Roller coaster physics problem centripetal force

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Thread starter Earn Success Start date Jan 6, Earn Success. A roller coaster car is on a track that forms a circular loop in the vertical plane. If the car is to just maintain contact with the track at the top of the loop, what is the minimum value for its centripetal acceleration at this point?

Chi Meson Science Advisor. Homework Helper. When the car is going at less than the minimum speed, then there will be too much force, and the car will fall from the track. At the minimum speed the centripetal force at the very top will be exactly equal to the force of gravity, mg, because no normal force will be required. I thought Nf was a contact force and didn't depend on speed or anything like that. As I understand, normal force is a reaction to the force that an object exerts on the surface it is in contact with.

So if an object near the surface of the earth i. The surface pushes back with an equal and opposite force, which is what we call the normal force. In the case of the roller coaster, if the object has just enough acceleration to barely maintain contact with the rail, then it is not pressing against the rail, and therefore there is no normal force at that position.

The only force acting on the object would be the force of gravity. And if the object is to continue moving in a circle, that gravitational force must provide the centripetal force to maintain circular motion. Earn Success said:. You must log in or register to reply here. Last Post Dec 20, The first roller coaster at Coney Island, which opened in Junewould barely rate in the kiddie section of a modern-day amusement park.

Nowadays, roller coasters can put you through loop-de-loops, send you screaming up 38 stories to momentarily rise up free of gravity, and even hang you from a shoulder harness, limbs a-dangle, shooting through corkscrews and switchbacks and cobra turns, with your life in the hands of engineering. Arguably, no other leisure activity makes physics quite so visceral as the roller coaster. Potential energy is invested in objects based on their position in a system—in this case, in a gravitational field.

There are actually other types of potential energy, too. When the roller coaster starts flying down the hill, it gains kinetic energy and loses potential energy. Controlling G-forces is one of the primary concerns in roller coaster design—too many Gs, or too swift a transition between positive and negative G, can tip from thrilling into uncomfortable or even dangerous.

To avoid this, roller coasters are often built with banked turns. This helps convert some of the lateral G into a positive or negative G, reducing the amount you slide about. How do you stay in your seat during a loop-de-loop? If you look at a modern roller coaster, you might notice that the loop-de-loops are shaped more like teardrops than like circles. This shape, called a clothoid, uses simple physics to make it easier on both the train and passengers.

The key factor is the fact that unlike a circular loop, which has a single radius, the clothoid loop has a smaller radius on top. The difference in radii is important because, in order for a train to complete a loop, the centripetal acceleration of the cars has to be more than or equal to the acceleration of gravity.

Since centripetal acceleration is the product of the velocity squared divided by the radius of the loop, the decrease in the radius at the top automatically increases the centripetal acceleration at the top.

As the train exits the loop, the wider radius at the bottom of the loop naturally decreases the centripetal acceleration, which in turn decreases the amount of Gs imposed on the riders. Your email address will not be published. All Rights Reserved. Get Involved Subscribe Donate.

BY: Roxanne Palmer. No Comments Share. Threading the Loop How do you stay in your seat during a loop-de-loop? Comments Leave a Reply Cancel reply Your email address will not be published. Contact your web host and ask them to enable imagepng for PHP. Related Videos. Related Content. Where Are They Now? Founding Benefactors.Hot Threads. Featured Threads. Log in Register. Search titles only. Search Advanced search…. Log in. Contact us. Close Menu. Support PF! Buy your school textbooks, materials and every day products Here!

JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding. Roller Coaster: Centripetal Forces. Hey there. Say we have a roller coaster trail which is roughly circular. When the roller coaster reaches the top of the trail, then the only forces acting on it are the force of gravity, the centripetal force, and the normal force, which are all acting downwards.

Thus, the net force acting on the roller coaster is also downwards, then why doesn't the roller coaster fall down? Can anyone please tell me what's going on? Homework Helper. Gold Member. Dearly Missed.

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Sure, it falls down, but not quickly enough, so the roller coaster stays on track. Remember that the track as well curves downwards. But if all the forces are acting downwards, how do we calculate the maximum speed which is needed for the roller coaster to prevent it from falling down?

