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Use a diagram of a roller coaster track containing at least two peaks and two valleys

Physics

Use a diagram of a roller coaster track containing at least two peaks and two valleys.
 The diagram should include the following information:

An initial height of 75 meters
At least two peaks and two valleys representing drops of over 20 meters
A set mass for your roller coaster cart between 400 and 600 kilograms


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

Describe the energy transfers that occur as the cart moves along the track. This should be a narrative description of the energy transfers that occur at the initial launching point, peaks, and valleys. In your descriptions, address the following:

At each of the identified points, how was kinetic energy transferred to potential energy, and vice versa?
What happens to the total energy of the cart as it moves along the track? Why?
How is the principle of conservation of energy applied in this situation?


Calculate the momentum and kinetic energy of the cart before and after an inelastic collision. In your calculations, be sure to explicitly state the equations you use and what values you will be substituting to calculate the final value.

Describe the energy transfers that occur as a cart inelastically collides with an object of equal mass at rest. This should be a narrative description of the energy transfers that occur as the cart inelastically collides with a cart of equal mass. In your descriptions, address the following:

What was the kinetic energy of each cart before and after the collision?
What happens to the total energy of the system, now including both carts, as a result of the inelastic collision?
Describe how the principle of conservation of energy is applied in this situation.


Calculate the work due to friction and frictional force. In your calculations, be sure to explicitly state the equations you use and what values you will be substituting to calculate the final value.

Describe the energy transfers that occur as the cart is brought to a stop. This should be a narrative description of the energy transfers—written to describe these concepts to a nontechnical 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 after it has been brought to a stop?
What happens to the total energy of the system as a result of this change in motion?
Describe how the principle of conservation of energy is applied in this situation.b

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