Lab 06 Force and Motion Part II
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Lab 06: Force and Motion Part II
I.
Develop an experimental mathematical model to describe the behavior of a system
a.
Select an IV to test
Hanging mass
b.
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:
Picture 1: Experimental setup
c.
Complete the experimental design.
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
Data table 1: Acceleration vs Hanging mass
e.
Enter collected data into Excel
0.5
0.7
0.9
1.1
1.3
1.5
1.7
1.9
2.1
2.3
2.5
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
f(x) = 0.29 x + 0.03
R² = 1
Hanging Force vs Acceleration
Hanging Force (N)
Acceleration (m/s^2)
Graph 1: Acceleration vs Hanging force
(The error bar for acceleration and hanging force is too small to be seen)
f.
Consider the mathematical model provided by Excel
a = 2.8663F + 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.
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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.
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
Data table 2: Acceleration vs System mass
e.
Enter collected data into Excel
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
f(x) = 0.23 x^-0.94
R² = 1
System Mass vs Acceleration
System Mass (kg)
Acceleration (m/s^2)
Graph 2: Acceleration vs System mass
(The error bar for acceleration and system mass are too small to be seen)
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
, 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 remarkably 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.
IV.
Newton’s Second Law
a.
Connect your experimental models to the general form of Newton’s Second Law as Σ F
=
m
system
a
, which can be rewritten for motion in one dimension as:
a
x
=
Σ F
m
system
=
F
1
x
m
system
+
F
2
x
m
system
+
F
3
x
m
system
+
…
i.
Compare your group’s mathematical model, which has the form
a
=
C
1
F
app
+
C
2
to the general form of Newton’s Second Law. In the section of your lab records that includes this model, indicate what the constants C
1
and C
2
physically represent. Then, determine what the value for C
1
should be based on your lab set-up and compare it to the value in your model. Knowing that your model describes the behavior of a real system, summarize the conditions of the lab set-up that might cause the values for C
1
and C
2
to be larger or smaller than expected.
Our group’s mathematical model is a = 2.8663F + 0.0295, with C
1
=2.8663 and C
2
=0.0295. This relates to the general form of Newton’s Second Law because C
1
represent 1
m
, and since F is multiplied by C
1
, it is the same as Newton’s second law. C
2
is the acceleration. Hanging mass
Acceleration
Force of gravity on system
System Mass
Fnet on cart in direction of cart's motion
(a)Accelerati
on of System
Experimental relationship: a=2.8663F+0.0295
Fnet increases with larger mhanging
Fnet increases with larger acceleration
Fnet increases with larger Fg
No impact (controlle
d)
Experimental relationship: a=0.2252/(m^(0.938)) Established relationship: a
∝1/m (when F is constant)
Mechanism explained: There is no mechanism to describe here
Established relationship: a
∝
Fnet (when msystem constant
Mechanism explained: There is no mechanism to describe here
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ii.
Repeat for your group’s mathematical model that has the form
a
=
C
3
(
m
sys
)
−
some power
. Put your group’s responses in the section of the lab records that includes this model.
Our mathematical model is a
=
0.2252
m
−
0.938
, with C
3
=
0.2252
N. C
3
represents the force of the system because Newton’s second law states
a
x
=
Σ F
m
system
. Our equation is similar as it also looks like a
=
0.2252
m
0.938
.
b.
Share experimental models.
i.
Write on your group’s two mathematical models (equations) from the previous lab on a whiteboard. Be sure the models are written in terms of the actual variables that represent the physical quantities under study and that units are included on all numerical values.
ii.
Indicate what the numerical values (constants) in your models physically represent as well as what values were determined for C
1
and C
3
based on your lab set-up.
Picture 2: Experimental models
Picture 3: Other group’s experimental models
c.
Revise experimental outcomes organizer
V.
Further exploration of the experimental mathematical models
a.
Investigate another IV for impact on the constants C
1
and in the mathematical model.
Experimental Design Template
Research Question:
How does tilt of the track impact the constants and in the model determined by the changing force experiment?
Dependent variable (DV):
C
1
and C
2
Independent variable (IV):
Tilt of the track
Control variables (CV):
length of the string: 0.888m, starting point: 0.7m, mass of the entire system (hanging mass included): 0.4794kg
Testable Hypothesis:
There is a no correlation between the tilt of the track and the values of C
1
and C
2
.
