Roller Coaster

Differential Equations

applying on Roller Coaster

Lucas Machado de Vasconcelos Differential Equations 7:00AM to 8:15AM

Principles of a Roller Coaster

Roller coasters are driven almost entirely by basic inertial, gravitational and centripetal forces, all manipulated in the service of a

great ride. Amusement parks keep upping the ante, building faster and more complex roller coasters, but the fundamental principles at work remain the same. Even though for the beginning of the ride it

has to have some type of propulsion or it has to start from the top of something using its own gravitational force with the inertia of it going

on for the all ride.

What is the roller coaster compose of? The Roller Coaster is composed for many items, and most and

all of then are created to give support and protection to the ride, and they are mainly: The track; The support for the track; The car;

The track-> On most of the places are made of steel because it gives a better stability, stoping it from moving when it is very windy. Although we still can find wood ones but those are usually smaller than the steel ones because they are not as firm as thrones made out of steel.

The support for the track-> Are basically the aims that connect the track on the ground giving it support in order to help it to stay at the position that was expected without any problem.

The car-> They are usually the object that will transports passengers around a roller coaster's circuit. On Roller coaster those cars are connected by specialized joints which increases the car safety principally on the loops.

Parts of a Roller Coaster:

-> Track.

-> Track Support

->Car or Train

What makes the Roller Coaster move? Part-1 The Roller Coaster movement are based

on its own forces during the entire circuit, although as every single vehicle it does needs a propulsion or something to start the ride. On the case of a Roller Coaster

they use, an electric winch winds the cars to the top of the first hill. Once at the top of the hill this winch pulls the Roller Coaster down, and right during this process the

energy for the entire circuit will be stored on the roller coaster using it to move

during he tracks even when they have loops. All this energy stored during the ride

is called Potential Energy.

What makes the Roller Coaster move?

Part-2This energy stored during some points of the

circuit will be transformed into Kinect Energy. According to

Newton’s First Law of Motion, “an object in motion tends to stay in motion, unless

another force acts against it”, wind resistance or the Friction along the track are forces that

work to slow down the train. So in theory with the potential energy

acquired by the roller coaster the ride could go forever and ever although this energy on

practice is constantly losing its own magnitude for the Air resistance and

Friction.

Why don’t I fall out when a roller coaster goes upside down on a loop?

Part-1

It’s all a matter of physics: energy, inertia, and gravity.When you go around a loop, you feel pushed

against the outside of the car and that can be explained by the force called Centripetal. This force is

the one that keeps you in your seat.

In the loop upside down, it’s Inertia that keeps you in your seat. Inertia is the force that presses your body to

the outside of the loop as the train spins around.

Although gravity is pulling you toward the earth, at the very top the acceleration force is stronger than gravity and is pulling upwards, thus counteracting gravity. The loop however must be elliptical, rather than a perfect circle, otherwise the centripetal (g) force would be too

strong for safety and comfort.

How do we know whether a roller coaster is safe? Engineers and designers follow industry standards and guidelines. The first “riders” are sandbags or dummies.

Then engineers and park workers get to try it out.

Why don’t I fall out when a roller coaster goes upside down on a loop? Part-2

Illustrating the movement of a Roller Coaster.

How much height does it have to be in order to

complete the loop?So during the circuit generally before a loop the height of the track has to be at least 5/2 (2.5) of the size of the loop in order for it to have force enough to go around facing no problems during the loop and having more than enough force in order to not get stuck on the top of it or not even pass the first half of the loop. (Calculation 1).