# A really SMALL rollercoaster

Let's build our own very small roller coaster here in the classroom. I'll set up a pair of towers, each of height h above the tabletop. A car of mass m will roll down the track from each tower to the edge of the table, then fly outwards with some initial horizontal velocity v. As it falls a distance H to the floor, the car will cover a horizontal distance x.

First, compute some quantities in general: use symbols only, no numbers.

1. Write an expression for the kinetic energy, potential energy, and total energy of the car when it is motionless at the top of the track. What is the origin of your coordinate system? What is the zeropoint of your potential energy?
2. Write an expression for the kinetic energy, potential energy, and total energy of the car when it is about to fly off the table.
3. What will the car's velocity v be when it flies off the table?
4. How far x will the car move horizontally as it falls to the floor?
5. Does this distance depend on the mass of the car?
6. Does this distance depend on the value g, the local acceleration due to gravity?

Now, I'll give you the quantities for the actual equipment in our example; that is, the height h, etc.

1. What is the car's total energy?
2. What will the car's velocity v be when it flies off the table?
3. How far x will the car move horizontally as it falls to the floor?
4. Should each track produce the same distance x?

At this point, we will run several trials to measure the actual distance the car flies after running down each of the two tracks. I'll write down the results on the board for everyone to see.

If we have time ...

1. Did the actual distance(s) match your predicted distance? If not, why not?
2. Was there a difference in the distances produced by each track? If so, why?
3. Look at the difference in x between the two tracks. You can use it to estimate the coefficient of rolling friction between car and track.