Hanging mass
Acceleration
Force of gravity on system
System Mass
Fnet on cart in direction of cart's motion
(a)Accelerati
on of System
Experimental relationship: a=2.8663F+0.0295
Fnet increases with larger mhanging
Fnet increases with larger acceleration
Fnet increases with larger Fg
No impact (controlle
d)
Experimental relationship: a=0.2252/(m^(0.938)) Established relationship: a
∝1/m (when F is constant)
Mechanism explained: There is no mechanism to describe here
Established relationship: a
∝
Fnet (when msystem constant
Mechanism explained: There is no mechanism to describe here
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Prediction:
Picture 4: Experimental Setup
x axis
y axis
tiles
protractor
C
1
(1/kg)
C
2
(m/s
2
)
Tilt
(m)
2.0141
0.0339
0. 0063
1.9896
0.0513
0.00945
2.0016
0.0629
0.01282
Data table 3: C
1 and C
2 vs Tilt
0.01
0.01
0.02
1.97
1.98
1.99
2
2.01
2.02
f(x) = − 1.85 x + 2.02
R² = 0.24
C1 and Tilt
Tilt (m)
C1 (1/kg)
0.01
0.01
0.02
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
f(x) = 4.44 x + 0.01
R² = 0.98
C2 and Tilt
Tilt (m)
C2 (m/s^2)
Tilt 1
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: 0.015kg, 0.025kg, 0.075kg, 0.125kg, 0.175kg
System mass: 0.4794kg, 0.4294kg, 0.3794kg, 0.3294kg, 0.3194kg
Control variables (CV):
Length of the string: 0.888m, Starting point: 0.7m, Forward tilt of system: 0.0063m
Testable Hypothesis:
There is a positive correlation between the hanging mass and the acceleration of a system.
Prediction:
Hanging mass
(kg)
Trial 1
(m/s
2
)
Trial 2
(m/s
2
)
Trial 3
(m/s
2
)
Average
(m/s
2
)
0.015
0.324 ± 6.2*10
-4
0.326 ± 4.7*10
-4
0.325 ± 6.3*10
-4
0.325
0.025
0.526 ± 5.6*10
-4
0.526 ± 4.9*10
-4
0.527 ± 6.6*10
-4
0.526
0.075
1.5 ± 0.012
1.53 ± 0.0015
1.52 ± 0.002
1.52
0.125
2.52 ± 0.0047
2.52 ± 0.0083
2.5 ± 0.013
2.51
0.175
3.52 ± 0.012
3.42 ± 0.034
3.5 ± 0.016
3.48
Data table 4: Acceleration vs Hanging mass with tilt 1
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0
0.5
1
1.5
2
2.5
3
3.5
4
f(x) = 2.01 x + 0.03
R² = 1
Hanging Force vs Acceleration
Hanging Force (N)
Acceleration (m/s^2)
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Graph 4: Acceleration vs Hanging force with tilt 1
(The error bars are too small to be seen)
Tilt 2
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: 0.015kg, 0.025kg, 0.075kg, 0.125kg, 0.175kg
System mass: 0.4794kg, 0.4294kg, 0.3794kg, 0.3294kg, 0.3194kg
Control variables (CV):
Length of the string: 0.888m, Starting point: 0.7m, Forward tilt of system: 0.00945m
Testable Hypothesis:
There is a positive correlation between the hanging mass and the acceleration of a system.
Prediction:
Hanging mass
(kg)
Trial 1
(m/s
2
)
Trial 2
(m/s
2
)
Trial 3
(m/s
2
)
Average
(m/s
2
)
0.015
0.338 ± 5.2*10
-4
0.338 ± 4.6*10
-4
0.34 ± 3.8*10
-4
0.339
0.025
0.539 ± 0.0014
0.539 ± 4.8*10
-4
0.539 ± 6.3*10
-4
0.539
0.075
1.53 ± 0.0038
1.53 ± 0.0022
1.54 ± 0.0018
1.53
0.125
2.4 ± 0.041
2.49 ± 0.015
2.53 ± 0.0027
2.47
0.175
3.47 ± 0.02
3.47 ± 0.016
3.48 ± 0.012
3.47
Data table 5: Acceleration vs Hanging mass with tilt 2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0
0.5
1
1.5
2
2.5
3
3.5
4
f(x) = 1.99 x + 0.05
R² = 1
Hanging Force vs Acceleration
Hanging Force (N)
Acceleration (m/s^2)
Graph 5: Acceleration vs Hanging force with tilt 2
(The error bars are too small to be seen)
Tilt 3
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: 0.015kg, 0.025kg, 0.075kg, 0.125kg, 0.175kg
System mass: 0.4794kg, 0.4294kg, 0.3794kg, 0.3294kg, 0.3194kg
Control variables (CV):
Length of the string: 0.888m, Starting point: 0.7m, Forward tilt of system: 0.01282m
Testable Hypothesis:
There is a positive correlation between the hanging mass and the acceleration of a system.
