This document provides an overview of teaching motion (kinematics) along a line. It defines key concepts like speed, velocity, and acceleration. It discusses common student misconceptions and challenges with graphs and equations. Examples of motion are given that could motivate students, like falling objects. The document emphasizes developing conceptual understanding qualitatively before quantitative relationships. It provides historical examples from Galileo to illustrate physics thinking and the development of concepts like uniform motion. Graphical and algebraic techniques for solving problems are demonstrated.
Concept of Particles and Free Body Diagram
Why FBD diagrams are used during the analysis?
It enables us to check the body for equilibrium.
By considering the FBD, we can clearly define the exact system of forces which we must use in the investigation of any constrained body.
It helps to identify the forces and ensures the correct use of equation of equilibrium.
Note:
Reactions on two contacting bodies are equal and opposite on account of Newton's III Law.
The type of reactions produced depends on the nature of contact between the bodies as well as that of the surfaces.
Sometimes it is necessary to consider internal free bodies such that the contacting surfaces lie within the given body. Such a free body needs to be analyzed when the body is deformable.
Physical Meaning of Equilibrium and its essence in Structural Application
The state of rest (in appropriate inertial frame) of a system particles and/or rigid bodies is called equilibrium.
A particle is said to be in equilibrium if it is in rest. A rigid body is said to be in equilibrium if the constituent particles contained on it are in equilibrium.
The rigid body in equilibrium means the body is stable.
Equilibrium means net force and net moment acting on the body is zero.
Essence in Structural Engineering
To find the unknown parameters such as reaction forces and moments induced by the body.
In Structural Engineering, the major problem is to identify the external reactions, internal forces and stresses on the body which are produced during the loading. For the identification of such parameters, we should assume a body in equilibrium. This assumption provides the necessary equations to determine the unknown parameters.
For the equilibrium body, the number of unknown parameters must be equal to number of available parameters provided by static equilibrium condition.
The term Machine Learning was coined by Arthur Samuel in 1959, an American pioneer in the field of computer gaming and artificial intelligence, and stated that “it gives computers the ability to learn without being explicitly programmed”. Machine Learning is the latest buzzword floating around. It deserves to, as it is one of the most interesting subfields of Computer Science. So what does Machine Learning really mean? Let’s try to understand Machine Learning
Lab 2/Lab 2- Kinematics.pdf
1/4/2017 Lab 2: Kinematics
https://moodle.straighterline.com/pluginfile.php/72219/mod_resource/content/17/CourseRoot/html/lab004s001.html 1/20
Learning Objec뙕ves
Disᣊ�nguish between scalar and vector quanᣊ�ᣊ�es
Apply kinemaᣊ�c equaᣊ�ons to 1‐D and projecᣊ�le moᣊ�on
Predict posiᣊ�on, velocity, and acceleraᣊ�on vs. ᣊ�me graphs
Calculate average and instantaneous velocity or acceleraᣊ�on
Determine that x and y components are independent of each other
Relate velocity, radius, and ᣊ�me period to uniform circular moᣊ�on.
Explain the direcᣊ�on of acceleraᣊ�on during uniform circular moᣊ�on
1‐D Kinema뙕cs
1‐D kinemaᣊ�cs occurs when an object travels in
one dimension and can be described using words,
equaᣊ�ons and graphs. Linear mo뙕on describes
how an object will move horizontally or verᣊ�cally
with constant acceleraᣊ�on, how an object will
1/4/2017 Lab 2: Kinematics
https://moodle.straighterline.com/pluginfile.php/72219/mod_resource/content/17/CourseRoot/html/lab004s001.html 2/20
Figure 1: Pool balls in moᾷon demonstrate
1‐D kinemaᾷcs.
Figure 2: Line secant to the path of the
object.
travel if dropped from the side of a cliff, and the
path it will follow if thrown straight up into the air.
Keep in mind the moᣊ�on of an object is relaᣊ�ve to
the viewer. Even though you do not feel like you
are in moᣊ�on right now, you are on planet earth
that has rotaᣊ�onal moᣊ�on in addiᣊ�on to orbital
moᣊ�on around the sun. In almost all cases here
moᣊ�on will be relaᣊ�ve to the Earth.
