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# Conservation of Energy

## Objectives:

To explore concepts of kinetic, potential and total energy with and without friction.

## Theory:

Kinetic Energy, KE=½mv2.

Gravitational Potential Energy PE=mgh

Total Mechanical Energy, E=KE+PE= mgh + ½mv2

Conservation of energy law:

Ef = Ei or Ef – Ei = 0 if Ffr = 0

Ef – Ei = Wfr if Ffr ≠ 0

Fg, the gravitational force, is a conservative force. The work done by the conservative force does not depend on the path. In an alternative formulation: the work done by the gravitational force only depends on the starting and ending elevations, the path taken between those points does not make any difference.

## Procedure:

The lab activity uses a simulation developed by the University of Colorado at Colorado Boulder.

· From the main page “Energy Skate Park” select “Playground”.

· (You may need to click twice.)

· From the right upper corner select: “Stick to Track” and “Speed”. Drag the 3 red dots from the bottom of the screen to design a ramp (straight line).

· Each of the three dots can be dragged individually to change the shape of the track.

· Select the “Grid” and “Reference Height” option in the lower left corner. Adjust the height = 0 reference by dragging the yellow up and down arrows so that the dashed blue line passes through the center of the lowest red dot.

· Drag the first dot to any height you wish.

· If you click on the middle dot you have the option to delete it. (X, not scissors!)

· Press the “Pause” button then place the skater on the top of the hill. Select “Slow”. The “Play” and “frame by frame” should be displayed. The picture below is a guide for the general settings with the skater at h=4m and v=6.2m/s

· There is a yellow tape measure tool in the lower right can be used to measure the height.

## Analysis:

### I Motion without friction.

· Click “Play” and watch the simulation and notice the “speedometer”. You can press “Pause” to record the exact values of speed and height in the table below as the skater goes down the hill.
The points 1-4 are part of the same run, do not start with the skater from 4 different height!

1st row, the skater starts from rest, v=0m/s, and
initial height is your choice. The last row corresponds to the skater reaching the ground level (h-0) and you need to record in the table the skater’s speed.

Choose 2 more points in the animation while the skater comes down the hill and record the heights and speeds in the table below.

You can use the “frame by frame” option to move the skater down the hill and “Reset Skater” if you want to start over.

· Calculate the initial KE, PE and total mechanical energy E for all points.

· DO NOT type the units in each cell of a table, they are in the table’s header. DO NOT include calculations in the tables, just your answers. Use rounding!

Mass of the skater, m= (
ENTER MASS HERE) kg

Move the slide bar on “Friction “to “
None” for this part of the lab.

PE= mgh

E=KE+PE

 Height (m) Speed (m/s) PE (J) KE (J) E (J) 1 0 2 3 4 0

## Questions

1. Does the Total Mechanical Energy for the skater stay the same? If you measured correctly the heights and the velocities, the answer is “YES”.

2. Place the skater at the same height that you initially started with but in the air. Click play and let the skater to free fall. What is the speed of the skater when they get to h = 0m?

Is it different than the speed from the table corresponding to h=0m?

3. What effect would you expect track-skateboard friction to have?

### II Motion with friction

Keep the same ramp that you used in part I but move the slide bar on “Friction toward “
Lots” for this part of the lab.

Place the skater on the top of the hill, select “Pause” and “Restart Skater” such as the frame by frame option is available.

Repeat the steps from part I of the lab activity and complete the table below.

 Height (m) Speed (m/s) PE (J) KE (J) E (J) 1 0 2 3 4 0

## Questions

1. Does the Total Mechanical Energy for the skater stay the same?

## image1.png

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