Conservation of ENERGY
PURPOSE: To study the law of conservation of energy.
THEORY: The law of conservation of energy states that energy is neither created nor destroyed. It changes forms. The kinds of energies examined in this experiment are kinetic energy and potential energy.
Kinetic energy is energy of motion. It is equal to the amount of work that must be done to accelerate an object from rest to that velocity. Kinetic energy is given by
KE = ½ M V²
where M is the mass of the object and V is the velocity. The units of energy is Joule (1 Joule =
kg m / s²).
Potential energy is the energy of position. It is equal to the work that must be done to change the position of the object. Potential energy is relative. The value of potential energy depends on the location of the point that is defined as the zero position. Gravitational potential energy is given by
PE = M g H
where M is the mass, g is the gravitational acceleration (9.81 m / s²), and H = D Y is the vertical distance above the zero point for potential energy.
The total energy an object has is the sum of its potential and kinetic energies. The conservation law states that this sum must be constant. Mathematically this would be
KE1 + PE1 = KE2 + PE2
or
½ m (V1)² + m g H1 = ½ m (V2)² + m g H2
In this experiment the initial total energy will be compared with the final total energy.
EQUIPMENT: Computer and VideoPoint software.
PROCEDURE: There are several video files from which to chose. From the "PASCO" subdirectory chose one of the following: pasco51, pasco52, pasco53, and pasco54. With the VideoPoint software mark the position of car on the top track. Pick a regions at the ends of the track where the height is constant. Find the average height of those points. The velocity should be constant in this region and the average velocity can be found by dividing the distance traveled by the elapsed time while in these regions. The mass of the object in the experiment are given on the first frame of the video. The total energy can be calculated from these heights, velocities, and mass. The total energy in these two regions will be calculated and the percent difference calculated.
STEP - BY - STEP Procedure for VideoPoint
Start VideoPoint.
Click left mouse button while the pointer is anywhere inside the "about VideoPoint" dialogue box.
In the "open" dialogue box do the following.
Select the drive letter of the CD drive in which VideoPoint is located.
Select movies folder and the appropriate folder under movies (here the "pasco" folder).
Under filename select the appropriate file to be loaded.
Press "OK".
The "Number of points" dialogue box will appear. Make sure "1" is selected and press "OK". The movie and software should now be loaded.
On the menu bar select "Movie" and "Full Screen" using the left mouse button.
Record data -When the cursor is inside the movie screen it appears as a target. Place this target cursor on a point on the top cart and press the left mouse button, the movie will advance one frame and the data is recorded. Repeat this process until all frames of the movie have been used. Be consistent and use the same point on the cart each time to record the data. Ignore any carts moving on lower tracks, they can be used for relative velocity experiments
Calibrate the movie.
Move the cursor to the "meter stick" tool button at the left of the screen (6th button from top) and click the left mouse button.
The "Scale Movie" dialogue box appears. Select continue with the left mouse button.
Put the target cursor on the left end of the meter stick in the first movie frame and press left mouse button - repeat for the right end of the meter stick.
On the menu bar select "Movie" and "Normal Size".
Transfer the data to your data table
With cursor inside table area click left mouse button to
select table.
Put mouse in title area of table and click and hold left mouse
button and drag the
table to top of window.
Place the pointer on lower right corner of table (cursor should be double arrow) and drag the corner of the table to make the table larger so all the data can be seem.
Record the time the Y-position and the X-position of data in data table.
The scroll bars can be sued to view all of the data
QUESTIONS:
1. What are some other types of energies.
2. Since kinetic energy depends on the velocity is it a vector quantity.
3. How would one write the conservation of energy equation to account for energy losses due to friction.
4. Is total energy lost or gained in this experiment.
DATA TABLE
N |
t |
X |
Y |
N |
t |
X |
Y |
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units |
units |
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1 |
16 |
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2 |
17 |
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3 |
18 |
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4 |
19 |
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5 |
20 |
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6 |
21 |
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7 |
22 |
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8 |
23 |
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9 |
24 |
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10 |
25 |
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11 |
26 |
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12 |
27 |
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13 |
28 |
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14 |
29 |
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15 |
30 |
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N |
t |
X |
Y |
N |
t |
X |
Y |
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units |
units |
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31 |
46 |
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32 |
47 |
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33 |
48 |
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34 |
49 |
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35 |
50 |
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36 |
51 |
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37 |
52 |
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38 |
53 |
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39 |
54 |
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40 |
55 |
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41 |
56 |
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42 |
57 |
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43 |
58 |
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44 |
59 |
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45 |
60 |
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Mass of car m = __________
At height H1 Average height H1 = __________
Distance traveled in X direction and time elapsed while at height H1
Xo = __________ To = __________
Xf = __________ Tf = __________
X = X f - Xo = __________ T = T f - To = __________
Velocity while at H1 V = X / T = __________
At height H2 Average height H2 = __________
Distance traveled in X direction and time elapsed while at height H2
Xo = __________ To = __________
Xf = __________ Tf = __________
X = X f - Xo = __________ T = T f - To = __________
Velocity while at H2 V = X / T = __________
Energy
E1 = ½ m (V1)² + m g H1 = __________
E2 = ½ m (V2)² + m g H2 = __________
Percent difference = __________