Scalar and Vector Quan뙕뙕es
In physics, quanᣊ�ᣊ�es can be scalar or vector. The
difference between the two lies in direcᣊ�on.
Scalar quanᣊ�ᣊ�es include magnitudes, which are numerical measurements. The distance an
object has traveled or the speed of an object is a scalar quanᣊ�ty. Scalars do not take direcᣊ�on
into consideraᣊ�on and can be described with only a number and a unit. For example,
somebody might say the temperature outside is 70°F. Seventy is the magnitude, and
Fahrenheit is the unit; there is no direcᣊ�on associated with the quanᣊ�ty. Vector quanᣊ�ᣊ�es, on
the other hand, include magnitude and direcᣊ�on. The displacement from an object's iniᣊ�al
posiᣊ�on, velocity, and acceleraᣊ�on are vector quanᣊ�ᣊ�es. The direcᣊ�on of vectors can be
described as being in the posiᣊ�ve direcᣊ�on, in the negaᣊ�ve direcᣊ�on, north, south, east, west,
leĀ, right, up, down, etc. One might describe an airplane's velocity as 450 miles per hour due
west where both magnitude and direcᣊ�on are given. It is important to disᣊ�nguish between
scalar and vector quanᣊ�ᣊ�es when trying to understand kinemaᣊ�cs.
Speed, Velocity, and Accelera뙕on
You may be familiar with speed outside of the physics classroom. When you drive in a car you
are traveling a distance over a certain amount of ᣊ�me: a speed. How then is velocity different
from speed? Velocity (v) is a vector quanᣊ�ty described as the rate at which an object's
posiᣊ�on changes divided by the ᣊ�me the ...
Track 6 - Mobile Apps and computational systems as learning tools
Authors: Santiago E. Moll, José-A. Moraño, Luis M. Sánchez-Ruiz and Nuria Llobregat-Gómez
Using recycled concrete aggregates (RCA) for pavements is crucial to achieving sustainability. Implementing RCA for new pavement can minimize carbon footprint, conserve natural resources, reduce harmful emissions, and lower life cycle costs. Compared to natural aggregate (NA), RCA pavement has fewer comprehensive studies and sustainability assessments.
Concept of Particles and Free Body Diagram
Why FBD diagrams are used during the analysis?
It enables us to check the body for equilibrium.
By considering the FBD, we can clearly define the exact system of forces which we must use in the investigation of any constrained body.
It helps to identify the forces and ensures the correct use of equation of equilibrium.
Note:
Reactions on two contacting bodies are equal and opposite on account of Newton's III Law.
The type of reactions produced depends on the nature of contact between the bodies as well as that of the surfaces.
Sometimes it is necessary to consider internal free bodies such that the contacting surfaces lie within the given body. Such a free body needs to be analyzed when the body is deformable.
Physical Meaning of Equilibrium and its essence in Structural Application
The state of rest (in appropriate inertial frame) of a system particles and/or rigid bodies is called equilibrium.
A particle is said to be in equilibrium if it is in rest. A rigid body is said to be in equilibrium if the constituent particles contained on it are in equilibrium.
The rigid body in equilibrium means the body is stable.
Equilibrium means net force and net moment acting on the body is zero.
Essence in Structural Engineering
To find the unknown parameters such as reaction forces and moments induced by the body.
In Structural Engineering, the major problem is to identify the external reactions, internal forces and stresses on the body which are produced during the loading. For the identification of such parameters, we should assume a body in equilibrium. This assumption provides the necessary equations to determine the unknown parameters.
For the equilibrium body, the number of unknown parameters must be equal to number of available parameters provided by static equilibrium condition.
