## Lab 4

### 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 log of your experimental procedures and your results.  This log will form the basis of your studio session report.  Address the points highlighted in blue.  Answer all questions.  Include the information that your answers are based on.

Exploration

Use an on-line simulation from the University of Colorado PhET group to track mechanical energy in a skate park.

• 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.  Paste a picture of your track into your log.
• 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.
• Explain why your track is successful in terms of conservation of mechanical energy.  Refer to Charts or Graphs to help explain your reasoning.
• Using conservation of mechanical energy, explain what things need to be considered when designing any successful track.

• Explain what changes in the simulation when you add friction.  How does the energy distribution change?

### 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.
 position (m) force (N) 0.22 0.1 0.255 0.2
• 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 Fapplied = kx,  ∆Fapplied = k∆x, and the slope of the straight line will be equal to the spring constant k.
What is the value of the spring constant k (magnitude and units)?
What is the equilibrium position xequ of the free end of the spring in units of cm, i.e. in your graph, what is x (in m) when y = 0?              Add two columns to your spreadsheet.  For each position, enter the elastic potential energy stored in the spring, ½k(x - xequ)2, and the work done by gravity, mg(x - xequ) = F(x - xequ).

 position (m) force (N) ½k(x - xequ)2 (J) mg(x - xequ)  (J) 0.22 0.1 0.255 0.2

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?
If not, approximately how much of the work done by gravity is stored in the spring, and what do you think happened to the rest of it?