Sample Lab Report
CONSERVATION OF ENERGY ON AN INCLINED PLANE
Larry Brown
Curly Jones
Moe Smith
Thursday, Jan. 8, 2004
Lab Section #2
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Table 1. Inclined Plane Data Table
Mass of glider (g)
Delta T (s)
Angle of incline (deg)
Time
(s)
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3.0
3.1
3.2
3.3
3.4
3.5
4.0
4.1
Position
(cm)
198.43
196.85
195.20
193.06
191.05
189.29
186.75
184.50
182.29
179.70
176.75
173.91
170.92
167.76
164.50
161.28
157.83
153.97
150.49
146.43
142.54
138.51
134.38
130.25
125.77
121.37
116.81
220
0.0500
2.70
Velocity
(m/sec)
0.316
0.330
0.428
0.402
0.352
0.508
0.450
0.442
0.518
0.590
0.568
0.598
0.632
0.652
0.644
0.690
0.772
0.696
0.812
0.778
0.806
0.826
0.826
0.896
0.880
0.912
0.932
Potential
Energy (J)
0.2015
0.1999
0.1982
0.1961
0.1940
0.1922
0.1897
0.1874
0.1851
0.1825
0.1795
0.1766
0.1736
0.1704
0.1671
0.1638
0.1603
0.1564
0.1528
0.1487
0.1448
0.1407
0.1365
0.1323
0.1277
0.1233
0.1186
Kinetic
Energy (J)
0.0110
0.0120
0.0202
0.0178
0.0136
0.0284
0.0223
0.0215
0.0295
0.0383
0.0355
0.0393
0.0439
0.0468
0.0456
0.0524
0.0656
0.0533
0.0725
0.0666
0.0715
0.0751
0.0751
0.0883
0.0852
0.0915
0.0955
Total
Energy (J)
0.213
0.212
0.218
0.214
0.208
0.221
0.212
0.209
0.215
0.221
0.215
0.216
0.218
0.217
0.213
0.216
0.226
0.210
0.225
0.215
0.216
0.216
0.212
0.221
0.213
0.215
0.214
Sample Calculations
Notes:
1.) The position data column represents the distance from the sonar unit to the glider.
2.) The frequency of the sonar unit was 20 Hz, which translates into a ∆t of .0500 seconds.
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Velocity Calculation:
Velocity is defined as:
∆Position
∆time
Each entry in the velocity column was calculated as:
Sample calculation:
Pn − Pn+1
∆t
198.43 − 196.85
0.005
Potential Energy Calculation:
Potential energy is defined as PE = (mass) (acceleration of gravity) (height).
Given that the data can be thought of as the hypotenuse of a right-hand triangle, the height
can be calculated as,
h = (position) sin θ
∴ P E = mg(position) sin θ
Sample calculation: (.220) (9.8) (1.9843) (sin (2.7°)) = .2015 J
Kinetic Energy Calculation:
Kinetic energy is defined as KE = 1/2 (mass) (velocity)2
Sample calculation: (.5) (.220) (.316)2 = .0110 J
Total energy is the sum of the potential and kinetic energies.
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Figure 1: Potential, kinetic, and total energy of a single glider on an inclined plane.
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Figure 2: The velocity of the glider on the track as a function of time.
Discussion
It can be seen from Fig. 1 that energy was conserved as the glider descended the air track.
There are some slight deviations from a constant energy value that appear to be due to
similar deviations in the kinetic energy values. This is probably due to slight errors in the
velocity values.
We checked to see if air resistance was a problem. We found that the velocity of the glider
(see Fig. 2) was linear and therefore air resistance did not affect our results. The fact that
the velocity was linear also tells us that acceleration on the air track is constant.
Measurement of the angle of the air track is a concern. If the angle is improperly measured the potential energy calculations will be inaccurate. The result could be an apparent
increase or decrease in the total energy when in reality energy is conserved.
We measured the angle several times and used the average value as the actual angle of
incline for the air track. We found the accuracy of the measurement to be about one half
of one degree. The limiting factor in measuring the angle is the carpenter’s level. The
experimental calculations are quite sensitive to the value used for the angle of incline. This
is because this angle is used to calculate the potential energy. Using the same data, and
varying the angle over a range of 1.5 degrees, we were able to get a variety of results. Over
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this range of angles we could show a loss of energy or a gain of energy.
Conclusion
Energy was conserved on the inclined plane.
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