PHY 105M Lab 7 (1)
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Apr 29, 2024
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Method:
For this lab, we were asked to take a closer inspection on collisions and how they are
related to conservation laws. By producing several different experiments with different
variations, we can observe how conservation laws can come into action through the
process of collisions. For this experiment, we were asked to use a PASCO collision cart
set up to make our discoveries and test the accuracy of the linear momentum equation
(
𝑃
=
𝑚
1
𝑣
1+
𝑚
2
𝑣
2) and the mechanical energy equation (
𝐸
=1/2
𝑚
1
𝑣
1+1/2
𝑚
2v2)
Given this information, we were able to hypothesize that the collisions would allow
conservation of energy, by testing the accuracy of the formulas and using them to prove
our theory.
To begin this experiment, we started out with 4 different experiment variations. These
variations would measure different aspects of the collisions using different circumstances.
Before we began, we aligned both the red and blue carts onto the PASCO setup. We also
recorded that the weight of the cars was 0.275 +/- 0.005kg. After we calibrated and
connected the setup to the carts, we began to set up our first experiment. We set up the
blue and red carts so that they were free and their magnetic sides were facing each other.
We started them at different sides of the track and gave both of the carts a push, resulting
in a collision. In this case, the magnets were opposite poles so the carts rebounded on
impact, creating a free elastic collision. Using the PASCO system, we were able to
calculate the speed of the carts. We dissected the graph to find the initial velocity and
final velocity points of the system before and after the collision (rebound) and collected
the data.
Table 1: Initial and Final Velocities of Collisions
Mass
(kg)
Velocity 1,
Blue (m/s)
Mass
(kg)
Velocity 2,
Red (m/s)
E
P
Propagated
Uncertainty of
E
Propagated
Uncertainty of
P
Elastic Fixed
Initial
0.275
+/-
0.005
0.081
+/- 0.001
0.275
+/-
0.005
0.878
+/- 0.001
0.1069
0.2637
0.0194
0.0213
Elastic Fixed
Final
0.275
+/-
0.005
0.088
+/- 0.001
0.275
+/-
0.005
0.383
+/- 0.001
0.0212
0.1295
0.038
0.0213
Elastic Fixed
Initial
0.275
+/-
0.005
0.935
+/- 0.001
0.275
+/-
0.005
0.707
+/- 0.001
0.1889
0.4515
0.254
0.121
Elastic Fixed
Final
0.275
+/-
0.005
0.734
+/- 0.001
0.275
+/-
0.005
0.346
+/- 0.001
0.0905
0.2970
0.140
0.011
Elastic Fixed
Initial
0.275
+/-
0.005
0.070
+/- 0.001
0.275
+/-
0.005
0.942
+/- 0.001
0.1226
0.2783
0.00223
0.009
Elastic Fixed
Final
0.275
+/-
0.005
0.039
+/- 0.001
0.275
+/-
0.005
0.004
+/- 0.001
0.0002
0.0118
0.0001
0.0271
Elastic Fixed
Initial
0.275
+/-
0.005
0.699
+/- 0.001
0.275
+/-
0.005
0.881
+/- 0.001
0.1739
0.4345
0.00231
0.288
Elastic Fixed
Final
0.275
+/-
0.005
0.377
+/- 0.001
0.275
+/-
0.005
0.209
+/- 0.001
0.0255
0.1612
0.0039
0.822
Follow Up
Elastic Fixed
Initial
0.525
+/-
0.005
0.688
+/- 0.001
0.525
+/-
0.005
0.681
+/- 0.001
0.2459
0.7187
0.167
0.218
Follow Up
Elastic Fixed
Final
0.525
+/-
0.005
0.591
+/- 0.001
0.525
+/-
0.005
0.595
+/- 0.001
0.1846
0.6227
0.126
0.012
Table 2: T-score for the comparison between initial and final velocities of collisions
-energy
T-score (Energy)
T-Score (E)
T-Score (P)
Elastic Fixed (i) v. Elastic Fixed
0.2497
1.4947
Elastic Free v. Elastic Free
23.8325
52.699
Inelastic Fixed v. inelastic Fixed
0.2095
—-
Conclusion:
Based on our data, our hypothesis is only partially correct, in that only of the two elastic
collisions were conserved. Based on our t-scores, the only one that was under 1 was our free
elastic collision (t=0.2497). Every other collision, fixed elastic, free inelastic, and fixed inelastic
were above 1, which means they were not indistinguishable. Both inelastic collisions were
accurate in our hypothesis but the fixed elastic collision was not correct in our hypothesis. That
being said, that means that the only system that was conserved was the free elastic collision. All
of the other three were not conserved. In our follow up, we found that the reaction was
conserved, even with the increase in mass for both carts. The t-score was 0.2095 for the follow
up free elastic collision and we found that it was also conserved. For other iterations of this lab, I
think having carts of different masses instead of similar masses, will increase the accuracy of
the experiment. Also, instead of colliding the carts by hand, using a mechanism that can propel
the carts forward automatically would be more efficient. The PASCO models have a limit in
terms of precision it can measure velocity, which is to three decimal places. In the future, a more
powerful model can be applied, to measure to less uncertainty. When comparing to other
groups, all of their t-scores were above the value of three, whereas ours only had half of then
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1
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0
75
1.50
?
