 m