A different loop-de-loop assignment

[riddledum]

My physics teacher gave us this follow-up to the classic loop-de-loop assignment where you have to calculate the height from where you have to drop a ball in order for it to just make it round the loop. The problem with this assignment is that our teacher refuses to help us, and there are no similar examples in our coursebook.

This time, he asked us to calculate the speed of the ball after it comes out of the loop. Here are some of the data I've collected so far:

The loop has a radius of 0.0675 cm
The ball weighs 0.0282 kg
The speed of the ball is 2.16 m/s when it enters the loop

I've have done some calculations, and got the speed at the top of the loop to 1.42 m/s, which seems plausible, but I have no idea how to get the speed at the end of the loop.

 

[kuruman]

What does the "end" of the loop look like? How high is it relative to the point where the speed is 2.16 m/s? Do you see what I am getting at?

 

[riddledum]

What does the "end" of the loop look like? How high is it relative to the point where the speed is 2.16 m/s? Do you see what I am getting at?

The whole thing looks like this:

[URL]http://pici.se/pictures/mnClqYBkT.jpg[/URL]

The end is at the same height as the point where the velocity of the ball is 2.16 m/s

 

[kuruman]

Has the ball lost any mechanical energy when it returns to the same height at which it had a speed of 2.16 m/s?