You have been asked by your supervisors at A&L Engineeringto design a roller coaster for a new theme park. Because thisdesign is in the initial stages, you have been asked to create atrack for the ride. Your coaster should have at least two peaks andtwo valleys, and launch from an initial height of 75 meters. Eachpeak and valley should represent a vertical change of at least 20meters. In your design, you should plan for a mass between 400 and600 kilograms.

Once you have designed the track, you have been asked tocalculate the kinetic energy, potential energy, momentum, and workdone by the cart at various points throughout the track. Unlessotherwise stated, you can ignore the effects of friction. Followingyour calculations, you have been asked to describe the energytransfers detailed by these equations.

Directions

To complete this roller coaster design report, complete thefollowing:

1. Create a diagram of a roller coaster track containingat least two peaks and two valleys. As you complete yourreport, you may wish to design a more complicated coaster. However,it should still have two peaks and two valleys that meet therequirements below and that you are comfortable using incalculations and descriptions of energy and momentum. Your diagramshould include the following information:
   • An initial height of 75 meters
   • At least two peaks and two valleys representing drops of over20 meters
   • A set mass for your roller coaster cart between 400 and 600kilograms

1. Calculate the kinetic energy, potential energy, andmomentum of the cart at the initial drop for both peaks,and for both valleys. If your coaster has more than two peaks andtwo valleys, select which peaks and valleys you wish to use in yourcalculations and clearly mark them on your diagram. In yourcalculations, be sure to explicitly state the equations you use andwhat values you will be substituting to calculate the finalvalue.

1. Describe the energy transfers that occur as the cartmoves along the track. This should be a narrativedescription of the energy transfers that occur at the initiallaunching point, peaks, and valleys. In your descriptions, addressthe following:
   • At each of the identified points, how was kinetic energytransferred to potential energy, and vice versa?
   • What happens to the total energy of the cart as it moves alongthe track? Why?
   • How is the principle of conservation of energy applied in thissituation?

In addition to your description of the motion of the cart on thetrack, you have been asked to model the motion of the cart as itcomes to a stop at the end of the coaster. For these calculations,assume that the cart will inelastically collide with a cart ofequal mass at rest on a flat surface.

1. Calculate the momentum and kinetic energy of the cartbefore and after an inelastic collision. In yourcalculations, be sure to explicitly state the equations you use andwhat values you will be substituting to calculate the finalvalue.

1. Describe the energy transfers that occur as a cartinelastically collides with an object of equal mass atrest. This should be a narrative description of the energytransfers that occur as the cart inelastically collides with a cartof equal mass. In your descriptions, address the following:
   • What was the kinetic energy of each cart before and after thecollision?
   • What happens to the total energy of the system, now includingboth carts, as a result of the inelastic collision?
   • Describe how the principle of conservation of energy is appliedin this situation.

Following the inelastic collision of the carts, the two cartsfuse into an object with double the mass of the original cart.There is then a frictional section of the track to slow the cart toa stop over 20 meters. Describe the amount of work due to frictionand frictional force exerted to stop both carts over 20 meters.

1. Calculate the work due to friction and frictionalforce. In your calculations, be sure to explicitly statethe equations you use and what values you will be substituting tocalculate the final value.

1. Describe the energy transfers that occur as the cart isbrought to a stop. This should be a narrative descriptionof the energy transfers—written to describe these concepts to anontechnical audience—that occur as the cart is brought to a stop.In your descriptions, address the following:
   • What is the kinetic energy of the cart system before and afterit has been brought to a stop?
   • What happens to the total energy of the system as a result ofthis change in motion?
   • Describe how the principle of conservation of energy is appliedin this situation.