Investigating the Minimum Release Height Needed to Loop the Loop

Investigating the Minimum Release Height Needed to Loop the Loop

Task

What is the minimum release height needed to “loop the loop.”

Investigate and validate.

To do this I will create a theoretical model to calculate the minimum

height required for the roller coaster to just reach the top of the

loop then look at the height required to fully complete a loop.

I will validate my theoretical model using a track.

Assumptions

So I can make a relatively simple model I will have to make some

assumptions:

* There is no friction because if there was there would be some work

done against it and would mean I could not use the conservation of

energy. Roller coasters run on wheels against smooth metal which

would not have much friction.

* Air resistance is negligible as most roller coasters are designed

quite aerodynamically and have a large mass which would not be

affected by a significant amount.

* No energy is lost e.g. sound and heat which would be a result of

friction.

* There are no resistive forces

* The loop is an exact circle to make calculations easier and allows

me use what I know about circular motion. My model loop starts and

finished at the same place which could not happen in reality

because the roller coaster could either not get on the loop or

would do continuous loops.

* The value for gravity is constant. In reality it changes depending

on the distance you are from the centre of the earth but the

roller coaster does not have a big enough height difference

between its highest and lowest points. This is the formula for