Download Conservation of Energy Melissa Stumbaugh Andrew Raymond

Conservation of Energy
Melissa Stumbaugh
Andrew Raymond
Physics 2115-010
October 17, 2013
Abstract:
This experiment test both kinetic and potential energy through the use of air track and pendulum
systems. Kinetic and potential both produced liner graphs, with kinetic having a positive slope and
potentials being negative. When potential and kinetic energy were added the total energy was
found to be a constant correlation. The calculated slope for kinetic energy versus potential energy
from the pendulum was found to be .9543. The theoretical value for this slope is one, giving a 4.57%
discrepancy.
Introduction:
Energy is commonly known as the ability of an object to do work. In this experiment we will
be looking at two types of energy: kinetic and gravitational potential energy. Kinetic energy is the
energy of an object due to motion. Since kinetic energy is so strongly dependent on movement,
velocity and mass are expected to play such key roles in the calculation of this type of energy.
KE= ½ mv²
This is the equation used to find kinetic energy, where “KE” stands for kinetic energy, “m”
represents mass, and “v” stands for velocity. In this experiment we will not be looking at the mass
of the object so kinetic energy can be defined as KE= ½ v². The second type of energy is potential
energy. Potential energy is energy that is stored in a system and dependent on the position of that
system and in relation to its surroundings. There are many different types of potential energy, but
this experiment uses gravitational potential energy. Position plays a key role in potential energy
since the height of an object will often determine how much potential energy it has due to
gravitational force.
PE= mgh
“PE” stands for potential energy, “m” is again representing mass, “g” is the gravitational constant
which is 9.8, and “h” is the height of the object. In this experiment we will not be looking at the
mass of the object so our equation will be PE= gh.
The total energy in the system is equal to the sum of the potential and kinetic energies.
E(tot)= = ½ mv²+mgh
“E(tot)” stands for total energy, “m” is again representing mass, “v” stands for velocity, “g” is the
gravitational constant, and “h” is the height of the object. In isolated conserved systems, like the air
track and the pendulum systems we use in this experiment, the total energy should remain
constant according to the principle of the conservation of energy. Therefore, the energy in the
system can be transferred between kinetic and potential forms. As the gravitational potential
energy in the system decreases, the kinetic energy should increase at the same rate. The main
objectives of this lab is to understand this relationship between kinetic and potential energy, and to
observe the conservation of energy in a closed system.
Apparatus:
Air tack, gliders, photo-gage, vernier caliper, elevating blocks, meter stick, ceiling mounted
pendulum, and small pendulum bobs.
Procedure:
This lab will be conducted in two parts. For the first part of the experiment place the air
track on an incline, and use the meter stick to measure the base height. Place the photogate at five
different positions along the air track, measuring the height of each position. By tearing the heights
against the base height and multiplying the true height with the gravitational constant of 9.8, we
will be able to find the gravitational potential energy for each of the five positions. In order to
determine the kinetic energy we must first find the velocity of the object at the differing heights.
Measure the length of the glider and divide that by the time it takes the glider to pass through the
photogate at each height respectively. Use the equation KE= ½ v² to find the kinetic energy at the
five different positions. Add the potential and kinetic energy to find the total energy. Create a
spreadsheet on excel listing the position, height, velocity, potential energy, kinetic energy, and total
energy. This will allow us to create a graph that with the position on the x-axis and the energy per
mass unit on the y-axis.
The second half of the experiment uses a ceiling mounted pendulum. The pendulum was
arranged so that the bob was able to pass through the photogate without disturbing it. Hold the
pendulum back and release the bob from five different positions, measuring the height for each.
Measure the width of the bob using the vernier caplier. This width divided by the time it takes the
bob to pass through the photogate will give us the velocity. Once all five positions have a calculated
height and velocity, the potential and kinetic energy can be calculated. Once more, create a
spreadsheet on excel listing the position, height, velocity, potential energy, kinetic energy. Use this
information to create a graph with kinetic energy on the x-axis, and potential energy on the y-axis.
Once your graph is complete, find the slope.
