Experiment seven_ Conservation of Energy
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Apr 3, 2024
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Alexis Ortiz
Experiment 7
A20532815
Experiment seven: Conservation of Energy
1.
Introduction:
The purpose of this experiment is to study the conversions of one type of energy
to another and recognize the relationships between spring potential energy and
gravitational potential energy and between kinetic energy and potential energy.
The total energy of a system is defined as:
(1)
? = 𝐾 + ?
Where E is the total mechanical energy of the system, K is the total kinetic energy
of the system, and U is the total potential energy of the system.
The mathematical equation used to calculate the potential spring energy is:
(2)
?
?
=
1
2
??
2
Where
is the spring potential energy of the system, k is the spring constant of
?
?
the spring, and x is the displacement of the spring.
The mathematical equation used to calculate the potential gravitational energy is:
(3)
? = ?𝑔?
Where
is the potential gravitational energy, m is the mass of the system, g is
?
𝑔
the gravitational acceleration of Earth (9.8
), and y is the height the mass dropped in
?
?
2
meters.
The mathematical equation used to calculate the kinetic energy of the system is:
K=
m
(4)
1
2
𝑣
2
Where m is the mass of the system and v is the velocity of the glider going
through the photogate.
The mathematical equation used to calculate the velocity of the glider is:
(5)
? =
?
?
Where V is the velocity of the glider, l is the length of the flag on the glider, and t
is the time through the photogate.
The equation used to calculate the force of the system is:
(6)
? =− ??
Alexis Ortiz
Experiment 7
A20532815
Where F is the force acting on the glider, k is the spring constant of the spring,
and x is the distance the spring is compressed.
2.
Experimental Procedures:
Materials and equipment needed for the experiment are: a photogate, a set of
assorted round weights, PASCO computer software and sensor, force sensor, measuring
tape, 3 blocks, linear air track, a balance, and a piece of string.
Part 0:
1.
The balance was zeroed, then the mass of the glider was measured.
2.
The PASCO software was connected to the force sensor. The force sensor was
connected to a pole to ensure the sensor didn’t move.
3.
The air track was turned on.
4.
A string was connected to the hook of the force sensor and glider.
5.
On the air track, the glider was pushed against the spring and the spring was
compressed a measured distance and then released.
6.
The force sensor calculated the resultant force of the glider. This process was
repeated twice.
7.
The compression distance was changed and steps 4 and 5 were repeated. This
process was repeated 3 more times.
8.
Using equation 6, the experimental spring constant of each point was calculated.
These values were plotted on a graph, which gave the spring constant.
Part 1:
1.
With the air track still turned on and the glider still connected to the string, the
photogate was connected to the PASCO software and was placed extremely close
to the glider to ensure accuracy in the recorded velocity.
2.
The glider was pushed against the string and the spring was compressed a
measured distance and then released.
3.
The photogate calculated the velocity of the glider using equation 5. This process
was repeated twice.
4.
40 grams of weights were added to the glider (20 on each side) and steps 3 and 4
were repeated. This process was repeated one more time.
5.
The distance the spring was compressed was changed 2 times and steps 3-5 were
repeated for every change in compression distance.
6.
Using equation 2, the potential spring energy of each point was calculated. Using
equation 4, the kinetic energy of the system was calculated.
Part 2:
Alexis Ortiz
Experiment 7
A20532815
1.
With the mass of the glider being constant (0.270 kilograms), a block was put
under the far side of the air track to create an upward slope for the glider to travel.
2.
The height of the glider at the higher photogate height and at the lower height
against the spring were measured, recorded, and then subtracted from each other
to find the change in vertical distance (height).
3.
The glider was pushed against the spring and the spring was compressed then
released.
4.
As the glider passed through the photogate, it measured the velocity of the glider
using equation 4, which was recorded.
5.
The height difference was changed 2 more times by adding blocks to the far
underside of the air track.
6.
Steps 3-5 were repeated for 2 other additional compressions.
7.
Using equation 2, the spring potential energy was calculated. Using equation 3,
the gravitational potential energy was calculated.
3.
Results and Analysis
:
Table 1: Table 1 shows the distance the spring was compressed, the resultant force, and
the calculated spring constant value of each trial from part 0.