Prediction:
Hanging mass
Trial 1
Trial 2
Trial 3
Average
(kg)
(m/s
2
)
(m/s
2
)
(m/s
2
)
(m/s
2
)
0.015
0.352 ± 5.5*10
-4
0.354 ± 4.2*10
-4
0.352 ± 5.6*10
-4
0.353
0.025
0.55 ± 9.1*10
-4
0.553 ± 6.8*10
-4
0.554 ± 7.9*10
-4
0.552
0.075
1.55 ± 0.0023
1.55 ± 0.0051
1.55 ± 0.0076
1.55
0.125
2.54 ± 0.0037
2.42 ± 0.058
2.55 ± 0.0039
2.50
0.175
3.5 ± 0.011
3.5 ± 0.026
3.49 ± 0.019
3.5
Data table 6: Acceleration vs Hanging mass with tilt 3
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0
0.5
1
1.5
2
2.5
3
3.5
4
f(x) = 2 x + 0.06
R² = 1
Hanging Force vs Acceleration
Hanging Force (N)
Acceleration (m/s^2)
Graph 6: Acceleration vs Hanging force with tilt 3
(The error bars are too small to be seen)
b.
Make a claim
i.
Based on your group’s experimental outcomes, include in your lab records a description of the relationship between the values for C
1
and
C
2
and the IV your group tested. Be sure that enough data has been collected to support this claim.
There was no relationship between the values for C
1
and C
2
and the tilt of
the system.
c.
Share findings
i.
Write the following on a whiteboard to share with the class:
The IV your group tested
Your model in the form of a
=
C
1
F
app
+
C
2
from last week’s lab
Your model in the form of a
=
C
1
F
app
+
C
2
from this week’s lab after testing a new IV
Group’s claim about the impact of the tested IV on C
1
and C
2
and whether this makes sense
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Picture 5: other group findings VI.
Final Wrap Up
a.
Summarize findings into a general conclusion.
i.
Briefly summarize how the outcomes from the groups support the general form of Newton’s Second Law. If any group’s outcome does not support Newton’s Second Law, discuss that as well.
The outcomes from the groups support the general form of Newton’s Second Law because their experimental equations from last week match the established model, which is based on Newton’s Second Law, and their experimental models from this week are the same as ours, which also support Newton’s Second Law because without friction, the tilt of the rail does not matter in
regard to the acceleration of the system.
b.
Evaluate observed patterns or trends
i.
Consider the claims of all groups that tested the same IV as your group. Discuss whether or not they were similar and how this impacts the level of trust you have in your own group’s claims. If any group’s outcomes were different, provider reasons for why this may be the case.
The groups that tested the same IV as our group had the same claim as our group. This increases our level of trust in our group’s claims.
ii.
Consider the claims of all groups that tested a different IV than your group. Discuss how their findings add to your understanding of Newton’s Second Law.
The claims of all groups that tested a different IV than our group were the same as our group’s. This increases our understanding of
Newton’s second law because on a frictionless surface, the tilt/angle is irrelevant to the acceleration of the system.
c.
Consider other possible factors
i.
Are there any other factors not tested that might impact your response to the research question regarding “what affects the acceleration of a system?” If so, what are they and how might they be investigated? What new research question could be asked? If not, explain why you believe you have investigated all possible factors.
Another factor not tested that might impact our answer to the question “what affects the acceleration of a system?” is the force of friction on the system, which could be investigated by testing the system on a variety of surfaces with different friction forces.
d.
Suggest improvements
i.
If given the opportunity to repeat the investigation, what could be done to improve the collected data or strengthen your interpretation of the evidence, both of which support your general conclusion? You may wish to discuss flaws in your experimental design, how you might employ better controls, etc.
