What Are the Physics Equations Behind Zero-G Rolls in Roller Coasters?

[physicsCU]

Hey,

Can anyone show me a site that talks about the physics equations involved in the zero-g rolls of a roller coaster?

I know they are called heartline spins and resemble a barrel roll, but I need help with the physics equations.

Thanks!

 

[andrewchang]

see if these link to anything:

http://www.Newton.dep.anl.gov/app/links.htm

http://www.Newton.dep.anl.gov/app/nau_links.htm

 

[quicknote]

Dear reader,

Thank you for your interest in the physics behind roller coasters, specifically the zero-g rolls. There are a few key equations that are involved in understanding the mechanics of these thrilling maneuvers.

Firstly, we must consider the concept of centripetal force. This is the force that keeps an object moving in a circular path, and it is crucial in understanding how roller coasters are able to perform zero-g rolls. The centripetal force can be calculated using the equation Fc = mv^2/r, where Fc is the centripetal force, m is the mass of the object, v is its velocity, and r is the radius of the circular path.

In the case of a roller coaster, the centripetal force is provided by the track itself, as it is designed to keep the train on a specific path. This force must be balanced with the force of gravity acting on the train and its riders. This leads us to another important equation, Newton's second law of motion, which states that force is equal to mass times acceleration (F=ma). In the case of a zero-g roll, the acceleration is equal to zero, as the train is not changing its speed. Therefore, the force of gravity (mg) must be equal to the centripetal force (Fc) to maintain this state of weightlessness.

Another important factor to consider is the conservation of energy. As the train approaches the zero-g roll, it has a certain amount of potential energy due to its height on the track. As it enters the roll, this potential energy is converted into kinetic energy, which is the energy of motion. The equation for kinetic energy is KE = 1/2 mv^2, where KE is kinetic energy, m is mass, and v is velocity. As the train completes the roll, it regains its potential energy and continues along the track.

In conclusion, the physics behind zero-g rolls involves concepts such as centripetal force, Newton's second law of motion, and the conservation of energy. I recommend further research on these topics to gain a deeper understanding of the equations and principles involved in roller coaster physics. Additionally, there are many online resources available that provide detailed explanations and demonstrations of these concepts in relation to roller coasters. I hope this helps in your pursuit of understanding the exciting world of roller coaster physics.