
Well, let's see. Here another car just has potential energy.

Over here, it will also have potential energy because at the top of the loop,

the car is still some distance off the ground.

And so, what I'm doing here implicitly is using the ground as my zero point of potential energy.

Now, if this is a circular loop, this height is going to be 2R,

but it will also have some kinetic energy here.

So from an energy point of view, the potential energy up here is getting converted

to both potential energy and kinetic energy.

Let's set up that equation. Well, here is my equation expressing the conservation energy.

Potential energy goes to potential plus kinetic.

The mass is cancelled and remember I'm solving for the minimum height.

I'm going to set this velocity equal to the minimum possible velocity

that the car could have as it goes to this loop.

When I worked this out, I get a minimum height of 25 m.

If I make the first hill any lower than that, the car will not have enough energy

to make it safely run this loop and you might have some people falling out of the car,

which isn't the best idea when designing a roller coaster.