Distance (m)
Force (N)
k (N/m)
Trials
0.22
21.11
95.95455
Trial 1
0.22
21.30
96.81818
Trial 2
0.22
22.42
101.9091
Trial 3
0.30
23.35
77.83333
Trial 1
0.30
20.20
67.33333
Trial 2
0.30
23.46
78.20000
Trial 3
0.37
29.84
80.64865
Trial 1
0.37
29.33
79.27027
Trial 2
0.37
29.97
81.00000
Trial 3
0.46
37.45
81.41304
Trial 1
0.46
36.23
78.76087
Trial 2
0.46
33.34
72.47826
Trial 3
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Alexis Ortiz
Experiment 7
A20532815
0.57
43.4
76.14035
Trial 1
0.57
39.96
70.10526
Trial 2
0.57
44.75
78.50877
Trial 3
Based on table 1, graph 1 shows the relationship between the force and compression of
the spring.
Graph 1:
From graph 1, the line of best fit was found to be 64.65, which demonstrates the
relationship between the force and distance the spring was compressed.This figure
represents the spring constant of the spring used in the experiment (based on equation 6).
There is a 6.09% error in this part of the experiment, which suggests that the found values
of the experiment are relatively accurate. Potential sources of minor error may be due to a
minimal external force having been applied to the glider as the point of release.
Table 2: Table 2 shows the compression distance of the spring, the mass of the glider (w/
added weights), the velocity of the glider, the calculated values of the spring potential
energy and kinetic energy, and the percent difference between the two energies.
Distance (m)
Mass (kg)
Velocity (m/s)
Us (J)
KE (J)
% diff
Alexis Ortiz
Experiment 7
A20532815
0.3
0.19
1.25
2.90925
0.148438
180.5817
0.3
0.19
1.19
2.90925
0.134530
182.3207
0.3
0.19
1.21
2.90925
0.139090
181.7488
0.3
0.23
1.04
2.90925
0.124384
183.5993
0.3
0.23
1.02
2.90925
0.119646
184.1994
0.3
0.23
1.00
2.90925
0.115000
184.7896
0.3
0.27
0.91
2.90925
0.111794
185.1980
0.3
0.27
0.91
2.90925
0.111794
185.1980
0.3
0.27
0.91
2.90925
0.111794
185.1980
0.5
0.19
1.54
8.08125
0.225302
189.1506
0.5
0.19
1.57
8.08125
0.234166
188.7358
0.5
0.19
1.56
8.08125
0.231192
188.8749
0.5
0.23
1.44
8.08125
0.238464
188.535
0.5
0.23
1.42
8.08125
0.231886
188.8424
0.5
0.23
1.46
8.08125
0.245134
188.2237
0.5
0.27
1.33
8.08125
0.238802
188.5192
0.5
0.27
1.35
8.08125
0.246038
188.1816
0.5
0.27
1.34
8.08125
0.242406
188.351
0.6
0.19
1.53
11.637
0.222386
192.4993
0.6
0.19
1.56
11.637
0.231192
192.208
0.6
0.19
1.52
11.637
0.219488
192.5952
0.6
0.23
1.42
11.637
0.231886
192.1851
0.6
0.23
1.4
11.637
0.2254
192.3995
Alexis Ortiz
Experiment 7
A20532815
0.6
0.23
1.41
11.637
0.228632
192.2926
0.6
0.27
1.31
11.637
0.231674
192.1921
0.6
0.27
1.28
11.637
0.221184
192.539
0.6
0.27
1.26
11.637
0.214326
192.7662
Based on Table 2, graph 2 shows the relationship between the kinetic energy of the glider
and the spring potential energy of the spring.
From graph 2, the line of best fit was calculated to be 0.0123, which represents the
experimental ratio between the spring potential energy and the kinetic energy. This result
is very different from the 1:1 ratio that is expected in a fully conserved system. With the
coefficient of determination being 0.7359, it is highly unlikely that the system conserved
all its energy and that the data was very accurate. The most probable source of error was
friction stemming from the glider and the air track. However, friction cannot fully
account for this disparity. Other likely sources of error include the spring not being
uniformly compressed, an external force on the glider at the point of release, the string
not being lined up perfectly with the rest of the system, and errors in the measurement of
the compression distance.
Table 3: Table 3 shows the compression distance of the spring, the height difference
between the release point and the photogate, the mass of the glider, the calculated values
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Alexis Ortiz
Experiment 7
A20532815
for the potential energies and kinetic energy, the energy after the release and the percent
difference between the potential spring energy and the energy after the release.
Distance
(m)
H-h (m)
Velocity
(m/s)
Mass
(kg)
Us (J)
Ug (J)
K(J)
Energy
after
release
(?
