Lab 3.1: Mechanical Energy of a Cart on an Inclined Plane

Question:
Is energy conserved for a cart rolling down an inclined plane on a frictionless surface?

Purpose:
The purpose of this lab is to use use previous knowledge of velocity to perform kinetic energy calculations, make calculations of gravitational potential energy and to determine what affects GPE and KE more.

The mechanical energy, the sum of the kinetic energy and gravitational potential energy, is said to be conserved for an object moving only under the influence of the gravitational force. That is, the mechanical energy remains constant throughout the motion of the object. This is known as the conservation of mechanical energy.

AP® Learning Objectives​:

• 4.C: Interactions with other objects or systems can change the total energy of a system.
  • ​4.C.1 :The energy of a system includes its kinetic energy, potential energy, and microscopic internal energy. Examples should include gravitational potential energy, elastic potential energy, and kinetic energy.​
• 5.B: The energy of a system is conserved.
  • ​5.B.1: Classically, an object can only have kinetic energy since potential energy requires an interaction between two or more objects.
  • 5.B.3: A system with internal structure can have potential energy. Potential energy exists within a system if the objects within that system interact with conservative forces.

Materials 
Required include, but are not limited to:
 

• Dynamics Cart and Track
• Track Inclinometer
• Motion Detector

Setup

Procedure (well ... part of it)

1. Set up the ramp and motion detector as shown above. The ramp should be inclined at an angle of 10° above the horizontal. Use the inclinometer to measure the angle. Remember that potential energy is relative, and we can set the zero of potential energy anywhere we want it to be. Let‘s agree to set it to be zero at the bottom. Then, when we hold the cart at rest at the top of the ramp at a height of y0 from the table, the gravitational potential energy is mgy0 . As it rolls down the ramp, this potential energy decreases. Its value at any position y is given by 
   GPE = mgh.
2. What values for GPE will you need to calculate? Create a table for collecting necessary data. Remember that you are trying to prove that GPE + KE is the same thought the entire system.
3. ​Prediction: As the cart rolls down the ramp, how will the kinetic energy change? How will the gravitational potential energy change? How will the mechanical energy change?
4. Verify that the motion detector ―sees the cart all the way along the ramp and that the ramp is set at a 10° angle.
5. Save your data and email it to yourself.

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Your lab report will include the following

• Title: on the front cover of your lab notebook and on the top of page 1
• Purpose / Objective: states the purpose of the lab
• Apparatus: list of materials used in the lab
• Setup: a diagram of the setup
• Procedure: the steps to recreate the lab
• Data: clear and organized measurements made during the lab

• Calculations: provide calculations in a neat and orderly outline form

• Conclusion: completely answer the question using complete sentences

• Discussion of Results: explanation of how the collected data provides support for the statement found in the conclusion; include an error analysis comparing your group's result to the class average

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