*Is It More Thrilling to Ride at the Front or the Back of a Roller Coaster*

Roller coasters are considered to be some of the best games to increase people’s adrenaline levels. Their popularity is due to the high speed, the sudden move of the vehicle and some effects built in the ride. However, there is physics behind the design and the curves of these devices. The below paper is attempting to reveal the rules and laws that effect people’s experience during the ride and try to answer the question: “Is it more thrilling to ride at the front or the back of a roller coaster?”

**Understanding Energy**

Energy does not get created or destroyed: it always stays the same within the system. This is called The Conversation of Energy. This also means that once the roller coaster is started it cannot gain more energy. The only thing that happens is that energy gets transformed from one form into another. The movement between kinetic and potential energy or heat energy creates the thrill in the ride. Kinetic energy is the energy of motion, and it has a connection with the object’s velocity. When the potential energy of the roller coaster goes down the kinetic energy goes up, and the sum of the two always needs to be equal. Below we are examining the different phases of the ride from an energy perspective.

** Top of the hill. **The kinetic energy is zero, as the velocity of the car is zero, while the potential energy is high.

** Bottom of the hill. **The velocity of the car is high, as well as the kinetic eneregy. While the height is zero (at the bottom of the hill) the potential energy gets reduced to zero. Therefore, all the potential energy has transformed into kinetic energy.

** Halfway down the hill. **This position represents the balance between kinetic and potential energy. Half of the potential energy is transformed into kinetic energy.

** Drop. **When the speed during the downhill ride is high, people stop feeling their weight is called free-fall.

** Friction. **It is also important to note that energy is lost through friction. That is the reason why the first hill of the ride is always the highest. The initial energy needs to be higher than the total energy needed for the next hills plus the energy lost during friction.

**Variables Determining the Quality of the Ride**

** Hill.** The hill has a role in the conversation of the energy. If the velocity of the car did not change the conversation of potential energy into kinetic energy would not happen.

** Drop.** Free-fall feeling as a result of the seat pushing the person upwards. If the seat was removed, this experience would not be present. This is when Zero g is reached.

* Curves. *These determine intertia.

* Loop. *This feature of roller coasters creates centripetal force on the human body.

**Other Variables: Velocity and Acceleration**

* Velocity* determines how fast something travels and is measured in seconds per meters.

* Acceleration* measures how fast an object changes its velocity.

**Newton’s Laws of Motion **

Newton states that “An object moving at a certain speed in a certain direction will continue moving at that same speed and direction unless acted upon by an outside force.” This is called the Law of Inertia. You can see this law in action during hoops, curves and when the roller coaster changes speed or direction.

According to Newton’s Second Law, “the force is equal to mass times acceleration”. The result is that the larger an object is and the faster it changes direction or speed, the higher the force is. This can be experienced during sharp bends and changing speed (downhill).

Newton’s Third Law says that “for every action there is an equal and opposite reaction”. This law can be proven when observing the pressure applied on the body throughout the ride. This force is generally greater when somebody sits at the back of the roller coaster. Similarly, for feeling “weightlessness” it is better to sit at the back.

** ****Conclusion: Is It More Thrilling to Ride at the Front or the Back of a Roller Coaster?**

In the above paper we have determined several laws that can be applied to roller coasters, have seen them working during the ride. However, in order to fully understand the physics of roller coasters, there is a need for a complete analysis, as well as measurements. The below overview of project and variables to be measured will enable the authors to prove the thesis: “Because Newton’s Third Law is more applicable for the back of the roller coaster than the front, it is more thrilling to ride at the back. In the example, the authors would like to examine a Renegade run K’NEX Roller Coaster using pre-determined measurements.

**Measurements**

** Length and Height. **The length and height of the roller coaster would be important to determine which position is more “thrilling.

** Weight of the Roller Coaster. **As velocity depends on the weight, it is important to measure the full weight of a car.

** Height of first hill / highest point, cm. **Measuring the height of the first (highest) hill is also important to determine acceleration and velocity.

** Height of lowest point on track, cm. **This would create the full “drop” measure which would be used to determine the energy used and the pattern of transforming potential energy into kinetic energy as a whole.

** Total Track Length, cm. **This is required to measure average speed and velocity throughout the ride.

** Change in Height (highest – lowest), cm. **This would be measured in every section of the roller coaster, in order to measure velocity.

** Time to complete one ride in seconds. **Average velocity would be determined using this data and the total length of the track.

** Average ride velocity. **Calculated from the time to complete the ride and total length.

** Number of loops. **This would be recorded to examine the gravity and the Third Law of Newton

** Loop sizes. **These would also be recorded to see the force applied to the body in seconds.

K’NEX Roller Coaster Data Analysis

*The below measurements show the velocity of the ride.*

The velocity of the car in the beginning of the ride is zero, as well as the kinetic energy. As potential energy is on the 100 percent level in the beginning it slowly starts to decrease as the car starts off downhill. In the middle of the hill the potential energy equals kinetic energy, it hits 50 percent of the total energy of the object. In the bottom of the hill, however, the kinetic energy decreases to zero, as well as the velocity, while the potential energy reaches the maximum 100 percent.

**Graphs for the Loops and G Force**

When the car moves along the circular path at any speed an inward force is applied that is described in Newton’s Third Law. The force of gravity acts against normal force, and their interaction creates the feeling of weightlessness.

**References**

Feynman, R. P.; Leighton, R. B.; Sands, M. (2005)*. The Feynma Lectures on Physics. Vol. 1 (2nd ed.). **Newton’s Laws of Motion. *

Newton, Isaac, “Mathematical Principles of Natural Philosophy”, 1729 English translation based on 3rd Latin edition (1726), volume 2, containing Books 2 & 3.

MIT Physics video lecture on Newton’s three laws. http://ocw.mit.edu/courses/physics/8-01-physics-i-classical-mechanics-fall-1999/

Motion Mountain – an on-line textbook. http://www.motionmountain.net/