𝑔
+ 𝐾)
Percent
difference
0.05
4.00E-03
1.22
0.27
0.080813
1.06E-02
2.01E-01
2.12E-01
8.94E+01
0.05
4.00E-03
1.22
0.27
0.080813
1.06E-02
2.01E-01
2.12E-01
8.94E+01
0.05
4.00E-03
1.25
0.27
0.080813
1.06E-02
2.11E-01
2.22E-01
9.31E+01
0.05
2.30E-02
1.14
0.27
0.080813
6.09E-02
1.75E-01
2.36E-01
9.81E+01
0.05
2.30E-02
1.14
0.27
0.080813
6.09E-02
1.75E-01
2.36E-01
9.81E+01
0.05
2.30E-02
1.15
0.27
0.080813
6.09E-02
1.79E-01
2.39E-01
9.91E+01
0.05
3.40E-02
1.05
0.27
0.080813
9.01E-02
1.49E-01
2.39E-01
9.89E+01
0.05
3.40E-02
1.07
0.27
0.080813
9.01E-02
1.55E-01
2.45E-01
1.01E+02
0.05
3.40E-02
1.1
0.27
0.080813
9.01E-02
1.63E-01
2.53E-01
1.03E+02
0.04
3.40E-02
0.72
0.27
0.05172
9.01E-02
7.00E-02
1.60E-01
1.02E+02
0.04
3.40E-02
0.71
0.27
0.05172
9.01E-02
6.81E-02
1.58E-01
1.01E+02
0.04
3.40E-02
0.71
0.27
0.05172
9.01E-02
6.81E-02
1.58E-01
1.01E+02
0.04
2.30E-02
0.83
0.27
0.05172
6.09E-02
9.30E-02
1.54E-01
9.94E+01
0.04
2.30E-02
0.84
0.27
0.05172
6.09E-02
9.53E-02
1.56E-01
1.00E+02
0.04
2.30E-02
0.83
0.27
0.05172
6.09E-02
9.30E-02
1.54E-01
9.94E+01
0.04
4.00E-03
0.91
0.27
0.05172
1.06E-02
1.12E-01
1.22E-01
8.12E+01
0.04
4.00E-03
0.93
0.27
0.05172
1.06E-02
1.17E-01
1.27E-01
8.45E+01
0.04
4.00E-03
0.93
0.27
0.05172
1.06E-02
1.17E-01
1.27E-01
8.45E+01
0.065
4.00E-03
1.78
0.27
0.136573
1.06E-02
4.28E-01
4.38E-01
1.05E+02
Alexis Ortiz
Experiment 7
A20532815
0.065
4.00E-03
1.79
0.27
0.136573
1.06E-02
4.33E-01
4.43E-01
1.06E+02
0.065
4.00E-03
1.78
0.27
0.136573
1.06E-02
4.28E-01
4.38E-01
1.05E+02
0.065
2.30E-02
1.73
0.27
0.136573
6.09E-02
4.04E-01
4.65E-01
1.09E+02
0.065
2.30E-02
1.74
0.27
0.136573
6.09E-02
4.09E-01
4.70E-01
1.10E+02
0.065
2.30E-02
1.75
0.27
0.136573
6.09E-02
4.13E-01
4.74E-01
1.11E+02
0.065
3.40E-02
1.66
0.27
0.136573
9.01E-02
3.72E-01
4.62E-01
1.09E+02
0.065
3.40E-02
1.66
0.27
0.136573
9.01E-02
3.72E-01
4.62E-01
1.09E+02
0.065
3.40E-02
1.66
0.27
0.136573
9.01E-02
3.72E-01
4.62E-01
1.09E+02
Based on Table 3, graph 3 shows the relationship between the spring potential energy and
the energy after the glider was released.
From graph 3, the line of best fit was calculated to be 0.2651, which is the ratio of the
spring potential energy and the energy after the release. This result differs from the
expected 1:1 ratio that would occur in a conserved system, which means that there were
nonconservative forces acting on the glider. This result also implies that 73.49% of the
energy of the system was lost. Friction between the air track and the glider or with the
string is the most probable of being a source of air. Additionally, a miscalculation in the
Alexis Ortiz
Experiment 7
A20532815
height difference of the glider’s positions and the system not being perfectly centered are
additional plausible sources of error
4.
Conclusion:
5.
