Investigation 10A: Inclined plane and the conservation of energy

Essential questionsWhat law governs the energy transformations of motion on an inclined plane?
This investigation uses a cart on a frictionless track to explore how gravitational potential energy and kinetic energy change as motion changes. For example, if you want to design a roller coaster to reach 30 mph, how high must it be at the start?
Part 1: Changes in energy for motion down an inclined plane

  1. Set up your equipment as in the picture. The plunger on the cart should be facing the end stop, and the ramp should have an incline of 15°.
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  1. Open file 10A_ApplyingConservationOfEnergy, and connect your Smart Cart using Bluetooth.
  2. Explore the motion of the cart on the ramp. Start recording data with the cart at the bottom of the ramp, then roll it to the top of the ramp and release it. Stop recording when the cart reaches the bottom. Answer the questions for the time the cart was rolling down the ramp.
  1. Sketch position and velocity. What are the shapes of the graphs? Why do you get these shapes?
  2. Sketch kinetic energy and potential energy. What are the shapes of the graphs? Why?
  3. What is the sum of the kinetic and potential energies at the top of the ramp when the cart is released? At the bottom? How are their changes related to each other?
  4. What is the speed at the bottom of the ramp? Try adding mass to the cart and take another set of data. How does the speed change in each case? Why?
Use this interactive simulation of an inclined plane to do Part 2 of the investigation and answer the questions. You can change the angle of inclination of the inclined plane as well as the initial height and velocity of the cart. You can also choose which physical quantities to graph: displacement, velocity, kinetic energy, or gravitational potential energy.
Part 2: Designing a roller coaster that reaches 30 mph

  1. Convert 30 mph into units of m/s. Make this the final speed of the block at the bottom of the ramp.
  2. Set the mass of the roller coaster to m = 2,000 kg.
  3. Vary the simulation parameters—such as the vertical height h0 or inclination angle θ—to produce a speed of 30 mph at the bottom of the ramp.
  4. The fastest roller coaster in the United States reaches a maximum speed of 128 mph. Use the interactive simulation to estimate the height of this roller coaster.
  1. How does changing the steepness of the roller coaster (while keeping the same initial height) affect the speed at the bottom of the ramp? Why?
  2. How does changing the mass of the roller coaster change its speed at the bottom? Why?
  3. Research the actual height of the roller coaster in step #4. How well does your estimate agree with it?

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