We could do a few more trials with more masses to increase our range and the validity of the correlation. The interpretation can be strengthened by describing the comparison between tilt height
versus C
1
and tilt height versus C
2
. In our experiment, our changes in mass for each trial was inconsistent, which we could change if repeated to have more consistent changes between acceleration values, making the data easier to interpret without a graph. Our controls could be changed so it’s easier to replicate for
future experiments.
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Write a function mySecond Derivative Order 3 that calculates the second derivative d²y/dx² of a data set (x, y) with at least
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The function input shall be
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Calculate d²y/dx² using only the following formulas that use the nomenclature of Table 8-1 and the lecture notes, but are different
from the formulas listed there:
f" (xi) 164f(xi) — 465f(xi+1) + 460ƒ (xi+2) − 170ƒ (xi+3) + 11f (xi+5) + O(h³)
=
60h2
56f(xi−1) − 105f(xi) +40f(xi+1) + 10f(xi+2) − f(x+4) + O(h³)
60h²
−5f(xi−2) +80f(xi−1) − 150f(xi) + 80f(xi+1) − 5ƒ(xi+2)
(1)
f"(xi)
=
(2)
f"(xi)
=
+0(h)
(3)
60h2
f"(xi)
-2f(x-4)+5f(xi-3)+50f(xi-1) — 110f(xi) +57f(xi+1)
=
+0(h³)
(4)
60h²
f"(xi) =
57f(x-5) 230f(xi-4) + 290 f (xi-3)-235…
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You are part of a car accident investigative team, looking into a case where a car drove off a bridge. You are using the lab projectile launcher to simulate the accident and to test your mathematical model (an equation that applies to the situation) before you apply the model to the accident data. We are assuming we can treat the car as a projectile.
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Motiyo
Add explanation
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Hello, I need help with the following (statistical) Thermodynamics problem. Thank you!
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I want to run several shocks in my calibrated DSGE model.
I want the shock “a” to happen at period 0, shock “b” at period 2 and shock “c” at period 5.
Also, I want to run a shock of 1 % to the variable “a”, 2 % to variable “b” and 10 % to variable “c”.
How would I write it in the Dynare code?
The model is log-linearized around the steady state and all endogenous variables are set at 0 at the steady state.
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I need help in MATLAB. I saw my professor run the following code. I can't seem to get it to work. Can you help me get it working?
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permanent-magnet (pm) genera x
Bb Blackboard Learn
L STAND-ALONE.mp4 - Google Dri x
O Google Drive: ülwgjuó jc lis u
O ME526-WindEnergy-L25-Shuja.p x
O File | C:/Users/Administrator/Desktop/KFUPM%20Term%232/ME526/ME526-WindEnergy-L25-Shuja.pdf
(D Page view
A Read aloud
T) Add text
V Draw
Y Highlight
O Erase
17
of 26
Wind Farms
Consider the arrangement of three wind turbines in the following schematic in which wind
turbine C is in the wakes of turbines A and B.
Given the following:
- Uo = 12 m/s
A
-XẠC = 500 m
-XBC = 200 m
- z = 60 m
- Zo = 0.3 m
U.
-r, = 20 m
B
- CT = 0.88
Compute the total velocity deficit, udef(C) and the velocity at wind turbine C, namely Vc.
Activate Windows
Go to Settings to activate Windows.
Wind Farms (Example Answer)
5:43 PM
A 4)) ENG
5/3/2022
I!
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1. For the following concentration expressions, indicate whether they are uniform or nonuniform
and in how many dimensions (OD, 1D, 2D, or 3D), and steady or unsteady. Then for the following
control volume and origin, and table of constants, use Excel or Matlab to graph profiles that
show how concentration changes within the control volume and over time to a limit of 20 for
the following: C(x,0,0,0), C(0,y,0,0), C(0,0,z,0) and C(0,0,0,t). On each graph, show which
parameters are held constant, the CV boundaries, and the point where all four plots overlap.
20
C(x=0)
10
a
0.0001
b
0.001
| 20
0.01
k
0.1
100
All of the following functions are C(space, time) and so not necessarily just x as suggested.
a. C,(x)= C,(x = 0)x exp{- ax}
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Chapter 12 - Lecture Notes.pptx: (MAE 272-01) (SP25) DY...
