What are the Physics of a loop-the-loop

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In summary, the conversation is about designing an investigation related to the circular motion of a body executing a vertical "loop". The key concept is centripetal acceleration and the importance of it being greater than the gravitational acceleration for the object to stay on the track. Energy conservation can also be used to calculate the speed of the roller coaster. Helpful resources for background research include a website on roller coasters and the formula a=v^2/r.
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AHUGEMUSHROOM
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What are the Physics of a "loop-the-loop"

I have to design an investigation that relates to the circular motion of a body executing a vertical "loop". Obviously, the physics involved varies quite significantly depending on the method of motion and the physical boundaries employed.

So, I was wondering if anyone one knew of some websites/links that would help with undertaking some background research before initiating the planning phase of the investigation.
 
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Maybe check out
http://ffden-2.phys.uaf.edu/211_fall2002.web.dir/shawna_sastamoinen/Roller_Coasters.htm

The main concept you need to know is centripetal acceleration.
[itex]a=v^2/r[/itex]
The key insight is that the downward centripetal acceleration at the top of the track must exceed the gravitational acceleration for the coaster to stay on the rails. You can calculate the speed such that |a| > |g| at the top of the loop. The roller coaster ought to be moving faster than this.

You can calculate the speed by invoking energy conservation, and using the gravitational potential energy = mgh.
 

What is a loop-the-loop?

A loop-the-loop is a type of roller coaster or amusement park ride that features a circular track with a vertical loop in which the riders experience a feeling of weightlessness as they travel through the loop.

What are the physics behind a loop-the-loop?

The main physics principles involved in a loop-the-loop are centripetal force, gravitational force, and inertia. Centripetal force is the force that keeps an object moving in a circular path, while gravitational force pulls the object towards the center of the Earth. Inertia is the tendency of an object to resist changes in its motion.

How is the centripetal force maintained in a loop-the-loop?

The centripetal force in a loop-the-loop is maintained by the shape of the track. The track is designed to create a normal force, which is the force that acts perpendicular to the surface of the track and keeps the riders from falling out of the loop. This normal force is what creates the necessary centripetal force to keep the riders moving in a circular path.

What happens to the riders' bodies during a loop-the-loop?

During a loop-the-loop, the riders experience a sensation of weightlessness at the top of the loop. This is because the normal force acting on their bodies decreases, causing a temporary decrease in their apparent weight. As they reach the bottom of the loop, the normal force increases, and they feel heavier. This change in apparent weight is due to the acceleration caused by the change in direction of their motion.

How is the speed of the ride calculated for a safe and enjoyable experience?

The speed of the ride is calculated based on the radius of the loop, the height of the loop, and the force of gravity. The ride must be designed to provide enough speed to maintain the necessary centripetal force while also ensuring that the riders do not experience excessive g-forces that could cause discomfort or injury. Engineers use mathematical formulas and computer simulations to determine the ideal speed for a safe and enjoyable ride.

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