Roller Coaster Physics

Trivia Quiz Answers

- The forces exerted on riders of roller coasters are usually expressed in units of G's. If a person weighs 150 lb
_{f}, what would the force be in lb_{f}at the top of a loop if it is equal to -1.5 G's?

G force is defined as the net force on an object divided by the weight of that object. Thus, if the net force on the person is -1.5 G's, it is equal to (-1.5)(150 lb_{f}) = -225 lb_{f}. The negative sign indicates that the force is directed downward.

- The force exerted on a roller coaster rider traveling through a loop is called centripetal force. What is the difference between the
centripetalforce andcentrifugalforce?

As stated in Newton's Third Law of Motion, whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first. In the case of a roller coaster rider moving through loop, the force that thecar seat exerts on the rideris called the centripetal force. The equal and opposite force that therider exerts on the car seatis called the centrifugal force.

- In a real roller coaster, the shape of vertical loops are never circles of constant radius. Why?

The centripetal force in a loop is proportional to the speed. When a roller coaster car enters a loop at the bottom at high speed, the velocity decreases as it nears the top. Thus, the centripetal force at the top is less than at the bottom. It turns out that for a large loop, the difference in speed is so great that the combined affect of gravity and the centripetal force at the bottom will be dangerously high (risking injury) in order for there to be enough force pushing the rider upward at the top (so that he won't fall out of his seat).

- The geometric shape used for loops in real roller coasters has a special name (it is not a circle or ellipse). What is it called?

A klothoid (or sometimes spelled clothoid). A klothoid has a continuously varying radius of curvature that is large at the bottom and small at the top. To learn why this shape is preferable to a circle, see theandCoaster Dynamics Physics PrimerCoaster Lab Lesson #8.

- If a roller coaster car were to roll over the top of a hill and then drop downward as if it were in free fall, what geometric shape would the path take?

A parabola.

- For a traditional, once-around loop roller coaster, with a single lift hill, where does the energy come from that powers the cars around the track? Where does the energy go?

All the energy comes from the work done to pull the train of cars up the lift hill. This is stored as potential energy. That energy is then converted into motion (kinetic energy) and is eventually consumed by the non-conservative forces acting on the cars -- mostly friction from the wheels, and air resistance.

- Roller coaster builders often brag about having the highest and steepest hills. If roller coaster A has a 300 ft high hill with a descent angle of 80°, and roller coaster B has a 310 ft high hill with an angle of 70°, which roller coaster will have the faster speed at the bottom of the hill?

Roller coaster B. If non-conservative forces (such as friction and air resistance) are neglected, the change in speed when going down a hill dependsonlyon the net change in height. However, a steeper descent angle will produce a higher acceleration (if the steepness does not exceed the free fall trajectory). Faster acceleration has an exhilarating physiological affect on riders... so, some may feel that roller coaster A has a more thrilling ride, despite its lower peak speed.

- If measured from two fixed points on the track, one shortly before and one shortly after the top of a hill, when a train of roller coaster cars travels over the hill, which car will have the fastest average and maximum speeds -- the first or last car in the train?

This is a trick question. Actually, the average and maximum speeds for the first and last cars are exactly the same (assuming we neglect the affect of non-conservative forces, such as friction and air resistance). However, thereisa difference in the motion between the first and last cars, which can make one or the other likely to provide a more thrilling ride. See Chapter #12 of thefor a discussion of this topic.Coaster Dynamics Physics Primer

- A new genre of roller coasters was introduced in the past decade featuring "linear induction motors" that "launch" roller coaster trains at extremely high acceleration rates (and at speeds up to 100 mph). For what purpose was linear induction motor technology originally developed?

Linear induction motor technology was developed by NASA during conceptual studies investigating the feasibility of alternate means of sending payloads into earth orbit (other than the Space Shuttle). The concept originally studied was to use a large linear induction motor to "shoot" payloads into earth orbit, destined for a permanently orbiting space station. After initial studies and feasibility testing of the technology, the proposal was abandoned. However, the project definitely wasn't a loss... since it spawned a new "space-age" of thrilling roller coasters!

- What is the name most frequently given to roller coasters throughout the history of amusement parks?

Cyclone. One of the earliest, and most famous, roller coasters ever built was theConey Island Cyclone, opened in 1927 at Coney Island, New York. Through the decades, that coaster has inspired dozens of replicas and hundreds of other roller coasters throughout the world namedCyclone, or coasters withCycloneas part of its name.

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