The term Machine Learning was coined by Arthur Samuel in 1959, an American pioneer in the field of computer gaming and artificial intelligence, and stated that “it gives computers the ability to learn without being explicitly programmed”. Machine Learning is the latest buzzword floating around. It deserves to, as it is one of the most interesting subfields of Computer Science. So what does Machine Learning really mean? Let’s try to understand Machine Learning
Lab 2/Lab 2- Kinematics.pdf
1/4/2017 Lab 2: Kinematics
https://moodle.straighterline.com/pluginfile.php/72219/mod_resource/content/17/CourseRoot/html/lab004s001.html 1/20
Learning Objec뙕ves
Disᣊ�nguish between scalar and vector quanᣊ�ᣊ�es
Apply kinemaᣊ�c equaᣊ�ons to 1‐D and projecᣊ�le moᣊ�on
Predict posiᣊ�on, velocity, and acceleraᣊ�on vs. ᣊ�me graphs
Calculate average and instantaneous velocity or acceleraᣊ�on
Determine that x and y components are independent of each other
Relate velocity, radius, and ᣊ�me period to uniform circular moᣊ�on.
Explain the direcᣊ�on of acceleraᣊ�on during uniform circular moᣊ�on
1‐D Kinema뙕cs
1‐D kinemaᣊ�cs occurs when an object travels in
one dimension and can be described using words,
equaᣊ�ons and graphs. Linear mo뙕on describes
how an object will move horizontally or verᣊ�cally
with constant acceleraᣊ�on, how an object will
1/4/2017 Lab 2: Kinematics
https://moodle.straighterline.com/pluginfile.php/72219/mod_resource/content/17/CourseRoot/html/lab004s001.html 2/20
Figure 1: Pool balls in moᾷon demonstrate
1‐D kinemaᾷcs.
Figure 2: Line secant to the path of the
object.
travel if dropped from the side of a cliff, and the
path it will follow if thrown straight up into the air.
Keep in mind the moᣊ�on of an object is relaᣊ�ve to
the viewer. Even though you do not feel like you
are in moᣊ�on right now, you are on planet earth
that has rotaᣊ�onal moᣊ�on in addiᣊ�on to orbital
moᣊ�on around the sun. In almost all cases here
moᣊ�on will be relaᣊ�ve to the Earth.
Scalar and Vector Quan뙕뙕es
In physics, quanᣊ�ᣊ�es can be scalar or vector. The
difference between the two lies in direcᣊ�on.
Scalar quanᣊ�ᣊ�es include magnitudes, which are numerical measurements. The distance an
object has traveled or the speed of an object is a scalar quanᣊ�ty. Scalars do not take direcᣊ�on
into consideraᣊ�on and can be described with only a number and a unit. For example,
somebody might say the temperature outside is 70°F. Seventy is the magnitude, and
Fahrenheit is the unit; there is no direcᣊ�on associated with the quanᣊ�ty. Vector quanᣊ�ᣊ�es, on
the other hand, include magnitude and direcᣊ�on. The displacement from an object's iniᣊ�al
posiᣊ�on, velocity, and acceleraᣊ�on are vector quanᣊ�ᣊ�es. The direcᣊ�on of vectors can be
described as being in the posiᣊ�ve direcᣊ�on, in the negaᣊ�ve direcᣊ�on, north, south, east, west,
leĀ, right, up, down, etc. One might describe an airplane's velocity as 450 miles per hour due
west where both magnitude and direcᣊ�on are given. It is important to disᣊ�nguish between
scalar and vector quanᣊ�ᣊ�es when trying to understand kinemaᣊ�cs.
Speed, Velocity, and Accelera뙕on
You may be familiar with speed outside of the physics classroom. When you drive in a car you
are traveling a distance over a certain amount of ᣊ�me: a speed. How then is velocity different
from speed? Velocity (v) is a vector quanᣊ�ty described as the rate at which an object's
posiᣊ�on changes divided by the ᣊ�me the ...
Track 6 - Mobile Apps and computational systems as learning tools
Authors: Santiago E. Moll, José-A. Moraño, Luis M. Sánchez-Ruiz and Nuria Llobregat-Gómez
Using recycled concrete aggregates (RCA) for pavements is crucial to achieving sustainability. Implementing RCA for new pavement can minimize carbon footprint, conserve natural resources, reduce harmful emissions, and lower life cycle costs. Compared to natural aggregate (NA), RCA pavement has fewer comprehensive studies and sustainability assessments.
