INTRODUCTION

I decided to start on this assignment after riding my first roller coaster ride recently. The roller coaster ride seemed very scary and dangerous, and I had this psychological fear that I would drop off any moment, even though I knew intellectually that the rides are safe. I also wondered about the different frightening thrills and sensations I felt throughout the ride. Then I thought: How did the different designs of roller coasters come about? What causes these different thrills and experiences throughout the ride? Can it be explained by physics? Thus, I decided to do a bit of research about the mechanics behind roller coasters to satiate my curiosities. 

This assignment has been a very enriching and fascinating experience and I had a lot of fun finding out the ‘secrets’ behind roller coasters. I feel that I have gained a lot of knowledge about roller coasters and realized that roller coasters were not so complicated after all. Maybe after getting in depth knowledge about how roller coasters inflict these different and freaky sensations on my body, I might not be so afraid of roller coasters the next time I ride one!

Now, let’s get into the physics of these “scream machines”!

CONVERSION OF ENEGRY

Roller coasters actually incorporate the simple physics that I have just learnt this year.  The cars on the roller coaster move not by self-powering. Instead, the roller coaster is pulled up with a chain or cable along the lift hill only to the first peak of the coaster track, which is the tallest hill of the ride. The law of the conversion of energy then comes into the picture; energy can neither be destroyed nor created, thus the loss in potential energy = the gain in kinetic energy.

As the roller coaster rise up the lift hill, it gains potential energy. The formula for potential energy is given by PE = mgh, where m is mass, g is acceleration due to gravity and h is the height above ground. Thus, the roller coaster will have the highest potential energy at the highest peak.

The potential energy accumulated by the rise in height is transferred to kinetic energy as the cars race down the first downward slope. The formula for kinetic energy is given by KE = 1/2mv². Thus, the roller coaster has the highest speed and kinetic energy at the lowest peak, when most of the potential energy has been converted to kinetic energy.

Kinetic energy can then be converted back into potential energy as the train moves up again to the second peak. This hill is necessarily lower, as some mechanical energy would be lost to friction. Through this, roller coasters are able to complete the rest of the ride without any mechanical assistance. 

CENTRIPETAL ACCELERATION

Centripetal acceleration is also involved in roller coasters, and explains the experience of a rider in a roller coaster while it moves in a circular motion. It is not a true force, but rather the result of an object’s inertia, or resistance to change in direction, as the object moves in a circular path. The "force" points toward the center of the circle, but a roller coaster rider would feel centripetal acceleration as a force pushing them toward the outer edge of the car.

Centripetal acceleration is given by a_r = v²/r where a_r is centripetal acceleration, v is velocity and r is the radius of the circular path. This shows that two roller coaster cars entering two loops of different size at the same speed will experience different acceleration forces: the car in the tighter loop will feel greater acceleration while the car in the wider loop will feel less acceleration.

INERTIA AND GRAVITY

The forces of inertia and gravity are involved in the loops of roller coaster tracks, and also help explain the different sensations and experiences of the rider in a loop.

1. When going around a roller coaster's vertical loop, the inertia that produces a thrilling acceleration force also keeps passengers in their seats. As the car approaches a loop, the direction of a passenger's inertial velocity points straight ahead at the same angle as the track leading up to the loop. As the car enters the loop, the track guides the car up, moving the passenger up as well. This change in direction creates a feeling of extra gravity as the passenger is pushed down into the seat.

2. At the top of the loop, the force of the car's acceleration pushes the passenger off the seat toward the center of the loop, while inertia pushes the passenger back into the seat. Gravity and acceleration forces push the passenger in opposite directions with nearly equal force, creating a sensation of weightlessness.

3. At the bottom of the loop, gravity and the change in direction of the passenger's inertia from a downward vertical direction to one that is horizontal push the passenger into the seat, causing the passenger to once again feel very heavy.

These forces exerted by the loop-the-loop coasters help to keep passengers from falling out.

The coaster tracks serve to channel this force -- they control the way the coaster cars fall. If the tracks slope down, gravity pulls the front of the car toward the ground, so it accelerates. If the tracks tilt up, gravity applies a downward force on the back of the coaster, so it decelerates.

Gravity also controls the way the coaster cars fall. If the tracks slope down, gravity pulls the front of the car toward the ground, so it accelerates. If the tracks tilt up, gravity applies a downward force on the back of the coaster, so it decelerates.

On a roller coaster, as you descent you would feel the upward pressure of the ground underneath you. This is the feeling of weight as the gravity is stopping your descent to the ground. 

NEWTON’S FIRST LAW OF MOTION

Since by Newton’s first law of motion, an object in motion tends to stay in motion, the coaster car will maintain a forward velocity even when it is moving up the track, opposite the force of gravity. Thus, roller coasters would be able to keep going up hills and converting potential energy to kinetic energy constantly.

Body sensations are also explained. From Newton’s first law of motion, it says that your body will keep going at the same speed in the same direction unless some other force acts on you to change that speed or direction. So when the coaster speeds up, the seat in the cart pushes you forward, accelerating your motion. When the cart slows down, your body naturally wants to keep going at its original speed, thus the harness in front of you accelerates your body backward, slowing you down. You would then feel yourself pressed against the restraining bar as the roller coaster speeds up or slows down.

THE SINKING FEELING

When your body is accelerated, each part of your body is accelerated individually. The seat pushes on your back, the muscles in your back push on some organs and those organs push on other organs. This is why you feel the ride with your whole body.

Normally, all the parts of your body are pushing on each other because of the constant force of gravity. However in the "free-fall" state of plummeting down a hill, there is hardly any net force acting on you. In this case, the various pieces of your body are not pushing on each other as much but are all falling individually inside your body. You would then feel a sinking sensation in your stomach as it is suddenly very light because there is less force pushing on it.