Scores
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Simulink Assignment- Filling a Tank
In fluid mechanics, the equation that models the fluid level in a tank is:
dh
1
-(min
Ap
- mout)
dt
h is the water level of the tank
A is the surface area of the bottom of the tank
pis the density of the fluid
Mim and mout are the mass flow rates of water in and out of the
tank, the flow out is a function of the water level h:
1
mout
Vpgh
Ris the resistance at the exit. Assume that the exit is at the bottom of the tank.
g is the gravitational acceleration
What to Do:
1. Build a model in Simulink to calculate the water level, h, as a function of time.
Your model should stop running as soon as the tank is full.
2. Assuming the height of the tank is 2 meters, after how many seconds does the
tank fill up?
Use the following constants to test your model:
• A: area of the bottom of the tank = 1 m?
• p: the density of fluid = 1000 kg/ m?
• R: the resistance at the exit = 3 (kg.m)-1/2
• ho: Initial height of the fluid in the tank = 0 m
• g: the gravitational…
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Need help, round answers to 3 sig figs please
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Please help Matlab
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I need help with a MATLAB code. I am trying to solve this question. Based on the Mars powered landing scenariosolve Eq. (14) via convex programming. Report the consumed fuel, and discuss the results with relevant plots. I am using the following MATLAB code and getting an error. I tried to fix the error and I get another one saying something about log and exp not being convex. Can you help fix my code and make sure it works.
The error is CVX Warning: Models involving "log" or other functions in the log, exp, and entropy family are solved using an experimental successive approximation method. This method is slower and less reliable than the method CVX employs for other models. Please see the section of the user's guide entitled The successive approximation method for more details about the approach, and for instructions on how to suppress this warning message in the future.Error using .* (line 173)Disciplined convex programming error: Cannot perform the operation:…
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Please Solve correctly [ Mechanical- Dynamics]
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How do I input this code for this MATLAB problem? Thanks!
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I am having trouble with the folloiwng MATLAB code. I am getting an error that says "unrecognized function or variable 'numericalPropogatorOptions". I have the aerospace toolbox and the aerospace blockset added. what add on do I have to download to use that function. How do I make this code work?
% Define Keplerian Elements
a = 29599.8; e = 0.0001; i = 0.9774; Omega = 1.3549; w = 0; M = 0.2645;
[RECI, VECI] = Kepler2RV(a, e, i, Omega, w, M);
initialState = [RECI * 1e3; VECI * 1e3]; % Initial position (m) and velocity (m/s)
% Define constants
mu = 3.986004418e14; % Gravitational constant (m^3/s^2)
earthRadius = 6378.1363 * 1e3; % Earth radius in meters
j2 = 1.08263e-3; % J2 perturbation coefficient
% Define propagator options
propOptions = numericalPropagatorOptions('CentralBody', 'Earth', ...
'GravitationalParameter', mu, ...
'InitialState', initialState, ...
'OutputTimeStep', 300); % Output every 300 seconds
% Add perturbations
addGravityModel(propOptions, 'Degree', 2,…
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2.1.28. [Level 2] In the year 2137 a hovering spacecraft
releases a probe in the atmosphere far above the surface of
New Earth, a planet orbiting Alpha Proximi. The gravita-
tional acceleration g1 is constant and equal to 7.5 m/s?. How
far will the probe have traveled when it has reached 98%
of its terminal speed? The probe's speed is governed by
ÿ = -g1 + cy
where y is the probe's position above the planet's surface
(expressed in m). c = 1.2 × 10-4 m-1.
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Excel File "LO1 Data'
Max
Max
Max Load Stress Elongation material
(mm) (Kg/m3)
10
7850
(Kg)
3000
Density of
rod
(Mpa)
200
young's
modulus for
the rod
(Gpa)
80
Length of
Rod (ft)
7
Cross-sectional area
of Rod (mm2)
9mm x 9mm
81
Poisson's coefficient of linear
ratio for expansion for rod,
rod a (x 106/°C)
0.25
10
The support rod has undergone complex loading due to the combination of axial loading and
thermal loading (as indicated in part vi). Critique the behavioral characteristics of the rod material
subjected to the complex loading. (See attached Excel File "LO1 Data")
As such you should also:
Construct a free-body diagram illustrating the forces acting on the rod and the effects of two-
dimensional and three-dimensional loading.
Discuss the elastic constants applicable in calculating the volumetric strain in this rod due to
loading via the weight of the load.
The rod has undergone complex loading. Critique the behavioral characteristics of the rod material
subjected to the complex…
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