In linear motion, I used to set the net force to zero for equilibrium and then solve for whatever variable. But I donno what to do here since the net force is non-zero This problem is probably much easier to do using the concept conservation of energy.

Physics of roller coasters

The reason I said "probably" and not "definitely" is just in case you have to account for friction, in which case it becomes slightly more complicated. I know that it is easier to do by using the conservation of energy but I really wanna know what is happening in terms of forces. BTW, I am not really worried about friction.

Last edited: Dec 10, I think the minimum speed at the top is the speed where there is zero centripetal force, and the roller coaster is in free fall for the instant it's at the top of the loop, but quickly expriences centripetal force from the curving track. In real life, modern roller coasters have wheels on the far side of the track to prevent them from falling off. Doc Al Mentor. Jeff Reid said:. Thanks Doc Al. Is this right?

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Also, in this sense there would only be two kinds of "real" forces that is causing the actual motion: cetripetal force one that only changes the direction and a -- newly invented -- "linear" force one that only changes the magnitude. Am I making sense? In this sense, it doesn't seem like it is a fundamental "force" like force of gravity or electromagnetic force.To create playlists you must logged in.

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Search for:. Add to playlist. Centripetal Force Problem - Car Doesn't Lose Contact With Ground This classic centripetal force problem describes a small hill in a road as "approximately circular", and then asks the maximum speed that a car can go over that hump without "loosing contact with the road", or some other description that translates to "set the normal force equal to zero. Maximum G-Force At Bottom of Plane Loop-to-Loop When a military jet does a vertical loop, the pilot is "pulling g's", getting squished down into her seat.

In this problem or similar ones involving roller coastersthey ask you to calculate the minimum radius such that the pilot doesn't pull more than a certain number of g's that would make her pass out. Jet Speed At Top of Loop To Experience Weightlessness This problem is just like the previous one about a car going over a hump in the road: calculate the speed such that the pilot feels weightless.

Once again you're setting normal force equal to zero, except this time it's normal force of air on the wings or the seat on the pilot's butt rather than the force of the tires on the road. Roller Coaster Speed at Top of Loop To Maintain Contact With Track Once again we're setting normal force equal to zero, except this time it's to find the speed at which a roller coaster car "loses contact with the track" or "passengers don't leave their seats".

Centripetal Force - Minimum Coefficient of Friction To Prevent Car Skidding In the first of a few problems about cars going around turns, in this case the road is level - not banked - and we'll calculate the minimum coefficient of static friction to prevent the car from skidding.

Centripetal Force - Bank Angle For Road To Prevent Car Sliding no friction This is another classic car problem, in which they tell you that the road is so slippery that there is no friction at all, and then they ask you to calculate the angle that the road should be banked to keep the car going nicely through the turn without sliding to the outside or inside of the turn.

roller coaster physics problem centripetal force

It's not impossible, but it does make for some juicy algebra and trig as you attempt to solve a system of two equations and two unknowns, one of which is stuck inside trig functions!

All rights reserved. Start your trial!A roller coaster is a machine that uses gravity and inertia to send a train of cars along a winding track. The forces experienced by the rider are constantly changing, leading to feelings of joy in some riders and nausea in others.

The basic principles of roller coaster mechanics have been known since[ citation needed ] and since then roller coasters have become a popular diversion. Centrifugal center fleeing force is not a true force, but rather the result of an object's inertiaor resistance to change in direction, as the object moves in a circular path.

The track's curve prevents the object from following the straight line it otherwise would, by applying a force on it via its outside edges towards the center of the circle, forcing it to travel in a curved path instead. This centripetal center seeking force actually points toward the center of the circle, but a roller coaster rider experiences feels the sensation of a centrifugal forcea pseudo force pushing them toward the outer edge of the car.

8.01x - Lect 5 - Circular Motion, Centripetal Forces, Perceived Gravity

This sensation is actually the result of the rider's inertia. 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.

Instead, the car is pulled to the top of the first hill and released, at which point it rolls freely along the track without any external mechanical assistance for the remainder of the ride. The purpose of the ascent of the first hill is to build up potential energy that will then be converted to kinetic energy as the ride progresses.

