Lab 06 Force and Motion Part II
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Mechanical Engineering
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Apr 3, 2024
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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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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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lail - Ahmed Amro Hussein Ali A x n Course: EN7919-Thermodynamic x
Homework Problerns(First Law)_S x
noodle/pluginfile.php/168549/mod_resource/content/1/Homework%20Problems%28First%20Law%29_SOLUTIONS.pdf
UTIONS.pdf
4 / 4
100%
Problem-4: When a system is taken from a state-a to a state-b,
the figure along path a-c-b, 84 kJ of heat flow into the system,
and the system does 32 kJ of work.
(i) How much will the heat that flows into the system along the
path a-d-b be, if the work done is 10.5 kJ? (Answer: 62.5 kJ)
(ii) When the system is returned from b to a along the curved path, the work done on
the system is 21 kJ. Does the system absorb or liberate heat, and how much?
(Answer:-73 k])
(iii) If Ua = 0 andU, = 42kJ , find the heat absorbed in the processes ad and db.
(Answer: 52.5 kJ, 10 kJ)
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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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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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Solve this problem
Thank
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Please help this for Matlab
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I am trying to plot an orbit in MATLAB. There is something wrong with my code because the final values I get are incorrect. The code is shown below. The correct values are in the image.
mu = 3.986*10^5; % Earth's gravitational parameter [km^3/s^2]
% Transforming orbital elements to cartesian coordinate system for LEOa_1 = 6782.99;e_1 = 0.000685539;inc_1 = 51.64;v_1 = 5;argp_1 = 30;raan_1 = 10;
[x_1, y_1, z_1, vx_1, vy_1, vz_1] = kep2cart(a_1, e_1, inc_1, raan_1, ... argp_1, v_1);
Y_1 = [x_1, y_1, z_1, vx_1, vy_1, vz_1];
% time_span for two revolutions (depends on the orbit)t1 = [0 (180*60)];
% Setting tolerancesoptions = odeset('RelTol',1e-12,'AbsTol',1e-12);
% Using ODE45 to numerically integrate for LEO[t_1, state_1] = ode45(@OrbitProp, t1, Y_1, options);
function dYdt = OrbitProp(t, Y)
mu = 3.986*10^5; % Earth's gravitational parameter [km^3/s^2]
% State Vector
x = Y(1); % [km]
y = Y(2); % [km]
z = Y(3); % [km]
vx = Y(4);…
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Please show all work for c,& d as I cannot solve it for the life of myself
A high-altitude skydiver of mass 100kg jumps from an altitude of 25km. Assume a near-standardatmosphere, with the following properties:
d) Produce computer-generated plots of the following four quantities experienced by the sky-diver: altitude, temperature, speed, and temperature rate of change (dT /dt|skydiver). Puttime on the horizontal axis for all plots.
Use code if possible, I really need help on this, so the sooner I can be leant a hand the better
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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…
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Given: Mass = M,
Radius = R,
Moment of Inertia = I,
Distance = H,
Gravity = g,
Initial timing = 0
Unknown =
How long will the [delta t] process take? (time)
Please keep in mind that almost every variable is unknown! We are given no numbers and are instructed to generate a solution using the variables [ "R, M, g, I and H." ]
Target =
Find an equation that, if we could substitute numbers, would determine how long the process would take.
Newton's second law and torque seem to be relevant based on how the problem is written.
* Also please show drawing based on what we are calculating
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Q: Find the steady-state response of the system shown in the figure below.
Pulley, mass moment of inertia Jo
寻
k2
00000
For the following data:
Fo sin of
m
00000
uu
x(t)
w
FO
JO
r
m
C
k2
[Rad/s]
[N]
kg-m
[cm]
[Kg]
[N.s/m]
[N/m]
kl
[N/m]
28
58
1.8
13
18
540
540
1080
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