Physics Riding a loop-the-loop?

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In summary, the conversation discusses the minimum height needed for a car on a frictionless track to successfully complete a loop-the-loop. The equations of energy, gravity, and kinetic energy are mentioned and the attempt at a solution involves setting the potential energy equal to the kinetic energy. However, it is noted that the car needs a specific speed to stay on the track, so the height of the loop-the-loop must be higher than the starting point.
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Eats Dirt
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Homework Statement



A car in an amusement park ride rolls without friction around the track it starts from rest at a point A from height H above the bottom of the loop. treat the car as a particle. what is the minimum value of height (in terms of R radius)such that the car doesn't fall off the very top of the ramp.

Homework Equations



E=mgh
gravity constant
Fc=.5mv^2
K=.5mv^2

The Attempt at a Solution



i don't really know where to start but ill give it a shot.
2R is the height of the

so mgh-mg2R= 1/2mv^2


i don't really know what else to do -_-

since mgh-mg2R=1/2mv^2 could you assume that v approaches 0 then mgh=mg2R which makes sense to me because if the surface is frictionless then energy is being conserved so does this mean if the height from which it came = the height of what it needed to go to?
 
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  • #2
Eats Dirt said:

Homework Statement



A car in an amusement park ride rolls without friction around the track it starts from rest at a point A from height H above the bottom of the loop. treat the car as a particle. what is the minimum value of height (in terms of R radius)such that the car doesn't fall off the very top of the ramp.

Homework Equations



E=mgh
gravity constant
Fc=.5mv^2
K=.5mv^2

The Attempt at a Solution



i don't really know where to start but ill give it a shot.
2R is the height of the

so mgh-mg2R= 1/2mv^2


i don't really know what else to do -_-

since mgh-mg2R=1/2mv^2 could you assume that v approaches 0 then mgh=mg2R which makes sense to me because if the surface is frictionless then energy is being conserved so does this mean if the height from which it came = the height of what it needed to go to?

You don't want to merely get the cart back up to the top of the loop-the-loop, you want it to stay on the track, so it has to have a specific speed [at least] so the hill will need to be higher. How much higher is the question.
 

1. How does physics explain the forces involved in riding a loop-the-loop?

Physics explains that the force of gravity and the normal force are the main forces involved. As the roller coaster goes through the loop, the force of gravity pulls the rider down towards the center of the loop while the normal force from the track pushes the rider up. These two forces work together to keep the rider on the track and prevent them from falling out of the loop.

2. How does the speed of the roller coaster affect the experience of riding a loop-the-loop?

The speed of the roller coaster is crucial in riding a loop-the-loop. If the roller coaster is too slow, the force of gravity will not be strong enough to keep the rider on the track, causing them to fall out of the loop. On the other hand, if the roller coaster is too fast, the normal force will not be strong enough to counteract the force of gravity, causing the rider to black out due to excessive g-forces. Therefore, the speed must be carefully calculated to ensure a smooth and safe ride.

3. How does the shape and size of the loop affect the physics of riding a loop-the-loop?

The shape and size of the loop determine the forces acting on the rider. A perfectly circular loop will provide a constant normal force throughout the ride, while a teardrop-shaped loop will have varying forces, making the ride more intense. The size of the loop also affects the speed needed to complete the loop, with larger loops requiring higher speeds to maintain the necessary centripetal force.

4. Can anyone ride a loop-the-loop regardless of their weight?

In theory, anyone can ride a loop-the-loop as long as they meet the minimum height requirement. However, the forces involved in riding a loop-the-loop can be dangerous for individuals who are extremely overweight or underweight. It is important for riders to follow the ride's weight restrictions to ensure their safety.

5. What role does friction play in riding a loop-the-loop?

Friction plays a crucial role in keeping the rider on the track. Without enough friction between the wheels of the roller coaster and the track, the roller coaster would slip and slide, causing the rider to fall out of the loop. This is why roller coasters are designed with wheels that have high friction to ensure a safe and thrilling ride.

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