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H₂N
OH
4-aminobenzoic acid
MM 137.14 g/m ol
A
+ CH3CH₂OH
ethanol
MM 46.10 g/mol
B
ethyl 4-aminobenzoate
ethanol
H+
4-aminobenzoic acid
benzocaine
none of the above
H₂N
OCH₂CH3 + H₂O
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ethyl 4-aminobenzoate
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с
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- Construct the expression for Kc for the following reaction. 1 3NO(g) = N20(g) + NO2(g) Construct the expression for Kc for the following reaction. 2 X 4HCI(aq) + O2(g) = 2H20(1) + 2C12(g) > Construct the expression for Kc for the following reaction. 3 CH4(g) + 2H2S(g) = CS2(g) + 4H2(g) Construct the expression for Kc for the following reaction. 4 X 2Cu*(aq) + Zn(s) = 2Cu(s) + Zn²*(aq) >arrow_forwardRoute 1:RME = 82.92%MI= 1.34 Route 2RME = 22.84%MI = 18.15 Route 3RME = 57.34%MI = 1.89 Compare the value of Reaction Mass Efficiency (RME) and Mass Intensity (MI) generally, and choose which metrics is more significant in green measurement. Justify your answer.arrow_forwardIn any manufacturing process, reaction monitoring ensures that a chemical reaction proceeds as expected. Table 1 shows the monitoring data for the formation of chlorohexane, collected using a technique called gas chromatography. Note that the concentrations of the chlorohexane solutions are given in millimoles per litre (mmol l–1). The abbreviation mM (millimolar) is frequently used. Plot a graph of the data in Table 1. The graph should be drawn on graph paper or use fine grid if it’s drawn on Excel. Elapsed Time/Hours Concentration of Chlorohexane/mM 0 0 2 40 4 65 6 80 8 90 10 95 12 99arrow_forward
- Use the information given here to answer both questions (4 and 5). For the fictitious reaction: AB → A + B Some data was collected measuring the [AB] at certain time intervals. This data was then graphed as described below. A graph of 1/[AB] versus time (s) gives a straight line with the equation: y = 0.0052x + 0.1135 and a R2 = 0.9995. A graph of ln[AB] versus time (s) gives a straight line with the equation: y = -0.0068x + 1.725 and a R2 = 0.8925. Assume the data doesn't fit a zero order reaction. What is the rate law for this reaction? Select one: a. Rate = k[AB]2 b. Rate = k[A][B] c. Rate = k[AB] d. Rate = k Using the data from the previous question. What is the value of the rate constant for the given reaction? Select one: a. k = 0.0052 M-1s-1 b. k = 0.0157 Ms-1 c. k = 0.0068 s-1 d. There is no way to determine the value of the rate constant from the given information.arrow_forwardSodium chlorate crystals are easy to grow in the shape of cubes by allowing a solution of water and sodium chlorate to evaporate slowly. a. If V is the volume of such a cube with side length x, calculate dV/dx when x = 3 mm and explain its meaning (be specific). b. Show that the rate of change of the volume of a cube with respect to its edge length is equal to half the surface area of the cube.arrow_forward5 Why is it important to be able to calculate steady-state variables such as temperature, pressure, concentration?arrow_forward
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ISBN:9781305264434
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Publisher:Brooks Cole