The initial hill, or the lift hillis the tallest in the entire ride. As the train is pulled to the top, it gains potential energy, as explained by the equation for potential energy below:. Two trains of identical mass at different heights will therefore have different potential energies: the train at a greater height will have more potential energy than a train at a lower height. This means that the potential energy for the roller coaster system is greatest at the highest point on the track, or the top of the lift hill.

As the roller coaster train begins its descent from the lift hill, the stored potential energy converts to kinetic energy, or energy of motion. The faster the train moves, the more kinetic energy the train gains, as shown by the equation for kinetic energy:. Because the mass of a roller coaster car remains constant, if the speed is increased, the kinetic energy must also increase.

This means that the kinetic energy for the roller coaster system is greatest at the bottom of the largest downhill slope on the track, typically at the bottom of the lift hill. When the train begins to climb the next hill on the track, the train's kinetic energy is converted back into potential energy, decreasing the train's velocity. This process of converting kinetic energy to potential energy and back to kinetic energy continues with each hill.

The energy is never destroyed, but is lost to friction between the car and track. Brakes bring the ride to a complete stop. When going around a roller coaster's vertical loopthe 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.Hot Threads. Featured Threads.

Roller Coasters and Amusement Park Physics

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roller coaster physics problem centripetal force

Support PF! Buy your school textbooks, materials and every day products Here! JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding. Centripetal Force and Roller Coasters. Thread starter N0ct Start date Nov 13, Homework Statement A A roller coaster has a vertical drop but followed by a loop.

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The total vertical height of the drop is 66m. It starts as a steep slope at an angle of 75 degrees relative to the horizontal and then enters into a circular path of radius R.

In order to stay below 4 times the force of gravity at the bottom of the bend what is the minimum radius of this bottom section of the loop. B After the bottom of the dip of radius R from above the track gradually transitions to the inverted top part of the loop.

roller coaster physics problem centripetal force

What is the force on the rider at the top of the loop if the loops height is 33 meters? Would the change fall out of the riders pockets? I found that by using the consrevation of Energy theory, I can equate the changes in Potential and kinetic energies by subbing the v found in the previous question to get Vf, the velocity at the top of the loop.Free Newsletter.

Sign up below to receive insightful physics related bonus material. It's sent about once a month. Easily unsubscribe at any time. Join me on Patreon and help support this website. There are many variations on roller coaster design.

But needless to say, they all involve going around loops, bends, and twists at high speed. The typical roller coaster works by gravity. There are no motors used to power it during the ride. Starting from rest, it simply descends down a steep hill, and converts the stored gravitational potential energy into kinetic energy, by gaining speed. A small amount of the energy is lost due to friction, which is why it's impossible for a roller coaster to return to its original height after the ride is over.

The roller coaster uses a motorized lift system to return to its original position at the top of the initial hill, ready for the next ride. The figure below illustrates the concept.

This can be expressed mathematically as follows.

roller coaster physics problem centripetal force

Let W be the gravitational potential energy at the top of the hill. Then, where m is the mass of the roller coaster, and g is the acceleration due to gravity, which equals 9. The kinetic energy of the roller coaster is: where v is the speed of the roller coaster.

If we assume no friction losses, then energy is conserved. Therefore, Thus, mass cancels out, and This result is nice because it allows us to approximate the speed of the roller coaster knowing only the vertical height h that it fell on any part of the track.

Of course, due to friction losses the speed will be a bit less than this, but it is very useful nonetheless. Another important aspect of roller coaster physics is the acceleration the riders experience. The main type of acceleration on a roller coaster is centripetal acceleration. This type of acceleration can produce strong g-forceswhich can either push you into your seat or make you feel like you're going to fly out of it. Centripetal acceleration occurs mainly when the roller coaster is traveling at high speed around a loop, as illustrated in the figure below.

The centripetal acceleration experienced by the riders going around the loop is: Centripetal acceleration can also occur when the riders twist around a track, as illustrated in the figure below. The acceleration experienced by riders on roller coasters can be quite high, as much as g which is times the force of gravity. In summary, the physics of roller coasters in general is a combination of gravitational potential energy converted into kinetic energy high speedand using this speed to create centripetal acceleration around different portions of the track.

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