The physics of roller coasters

If you have visited an amusement park in the past, you have probably been on a roller coaster before. You know that they allow you to experience death-defying drops, extremely tight turns, and dizzying corkscrews without the risk of death or injury that you would expect to be a part of an such an adrenaline-pumping activity.

However, roller coasters a more complicated than that. Much more complicated. With every roller coaster, the laws of physics are at play, both keeping you as safe as possible, and ensuring you didn't waste your money purchasing the admission tickets.

Most roller coasters rely on gravity to supply the car with the energy needed to complete the circuit. The car is winched up to the top of the first hill, supplying it with gravitational potential energy as it starts to come down the first drop. Some roller coasters use magnetic catapults to supply the car with kinetic energy. Magnets allow the roller coaster car to accelerate extremely fast and reach mind boggling speeds in a very short period of time.

Once the roller coaster is going around the track, you experience a lot of G-forces. You feel heavier if you are going up a hill and lighter if you are going down a hill. The rider also experiences centrifugal force when going around a tight turn, and acceleration when going down hills.

While the roller coaster is going around the track, it is not propelled by any motor. It travels all by itself, with its own momentum and gravity as its sole means of propulsion. In the end, just enough kinetic energy is supplied to your roller coaster car for it to make one complete circuit around the track.

Once you complete one circuit around the track, hydraulic brakes are usually used to stop the roller coaster car. The car experiences an acceleration in the direction opposite its motion.

Here are some related to roller coasters:

How to add vectors

This blog entry will explain how to add vectors. If you follow these simple steps, you'll be adding vectors like Albert Einstein in no time:

1. First step is setting your positive and negative axes. This step is crucial because it will allow you to determine whether your vectors are going in a positive or negative direction.
2. Next, you must break down all of the vectors into their individual x and y vector components. For this you use the sine and cosine ratios to find the magnitudes of two x and y vector components. Next, you find the directions of the x and y components based on the positive axes you set earlier.
3. You then organize these vector components in a chart while at the same time applying all of the vector transformations to the vector components. For example the vector 2A would involve multiplying Ax component by 2 and the Ay component by 2. The vector -A would involve reversing vector A and making it go in the opposite direction. Therefore, you multiply Ax by -1 and Ay by -1.
4. You find the net values of all of the x and y vector components. Essentially add up all of the x values and all of the y values.
5. You then use the Pythagorean theorem to calculate the magnitude of the resultant vector.
6. Finally, you use the tangent angle ratio to calculate the angle of the resultant vector while paying close attention to - and +, and N, S, E, W. 
7. Congratulations!! You have just learned how to add vectors.

Deriving Equation 4 from a velocity-time graph

Deriving Equation 3 from a velocity-time graph

Results of the Walking the Graphs Lab

Last week, our class did a lab which involved trying to match various distance-time and velocity-time graphs by walking back and forth in front of a Vernier motion detector. Here are my group's results:

The result for experiment b.

The result for experiment c.

The result for experiment d.

The result for experiment e.

The result for experiment f.

The result for experiment g.

Building an Electric Motor

Today in physics class we built a simple electric motor with groups of two. To build the motor, we used:

1. a piece of wood
2. four 4-inch nails
3. two strips of aluminum from a pop can
4. 2 smaller nails
5. a couple pieces of Lego
6. two thumbtacks
7. a kebab skewer
8. a long piece of wire
9. a cork
10. two magnets
11. some tape

The motor took me and my partner most of the period to construct. There were some minor hitches when we were unable to push the kebab skewer through the cork, but we fixed the problem by first hammering a nail through the cork to make it easier to insert the skewer.

Our motor worked based on the motor principle, which is based on the fact that when two magnetic fields interact with each other, a force is produced. In this case, the magnets produce one magnetic field, and the current running through the wires coiled around the cork produces the other magnetic field. In order for the motor to spin continuously, the current must be reversed after every half-turn. This will allow the cork to spin in one direction continuously. Our motor's spin was a bit wobbly and unstable, but it still managed to make quite a few revolutions before the power was turned off. This activity was very fun and allowed us to not only learn about the motor principle, but to apply it in a real life situation.

If we did this activity again, I would fix the motor so that spins more smoothly. I think the reason why our motor was so twitchy was because our aluminum strips were too thick, thereby slowing our motor down. If I did this activity again in the future, I would make the aluminum strips thinner.

Here is a video of our motor spinning:



Here are some pictures of our motor:

Our motor during the early stages of its construction.

Just need to add the aluminum strips...

The finished product.

Right-Hand Rules

Here are some pictures explaining the two right hand rules that I've learned so far:

The first right-hand rule (RHR#1) for conventional current flow.

The second right-hand rule (RHR#2) for conventional current flow.