(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A 'loop a loop' cart runs down an incline and then inside a circular track of radius 3.0 meter and describes a complete circle. Find the minimum height above the top of a circular track from which the cart must be released.

2. Relevant equations

So given data is:

r=3 m

To find: Height between the top of the circle and the point from which the cart is thrown.

We have to use law of conservation of energy.

3. The attempt at a solution

Okay I'm a little confused here. The final answer is 1.5 m. My solution book has done it like this:

Then it goes like :

##mgh=\frac{1}{2}mv^2##, then ##mgh=\frac{1}{2}mrg## since velocity at top is ##\sqrt{rg}##

Then ##h=\frac{r}{2}=1.5 m##

But how can the P.E at the top become zero?

The way I've done it is, I've taken the reference point at the bottom of the circle. So it's like:

From the image, the total energy at the top of the circle must equal the energy at the starting point. SO,

##mg(2r) + \frac{1}{2}m(v_1)^2=mg(2r+h)+0##

Evaluating that, we get ##rg=2gh## and therefore ##h=\frac{r}{2}=1.5m##.

So, who's right ? My book or me? Is the energy at the top of the circle really zero? Answer is the same. Sorry my question is noobish. Please help. I like mechanics but these kind of sums always confuse me.

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# Circular Motion problem

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