Work and Energy

Energy conservation for an isolated system is a fundamental principle of physics.  Energy for an isolated system is always conserved.  It may change forms, but the total amount of energy in an isolated system is constant.  Energy can, however, be converted from one form to another form.  Work is the conversion of one form of energy into another.  Energy comes in different forms, kinetic energy, potential energy, chemical energy, thermal energy, etc.  If an object has energy, it has the potential to do work. 

There are several forms of potential energy.  Kinetic and potential energy are called mechanical energy or ordered energy.  Thermal energy is disordered energy.  Friction converts mechanical energy into disordered energy.  When no disordered energy is produced, then mechanical energy is conserved.

Today we will track the mechanical energy in various systems and explore the relationship between work and energy.

Open a Microsoft Word document to keep a live journal of your experimental procedures and your results.  Include all deliverables, (data, graphs, analysis, outcome).  Write a 'mini-reflection' immediately after finishing each investigation, experiment or activity, while the logic is fresh in your mind.

Exploration

Use an on-line simulation from the University of Colorado PhET group to track mechanical energy in a skate park.
Link to the simulation: https://phet.colorado.edu/en/simulations/energy-skate-park-basics

• You can build tracks, ramps and jumps and view graphs of kinetic energy, potential energy and friction as the skater moves.

(a)  Click the Playground image.  Explore the interface!
Note:

• You can Pause the simulation and then put the Skater anywhere.  Restart Skater returns the Skater to this spot and you can rerun the scenario.
• You can fix the skater to the track or let him loose contact with the track.

(b)  Design your own frictionless track.  You can ask for some design guidelines in the discussion forum.

• Design a track that is fun, challenging and relatively safe.  Use the Energy Graphs to track the Skater's mechanical energy.  Decide which graphs or charts best help you understand what makes your track successful.
• Ask an AI: 'I am designing a PhET Skate Park track with a loop.  What is the minimum height the skater must start from to complete the loop without falling off, and why?'   Use the simulation to test the AI's claim.  Was the AI was right?  Why?

(c)  Add friction to your track.

• Explain what changes in the simulation when you add friction.  Paste you explanation of friction into an AI with this prompt: 'I am a physics student. Here is my explanation of how friction affects energy in a skate park: [Insert Explanation].  Play the role of a skeptical physics professor and point out any gaps in my logic or ask me two challenging follow-up questions.  Include the AI's "critique" and your rebuttal in your journal.

Exploration Deliverables: (to be included in the your journal)

• Analysis:  What makes a successful track in terms of conservation of mechanical energy?  Refer to your conversation with the AI and Charts or Graphs to explain your reasoning.

• Outcome:   A picture of a successful track with a loop that you have designed.

Experiment

One end of a spring is attached to a rigid support.
Different weights are hung on the other end, and the spring stretches to different lengths.

Procedure:

• In the pictures below measure the position of the free end of the spring as a function of the applied force.  Always measure the position of the same physical point. 
• Measure the position in units of meter and the force in units of Newton.  Enter your data into a spreadsheet.  Your first rows should look similar to this.

• Use the spreadsheet to plot the applied force versus the position of the free end of the spring.
  Scatter plot:  Vertical axis: force,  Horizontal axis: position.
• Use the spreadsheet's trendline to determine slope of the straight line that best fits the data.  Format the trendline label to show a number with at least 2 decimal places.
  Since F_applied = kx,  ∆F_applied = k∆x, and the slope of the straight line will be equal to the spring constant k.
  What is the equilibrium position x_equ of the free end of the spring in units of cm, i.e. in your graph, what is x (in m) when y = 0?
  You can also provide your table of data to an AI with this prompt:  'I have table with columns "position" and "force" for the free end of a spring.  Write a Python script using Matplotlib to calculate the slope and plot force versos position.'  Run this code in Google Colab.  How does the AI's value  for k compare to your Excel trendline?

Add two columns to your spreadsheet.  For each position, enter the elastic potential energy stored in the spring, ½k(x - x_equ)², and the work done by gravity, mg(x - x_equ) = F(x - x_equ).

Gravity does work, converting gravitational potential energy into other forms. 

• Is the gravitational potential energy lost equal to the elastic potential energy stored in the spring?
• Use AI to explain why for a real-world springs the ravitational potential energy lost may not be ual to the elastic potential energy stored in the spring.
• Plot ½k(x - x_equ)² (J) versus position (m) using your data.
  

Experiment 1 Deliverables: (to be included in the your journal)

• Visuals:  Data table and labeled plots of force versus position (Excel or Python, including trendline) and elastic potential energy stored in the spring versus position (Excel).

• Analysis:  For masses hanging from a spring in equilibrium you have plots of force versus position of the free end, and elastic potential energy stored in the spring versus position of the free end. What can you learn from these plots?

• Outcome:  The values (with units) of the spring constant and the equilibrium position.

Convert your log into a lab report.

Name:
E-mail address:

Laboratory 4 Report

• Make sure you completed the entire lab and answered all parts.  Make sure you show your work and inserted and properly labeled relevant tables and plots in your journal.
• Add a summary reflection at the end of your report in a short essay format.

Save your Word document (your name_lab4.docx), go to Canvas, Assignments, Lab 4, and submit your document.