Lab 05 Force and Motion Part I
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Lab 05: Force and Motion Part I
I.
Develop an experimental mathematical model to describe the behavior of a system
a.
Brainstorm
Mass of the system, hanging mass, force of gravity, air resistance
b.
Select an IV to test
Experimental Design Template
Research Question:
How does the acceleration of a system change when hanging mass changes?
Dependent variable (DV):
Acceleration of a system
Independent variable (IV):
Hanging mass
Control variables (CV):
Mass of the system: 0.3044kg, length of the string: 1.04m, starting point: 0.85m
Testable Hypothesis:
There is a positive correlation between the hanging mass and the acceleration of a system.
Prediction:
c.
Complete the experimental design.
x-axis
y-axis
Air track
Glider system
Hanging mass hook
Weights
Meter stick
Scale
We will be doing 8 trials and will use values of 0.0094kg, 0.0144kg, 0.0194kg, 0.0244kg
d.
Conduct the experiment.
The uncertainty of the measured values for acceleration is ±0.001m/s2 due to the rotary motion sensor’s estimated scale uncertainty, given in this lab.
The uncertainty of the measured values for the length of the string and position of the system is ±0.0005m due to the meter stick’s estimated uncertainty, given in a previous lab.
The uncertainty of the masses is ±0.001kg due to the scale’s estimated uncertainty, given in a previous lab.
Hanging mass
(kg)
Trial 1
(m/s
2
)
Trial 2
(m/s
2
)
Trial 3
(m/s
2
)
Average
(m/s
2
)
0.0094
0.288 ± 5.2*10
-4
0.289 ± 2.8*10
-4
0.290 ± 2.2*10
-4
0.289
0.0114
0.349 ± 3.0*10
-4
0.346 ± 6.2*10
-4
0.349 ± 5.1*10
-4
0.348
0.0134
0.407 ± 3.4*10
-4
0.407 ± 4.2*10
-4
0.404 ± 1.1*10
-3
0.406
0.0154
0.467 ± 5.0*10
-4
0.467 ± 5.3*10
-4
0.466 ± 4.9*10
-4
0.467
0.0174
0.525 ± 2.8*10
-4
0.526 ± 6*10
-4
0.524 ± 6.4*10
-4
0.525
0.0194
0.575 ± 7.1*10
-4
0.574 ± 5.7*10
-4
0.575 ± 5.5*10
-4
0.575
0.0214
0.630 ± 5.3*10
-4
0.630 ± 6.5*10
-4
0.630 ± 6.9*10
-4
0.630
0.0234
0.683 ± 6.8*10
-4
0.684 ± 9.4*10
-4
0.677 ± 2.8*10
-3
0.681
e.
Enter collected data into Excel
f.
Consider the mathematical model provided by Excel
a
=
2.8663
F
+
0.0295
2.8663 (1/kg) and 0.0295 (m/s
2
)
A causal relationship exists between the acceleration (a) and the gravitational force (F) if the mass of the system, length of the string, starting point is held constant, indicating a positive linear function.
II.
Developing a second experimental mathematical model to describe the behavior of the system.
a.
Select a second IV.
Mass of the system
b.
Repeat all steps in Part I.
Experimental Design Template
Research Question:
How does the acceleration of a system change when the mass of the system changes?
Dependent variable (DV):
Acceleration of a system
Independent variable (IV):
Mass of the system
Control variables (CV):
Hanging mass: 0.0234kg, length of the string: 1.04m, starting point: 0.85m
Testable Hypothesis:
There is a negative correlation between the mass of the system and the acceleration of a system.
Prediction:
c.
Complete the experimental design.
8 trials, values of 0.3044kg, 0.3544kg, 0.4044kg, 0.4544kg, 0.5044kg, 0.5544kg, 0.6044kg, 0.6544kg
d.
Conduct the experiment.
The uncertainty of the measured values for acceleration is ±0.001m/s2 due to the rotary motion sensor’s estimated scale uncertainty, given in this lab.
The uncertainty of the measured values for the length of the string and position of the system is ±0.0005m due to the meter stick’s estimated uncertainty, given in a previous lab.
x-axis
y-axis
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The uncertainty of the masses is ±0.001kg due to the scale’s estimated uncertainty, given in a previous lab.