Results:
Position
1
2
3
4
5
Height (m) Time (s) Velocity (m/s) Potential Energy (gh) Kinetic Energy= 1/2V^2
Total energy=PE + KE
0.07
0.1987
0.503
0.686
0.1265
0.8125
0.059
0.1547
0.646
0.5782
0.2087
0.7869
0.05
0.1308
0.764
0.49
0.2918
0.7818
0.043
0.116
0.862
0.4214
0.3715
0.7929
0.026
0.0967
1.03
0.2548
0.5304
0.7852
0.79186
Table 1: Shows all of the results of the five different positions we used in the air track part of the
lab.
Conservation of energy in an Isolated System
0.9
0.8
0.7
Energy (J)
0.6
0.5
Potential Energy (gh)
0.4
Kinetic Energy= 1/2V^2
0.3
Total energy=PE + KE
0.2
0.1
0
1
2
3
4
5
Position
Figure 1. This graph depicts the results of kinetic, potential, and total energy measured on the air
track based on its position in meter.
Position Height (m) Time (s) Velocity (m/s) Potential Energy (gh) Kinetic Energy= 1/2V^2
1
0.004
0.0523
0.290630975
0.0392
0.042233182
2
0.016
0.0277
0.548736462
0.1568
0.150555852
3
0.03
0.0204
0.745098039
0.294
0.277585544
4
0.047
0.0155
0.980645161
0.4606
0.480832466
5
0.072
0.0132
1.151515152
0.7056
0.662993572
0.322840123
Table 2: Shows all of the results of the five different positions we used in the pendulum part of the
lab.
Conservation of Energy Using a Pendulum
0.8
y = 0.9543x + 0.0067
0.7
Energy (J)
0.6
0.5
0.4
Series1
0.3
Linear (Series1)
0.2
0.1
0
0
0.2
0.4
0.6
0.8
Position
Figure 2. This graph represents the positive linear relationship between potential energy and kinetic
energy based on the position of the pendulum.
Percent Discrepancy = ((Theoretical Slope-Experimental Slope)/(Theoretical Slope))x100
PD=((1-0.9543)/(1))X100= 4.57%
Discussion:
Figure 1 depicts the results from the air track portion of the lab. The graph shows that as the
potential energy decreases, the kinetic energy increases. This trade off supports the principle of
conservation of energy. When the total energy was plotted against position, a relatively straight
across line was formed. This even line is because each of our total energies falls within the
experimental uncertainty of 0.02 meters. When both the equation for KE and PE are added the
energy is constant within the allowed error. There has to be some room for experimental
uncertainty because some of the measurements may not be completely accurate.
Figure 2 depicts the results of the pendulum portion of the lab. Potential energy was plotted
against kinetic energy and resulted again in a positive linear relationship. The slope for this graph
was found to be 0.9543. Using this experimental slope, and the theoretical slope which is 1 we are
able to find the percent discrepancy, which is 4.57%. If we had been taking mass into account in this
experiment it would have affected the graph, but in this experiment we use the same bob the entire
time and we also omit mass from our equations so there will be no effect on the graph. To have zero
percent discrepancy means that all potential energy would be converted into kinetic energy, therefor
the slope would be equal to 1. In this experiment we see a percent discrepancy because the system
is not completely closed so some energy is lost due to air resistance. While we do see some
discrepancy, our potential and kinetic energies do fall within the limits of the experimental error as it
should if the principle of the conservation of energy is true.
Conclusion:
Both kinetic and potential energy were successfully observed through the use of both air
track and pendulum systems. Results demonstrate that the sum of potential and kinetic energy is
constant, producing an almost straight, linear graph. Furthermore, it was seen that potential energy
is correlated with position, whereas kinetic energy is dependent on motion. When both energy
values were added, a constant result was observed representing the concept of conservation of
energy.
References:
Giancoli, Douglas. Physics. Ed 6 . Pearson: Prentice Hall, Upper Saddle River, NJ. 2005. Pg 141th
144.
Nickles, C et al. “Physics for Life Sciences (PHYS 2115)” Laboratory Exercises, Applied Physics
Program. Richard Stockton College of New Jersey. Fall 2013.