Ask a New Question
Menu

Energy Transformations

Project: Modeling Conservation of Energy
For this assignment, you will develop a model that shows a roller coaster cart in four different positions on
a track. You will then use this model to discuss the changes in potential, kinetic, and thermal energy of
the cart as it moves along the track.
Background Information
The two most common forms of energy are potential energy and kinetic energy. Potential energy is the
stored energy an object has due to its position. When related to the height of an object in a gravitational
field, potential energy is known as gravitational potential energy. Kinetic energy is the energy an object
has due to its motion. A third form of energy, thermal energy, is an internal energy due to the motion of
the particles in an object. Thermal energy can be a result of friction generated while an object is in
motion. In most situations, thermal energy cannot be transformed to kinetic or potential energy. While an
object’s potential, kinetic, and thermal energies will vary, the total amount of energy stays the same.
Energy transformations can be represented by pie charts. The total energy in the system is represented
by the size of the pie. If energy flows into or out of the system, the size of the pie is increased or
decreased to represent the change in energy within the system. Pies are divided according to the forms
of energy present in the system. Energy transformations are represented by changing the size of the
division or the number of the divisions as time progresses.

1 answer

Energy Transformations Project: Modeling Conservation of Energy in a Roller Coaster

Project Overview

In this project, we will create a model of a roller coaster cart moving along a track at four different positions. At each position, we will analyze the changes in gravitational potential energy, kinetic energy, and thermal energy and represent these changes using pie charts.

Key Concepts

  • Potential Energy (PE): The energy possessed by an object due to its position relative to others. For a roller coaster, this is primarily gravitational potential energy (PE = mgh, where m = mass, g = acceleration due to gravity, h = height).

  • Kinetic Energy (KE): The energy an object possesses due to its motion. It is calculated using the formula KE = 1/2 mv² (where m = mass and v = velocity).

  • Thermal Energy (TE): The energy related to the temperature of an object or the sum of the kinetic energy of particles within it. In the context of a roller coaster, it may increase due to friction between the cart and the track.

  • Conservation of Energy: The total mechanical energy (PE + KE) in a closed system remains constant when ignoring losses (like thermal energy due to friction).

Model Positions

We will consider the roller coaster cart at four different positions on the track: Position A (the highest point), Position B (the descent), Position C (the lowest point), and Position D (the ascent).

Energy Analysis at Each Position

  1. Position A (Highest Point)

    • Height (h): Maximum
    • Potential Energy (PE): Maximum (PE = mgh)
    • Kinetic Energy (KE): Minimum (the cart is momentarily at rest)
    • Thermal Energy (TE): Low (assuming negligible friction occurs at this point)

    Pie Chart Representation:

    • PE: 90%
    • KE: 0%
    • TE: 10%

  2. Position B (Descending)

    • Height (h): Decreasing
    • Potential Energy (PE): Decreasing
    • Kinetic Energy (KE): Increasing (cart speeds up as it descends)
    • Thermal Energy (TE): Slightly increasing due to friction

    Pie Chart Representation:

    • PE: 70%
    • KE: 20%
    • TE: 10%

  3. Position C (Lowest Point)

    • Height (h): Minimum
    • Potential Energy (PE): Minimum
    • Kinetic Energy (KE): Maximum (cart has maximum speed)
    • Thermal Energy (TE): Increases due to maximum friction

    Pie Chart Representation:

    • PE: 10%
    • KE: 80%
    • TE: 10%

  4. Position D (Ascending)

    • Height (h): Increasing
    • Potential Energy (PE): Increasing
    • Kinetic Energy (KE): Decreasing (cart slows down while moving up)
    • Thermal Energy (TE): Remains steady or slightly increases due to friction

    Pie Chart Representation:

    • PE: 60%
    • KE: 30%
    • TE: 10%

Discussion Points

  • As the roller coaster cart moves along the track, energy continuously transforms from one form to another, demonstrating the conservation of total energy.
  • At the highest point, potential energy is at its maximum, and kinetic energy is minimal.
  • As the cart descends, gravitational potential energy transforms into kinetic energy, causing an increase in speed.
  • At the lowest point, the cart's speed is greatest, maximizing kinetic energy while potential energy decreases.
  • During ascent, kinetic energy decreases while potential energy increases, indicating energy transformation.
  • The small amount of thermal energy indicates energy lost due to friction, but this does not significantly affect the overall energy flow in a high-level analysis.

Conclusion

This project highlights the principles of energy transformation and conservation within a roller coaster scenario. By using pie charts to represent the distribution of energies at various points on the track, you can visually interpret how energy shifts from potential to kinetic and the minor thermal losses experienced along the way.