System mass
(kg)
Trial 1
(m/s
2
)
Trial 2
(m/s
2
)
Trial 3
(m/s
2
)
Average
(m/s
2
)
0.3044
0.687 ± 4.8*10
-4
0.688 ± 5.6*10
-4
0.687 ± 1.3*10
-4
0.687
0.3544
0.596 ± 9.5*10
-4
0.595 ± 1.0*10
-4
0.597 ± 3.4*10
-4
0.595
0.4044
0.528 ± 6.7*10
-4
0.528 ± 5.2*10
-4
0.528 ± 5.6*10
-4
0.528
0.4544
0.473 ± 4.4*10
-4
0.472 ± 4.8*10
-4
0.471 ± 8.1*10
-4
0.472
0.5044
0.428 ± 4.6*10
-4
0.429 ± 4.1*10
-4
0.428 ± 4.7*10
-4
0.428
0.5544
0.391 ± 4.1*10
-4
0.392 ± 2.2*10
-4
0.392 ± 5.8*10
-4
0.392
0.6044
0.361 ± 4.0*10
-4
0.362 ± 4.0*10
-4
0.361 ± 3.3*10
-4
0.361
0.6544
0.335 ± 2.5*10
-4
0.335 ± 3.9*10
-4
0.335 ± 3.1*10
-4
0.335
e.
Enter collected data into Excel
f.
Consider the mathematical model provided by Excel
a
=
0.2252
m
−
0.938
0.2252 (N) and -0.938
A causal relationship exists between the acceleration (a) and the system mass (F) if the hanging mass, length of the string, starting point is held constant, indicating a negative power function.
III.
Connecting Experimental Model to Established Scientific Model
a.
Define established scientific model for the acceleration of a system.
a
∝
F
net
, hanging mass vs. acceleration of a system
a
∝
1
m
, mass of a system vs. acceleration of a system
b.
Compare your experimental model with the established scientific model.
a
=
2.8663
F
+
0.0295
, hanging mass vs acceleration of system
a
=
0.2252
m
0.938
, mass of system vs acceleration of system
The relationships represented in our mathematical models and the scientific equation are very similar to the established models for the acceleration of a system in relation to the hanging mass, as the hanging mass and the acceleration of a system are proportional, while the mass of the system is inversely proportional to the acceleration of the system. The only difference in the models is that the mass value in the equation for the mass of a system vs. acceleration of a system has an exponential value of 0.938, which may be partially attributed to the uncertainty values of the data.
c.
Create an Experimental Outcomes Organizer
IV.
Final Wrap-Up Questions
a.
Summarize the group’s findings into a general conclusion.
The results of the experiment for hanging mass vs. the acceleration of a system indicated a positive linear relationship when the mass of the system, string length, and starting point held constant. We conducted 3 trials for each of 8 masses, taking the average acceleration of each mass and using that result in the
graph. The R^2 value of the trend line for this data was 0.999, indicating a very Hanging mass (IV 1)
Mass of the system (IV 2)
Acceleration of system (DV)
Experimental Relationship: a=2.8663F+0.0295 found when the length of the string, starting point, and mass of the system held constant
Experimental Relationship: a=0.2252/(m^(0.938)) found when the length of the string, starting point, and hanging mass held constant
Established relationship: a
∝
Fnet
Mechanism explained: There is no mechanism to describe here
Mechanism explained: There is no mechanism to describe here
Established relationship: a1/m
∝
strong fit. The results for the experiment for the mass of a system vs. the acceleration of a system indicated a negative power relationship when the hanging mass, string length, and starting point held constant. We conducted 3 trials for each of 8 masses, taking the average acceleration of each mass and using that result in the graph. The R^2 value of the trend line for this data was 1, indicating a perfect fit. Therefore, we found that the hanging mass is directly proportional to the acceleration of a system and the mass of a system is inversely proportional to the acceleration of a system.
b.
Evaluate the evidence and resulting experimental model using the questions below as a guide.
Should the measurements collected when testing each IV be trusted? Would you expect similar numbers and/or a similar pattern if the experiment were repeated? Provide justification. Consider the ranges of measurement uncertainty and how closely the plotted points follow a pattern or trend
1.
Yes, the measurements collected when testing each IV should be trusted, and we would expect similar numbers and/or a similar pattern if the experiment were repeated, as the uncertainty values of all measurements were significantly small, the equations
for both IVs match the established equations well, and the range of values for each independent variable tested was large, as we did 8 different values with 3 trials for each, then took the average for each value for the graphs.
