Physics in the Roller Coaster's "Loop-the-Loop"
One of the all-time classic vacation spots for people of all ages and backgrounds is the amusement park. If you've ever been to one of these exhilarating parks, chances are you've also been on a roller coaster. These adrenaline-pumping rides have left thrill-seekers in awe for decades. With the soaring high speeds, numerous twists and turns, and hundred foot drops, roller coasters create a feeling of excitement that is inimitable. However, it's not only tourists who love these intense rides, but also scientists who are intrigued by the physics behind the machine. Specifically, physicists are interested by the "loop-the-loop," which is the part of a roller coaster that sends riders in a 360 degrees rotation along the track. These loops are prime examples of how centripetal acceleration and circular motion can be applied in the real world.
Gravity and Weightlessness
The inertia produced by the roller coaster's sudden change of path is not only a source of great exhilaration for riders, but it also helps prevents passengers from falling out of their cart. When the coaster first enters into the loop, it is guided upwards by the track, causing the passengers to also be dragged upwards. This creates a feeling of extra gravity on the passengers as they are pushed down into their seats. When the cart reaches the very top of the loop, the centripetal acceleration of the roller coaster is pulling the passengers down toward the center of the circle, while inertia simultaneously pushes passengers back into their seats. While this happening, gravity and acceleration are pulling the passengers in two opposite directions, creating a sensation of weightlessness in the riders. However, since the force of outward inertia is greater than gravity, the rider remains in the seat while upside down. Though there are safety harnesses on most roller coasters, the rider would not fall out anyway. In contrast, at the bottom of the loop, the passenger's inertial direction changes from a downward pull to a horizontal path. This alteration in direction, along with gravity, give the passengers the feeling of being very heavy.
The gravitational forces, also known as G-force, one experiences on a roller coaster are responsible for the feeling of "butterflies-in-your-stomach" as you begin to descend the loop. The normal gravitational force a person standing on Earth would feel is 1 g or -9.8 m/s^2. A person's weight is included in this of gravitational acceleration. At 2 g, a person will weigh double their weight. However, at the top of the loop, a person will experience weightlessness, and therefore will be in the state of free fall, or 0 g. This means that gravity is the only force acting upon the rider. If the top of the loop is narrow enough, the rider will experience negative G's and will be lifted out of their seat. This is what creates the "butterfly" sensation, which is known to make some riders nauseous.
The picture below is an effective visualization of these concepts.
Sources:
“Amusement Park Physics.” The Physics Classroom, www.physicsclassroom.com/class/circles/Lesson- 2/Amusement-Park-Physics.
Centripetal Acceleration on Roller Coasters
Firstly, when a roller coaster rider is going through the loop, they are experiencing a form of centripetal acceleration. Though the centripetal acceleration of the rider is actually pointing towards the center of the loop, they will feel as if they are being pushed to the outer edge of the circular path. This is known as centrifugal force. However, it is not actually a force. In reality, it is the body's inertia, which is the resistance to the roller coaster's change in direction. Since the body was originally traveling in a linear motion, it attempts to keep going that way even as the roller coaster changes paths. If it weren't for the firm constraints of the roller coaster, riders would continue in a straight path and slam into the seat in front of them, possibly resulting in serious injuries.
The formula for centripetal acceleration is:
Where ac is the centripetal acceleration, v is the velocity, and r is the radius. Through this formula, it's apparent that roller coasters that travel in smaller loops will generally have greater centripetal acceleration than those with larger loops.
The diagram below demonstrates the centripetal and tangential acceleration of the rider as they travel through the loop.
The diagram below demonstrates the centripetal and tangential acceleration of the rider as they travel through the loop.
Gravity and Weightlessness
The inertia produced by the roller coaster's sudden change of path is not only a source of great exhilaration for riders, but it also helps prevents passengers from falling out of their cart. When the coaster first enters into the loop, it is guided upwards by the track, causing the passengers to also be dragged upwards. This creates a feeling of extra gravity on the passengers as they are pushed down into their seats. When the cart reaches the very top of the loop, the centripetal acceleration of the roller coaster is pulling the passengers down toward the center of the circle, while inertia simultaneously pushes passengers back into their seats. While this happening, gravity and acceleration are pulling the passengers in two opposite directions, creating a sensation of weightlessness in the riders. However, since the force of outward inertia is greater than gravity, the rider remains in the seat while upside down. Though there are safety harnesses on most roller coasters, the rider would not fall out anyway. In contrast, at the bottom of the loop, the passenger's inertial direction changes from a downward pull to a horizontal path. This alteration in direction, along with gravity, give the passengers the feeling of being very heavy.
The gravitational forces, also known as G-force, one experiences on a roller coaster are responsible for the feeling of "butterflies-in-your-stomach" as you begin to descend the loop. The normal gravitational force a person standing on Earth would feel is 1 g or -9.8 m/s^2. A person's weight is included in this of gravitational acceleration. At 2 g, a person will weigh double their weight. However, at the top of the loop, a person will experience weightlessness, and therefore will be in the state of free fall, or 0 g. This means that gravity is the only force acting upon the rider. If the top of the loop is narrow enough, the rider will experience negative G's and will be lifted out of their seat. This is what creates the "butterfly" sensation, which is known to make some riders nauseous.
The picture below is an effective visualization of these concepts.
Sources:
“Amusement Park Physics.” The Physics Classroom, www.physicsclassroom.com/class/circles/Lesson- 2/Amusement-Park-Physics.
“Centripedal Acceleration.” Centripetal Acceleration, ffden-2.phys.uaf.edu/211_fall2002.web.dir/Shawna_Sastamoinen/Centripetal.htm.
“Centripetal Force - Real-Life Applications.” Science Clarified, www.scienceclarified.com/everyday/Real-Life-Chemistry-Vol-3-Physics-Vol-1/Centripetal-Force-Real-life-applications.html.
Genetics, Nick Berry - Data. “Why Roller Coaster Loops Are Never Circular.” Gizmodo, Gizmodo.com, 24 Mar. 2014, gizmodo.com/why-roller-coaster-loops-are-never-circular-1549063718.
Harris, Tom. “How Roller Coasters Work.” HowStuffWorks Science, HowStuffWorks, 9 Aug. 2007, science.howstuffworks.com/engineering/structural/roller-coaster.htm.
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