Data sheets:
see below
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- THERMODYNAMICS TOPIC: FIRST LAW OF THERMO/THERMODYNAMIC SYSTEM PLEASE ANSWER COMPLETELY THE QUESTION IN HANDWRITING AND SUPPORT YOUR SOLUTION WITH DIAGRAMS. THANK YOUarrow_forward1. For your science fair project, you decided to design a model rocket ship. The fuel burns exerting a time-varying force on the small 2.00 kg rocket model during its vertical launch. This force obeys the equation F= A + Bt2. Measurements show that at t=0, the force is 25.0 N, and at the end of the first 2.00 s, it is 45.0 N. Assume that air resistance is negligible. a. What are the forces acting on the rocket? b. Draw its free-body diagram. c. Find the constants A and B, including their SI units using this equation F= A + Bt². d. Find the net force on this rocket and its acceleration the instant after the fuel ignites. e. Find the net force on this rocket and its acceleration 3.00 s after fuel ignition. f. Suppose you were using this rocket in outer space, far from all gravity. What would its acceleration be 3.00 s after fuel ignition? g. What is the rocket's mass in outer space? What is its weight?arrow_forwardaccount_circle Science PhysicsQ&A LibraryA child’s toy consists of a m = 31 g monkey suspended from a spring of negligible mass and spring constant k. When the toy monkey is first hung on the spring and the system reaches equilibrium, the spring has stretched a distance of x = 17.6 cm, as shown in the diagram. This toy is so adorable you pull the monkey down an additional d = 7.6 cm from equilibrium and release it from rest, and smile with delight as it bounces playfully up and down. 1. Calculate the speed of the monkey, ve, in meters per second, as it passes through equilibrium. 2. Derive an expression for the total mechanical energy of the system as the monkey reaches the top of the motion, Etop, in terms of m, x, d, k, the maximum height above the bottom of the motion, hmax, and the variables available in the palette. 3. Calculate the maximum displacement, h, in centimeters, above the equilibrium position, that the monkey reaches. A child’s toy consists of a…arrow_forward
- 1. In the laboratory, when you hanged 100 grams at the end of the spring it stretched 10 cm. You pulled the 100-gram mass 6 cm from its equilibrium position and let it go at t = 0. Find an equation for the position of the mass as a function of time t. 2. The scale of a spring balance found in an old Physics lab reads from 0 to 15.0 kg is 12.0 cm long. To know its other specifications, a package was suspended from it and it was found to oscillate vertically with a frequency of 2.00 Hz. Calculate the spring constant of the balance? (b) How much does the package weigh?arrow_forwardQ1 A and Barrow_forwardHW help: Just part c please.arrow_forward
- Newton's second law of motion leads to: the rate of change of linear momentum is equal to the applied moment the rate of change of linear momentum is equal to the applied force the rate of change of angular momentum is equal to the applied force the mass times acceleration of a particle is equal to the applied forcearrow_forward1) A building consists of two floors. The first floor is attached rigidly to the ground, and the second floor is of mass m = 1000 slugs (fps units) and weighs 16 tons (32,000 lb). The elastic frame of the building behaves as a spring that resists horizontal displacements of the second floor; it requires a horizontal force of 5 tons to displace the second floor a distance of 1 ft. Assume that in an earthquake the ground oscillates horizontally with amplitude A, and circular frequency w, resulting in an external horizontal force F(t) What is the natural frequency (in hertz) of oscillations of the second floor? b. If the ground undergoes one oscillation every 2.25 s with an amplitude of 3 in, what is the amplitude of the resulting forced oscillations of the second floor? mA,w²sin(wt) on the second floor. а. 2) A mass m hangs on the end of a cord around a pulley of radius a and moment of inertia I, rotating with an angular velocity w, as shown in the figure below. The rim of the pulley is…arrow_forwardDuring lab, Table Group 9 accidentally launches their spring from the tabletop onto the light fixture shown in the diagram. The spring has a mass of 12 grams. The instructor gave clear instructions not to stretch the spring by more than 70 cm to protect it from damage. If this spring's stiffness is k= 15 N/m, did the group follow instructions or did they stretch the spring too far? 3.0 m 1.2 marrow_forward
- A cryogenic substance is found to have a specific heat capacity (at constant volume) c_v that varies with temperature according to c_v = AT^2, where A is an empirically derived constant with units J/(K^3 kg). If 220 J of energy must be transferred thermally (at constant volume) to an 8,750 mg sample of this substance to raise the temperature of the sample from 1.0 K to 6.6 K, what is the value of A? Your Answer: Answer unitsarrow_forwardFind the value of M1, M2, and what is the percent error if the true value is 149 grams?arrow_forward9. A spring has a stiffness of 100N/m. A mass of 3 kg was attached to the spring. The mass was pushed 10cm upward from the equilibrium position and was released from rest. After 5 seconds from release, determine the acceleration of the mass in m/s^2? 10.What Law governs the statement, "For every object applied with a load, the displacement or size of deformation is directly proportional to the magnitude of the applied load"?arrow_forward
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