Should the equation determined using Excel be trusted for making accurate predictions for the acceleration of a system for masses and applied forces different from those tested in lab? Provide justification. Possibly include fit of the trendline, R^2 value, range of IV values tested and plotted on graph, and how well the experimental equation matches the established equation.
1.
Yes, the equation determined using Excel should be trusted for making accurate predictions for the acceleration of a system for masses and applied forces different from those tested in lab, as the trendline fits the data very well, the graphs have an R^2 value of 1 and 0.999, we did three trials for 8 values each for the hanging mass and the mass of the system, and the experimental equation matches the established equation well for both independent variables.
c.
Identify limitations by stating conditions for which claims hold.
Include the CV values, range of values used for IV. For each IV, state conditions for which the resulting claim holds
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1.
The limitations for these experiments are that the mass of the system, length of the string, and starting position must remain constant when testing the hanging mass in relation to the acceleration of a system, and the hanging mass, length of the string, and starting position must remain constant when testing the mass of the system in relation to the acceleration. Also, the range of values for the mass of the system must not be too large, as the system will not move if the mass exceeds a certain amount.
d.
Consider a hypothetical scenario
e.
A physics student claims that Newton's second law (
= ) can be used to 𝐹
𝑚𝑎
predict the net force necessary to obtain a desired acceleration. What relationship, correlational or causal, exists between net force and acceleration if mass is constant? Explain
If the mass is constant, there is a causal relationship between the net force and acceleration if the mass is constant because as the acceleration increases, so too does the net force, and the acceleration is the only factor that is changing/would affect the net force. A change in acceleration would have a direct impact on the net force.
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- is a mass hanging by a spring under the influence of gravity. The force due to gravity, Fg, is acting in the negative-y direction. The dynamic variable is y. On the left, the system is shown without spring deflection. On the right, at the beginning of an experiment, the mass is pushed upward (positive-y direction) by an amount y₁. The gravitational constant g, is 9.81 m/s². DO C.D Frontly у Your tasks: No Deflection m k Fg = mg Initial Condition y m k Write down an expression for the total energy If as the sum Write down an expression for the total energy H Fg = mg Figure 3: System schematic for Problem 4. Yi & X Write down, in terms of the variables given, the total potential energy stored in the system when it is held in the initial condition, relative to the system with no deflection. as the sum of potential and kinetic energy in terms of y, y, yi C After the system is released, it will start to move. Write down an expression for the kinetic energy of the system, T, in terms of…arrow_forwardPlease help me Matlabarrow_forwardA Do Now- Work and Energy Tran: x + ure.com/courses/44384/assignments/1494085 Al. O Google Drive LTI TumingPoint-Parti.. 4 Roots, Multi, and Fu.. A Roots, Multi, and Fu. A Roots, Multi, and Fu. O https://student.pas. y = 0 h Write down an equation for the total energy in the system at point 1 and point 2, before and after the change in height and speed. Part 2- Complete the Table using the image above: Use the tables below to calculate the kinetic energy of the cart at point 2 for the following values: m=2,000 kg, h; = 30 m, hf= 16 m Point 1 (initial) Point 2 (final) Ep (J) Ex (J) Ep (J) Ek (J) ETotal J) ETotal (1)arrow_forward
- Please provide steps on how to derive the output of each container.arrow_forwardFrom 1.31 1.32 and 1.33 show all workarrow_forwardT'sec In helical spring experiment a student plotted the graph of T2 versus the oscillating mass (M), and Used the slope to find the spring :constant, the value of k is 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 O. O a. 13.3 N/m O b. 6.8N/m O c. 5 N/m O d. 3.3 N/m O e. 24 N/m 5 10 15 20 25 30 35 40 45 50 55 60 65 M (9) 70 75 80arrow_forward
- Help please I'm stuck on these two problems.arrow_forwardi just need part 3arrow_forwardGiven: The plane accelerates in its current trajectory with a= 100 m/s^2 Farag Angle theta= 5° W=105 kips F_drag= 80 kips m= 1000 lbs Find: F_thrust, F_lift Please include the KD. Fthrust Futel t Fueight 000 BY NC SA 2013 Michael Swanbomarrow_forward
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