6th International Conference on Machine Learning & Applications (CMLA 2024)ClaraZara1
6th International Conference on Machine Learning & Applications (CMLA 2024) will provide an excellent international forum for sharing knowledge and results in theory, methodology and applications of on Machine Learning & Applications.
NUMERICAL SIMULATIONS OF HEAT AND MASS TRANSFER IN CONDENSING HEAT EXCHANGERS...ssuser7dcef0
Power plants release a large amount of water vapor into the
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requirement. One of the most practical way to recover water
from flue gas is to use a condensing heat exchanger. The power
plant could also recover latent heat due to condensation as well
as sensible heat due to lowering the flue gas exit temperature.
Additionally, harmful acids released from the stack can be
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phenomenon since heat and mass transfer of water vapor and
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2. Learning outcomes
• define speed and acceleration, instantaneous and average values
• explain the difference between relevant scalar and vector quantities
• apply Galilean relativity to motions in inertial frames of reference
• present a historical ‘thought experiment’ to illustrate physics thinking
• establish concepts qualitatively (using proportional reasoning) before
introducing quantitative relationships (equations)
• choose contexts for teaching kinematics that motivate student learning
• understand basic algebra and use it to rearrange kinematic equations
• draw and interpret graphs of position, velocity, acceleration
• translate information about uniform motions between words, pictures,
graphs and equations
• begin to develop a strategy for solving quantitative problems
3. Starting points
Misconceptions:
Heavier objects are commonly thought to fall faster than lighter objects.
Teaching challenges:
• Concepts: Some students fail to grasp the distinction between velocity
and acceleration – to them it’s simply ‘motion’. Acceleration is not
simple idea: it is the rate of change of velocity, and velocity itself is the
rate a change of distance (making acceleration the rate of change of a
rate of change).
• Graphs: Most students have difficulty with drawing and interpreting
graphs representing motion (distinguishing s - t graphs from v - t
graphs; appreciating significance of area under a v - t graph, of
gradients of s - t and v - t graphs).
• Equations: Students need help understanding that some equations
constitute definitions and that other equations apply only when there is
constant acceleration.
4. Kinematics – describing motion
Object is treated as a particle (a point-like concentration of
matter that has no size, no shape and no internal structure).
Questions to ask:
• Where is the particle?
• How fast is it moving?
• How rapidly is it speeding up or slowing down?
This is modelling.
Restricted to motion along a line.
5. Contexts
In pairs:
List other examples of real motion that might be
modelled as a particle moving along a line.
• Include some examples that can motivate students.
6. Uniform motion
Galileo (1638) Dialogue concerning two new sciences
Definition:
By steady or uniform motion, I mean one in which the
distances traversed by the moving particle during any
equal intervals of time, are themselves equal.
7. Galileo’s Two new sciences
Axioms
I The distance traversed during a _______ interval of time is greater
than the distance travelled during a _______ interval of time.
II The time required to traverse a _______ distance is longer than the
time required for a _______ distance.
III Over the same time interval, the distance traversed at a greater
speed is _______ than the distance traversed at a ______ speed.
IV The speed required to traverse a longer distance is greater than
that required to traverse a ________ distance during the same time
interval.
8. Galileo’s Two new sciences
Theorems
I If a moving particle, carried at a constant speed, traverses two
distances, the time intervals required are to each other in the
ratio of these distances.
II If a moving particle traverses two distances in equal intervals of
time, these distances will bear to each other the same ratio as
the speeds. And conversely, if the distances are as the speeds,
then the times …
III In the case of unequal speeds, the time intervals required to
traverse a given space are to each other inversely as the
speeds.
9. We say …
In symbols,
taken
time
travelled
distance
speed
t
s
v
10. Other essential ingredients
• a coordinate system
• units: metres, seconds
• scalar or vector?
– distance, displacement
– speed, velocity
11. Measuring distances & times
For class experiments & demonstrations
• metre rules and stopwatches
• ticker timers
• light gates
• sonic (ultrasound) sensor
• video capture
Discuss in small groups: What do you use?
12. Graphical representation
Uniform motion
a) List the objects below in order of increasing
speed.
b) Which of the objects have positive velocity?
c) List the objects in order of increasing velocity.
13. Ticker timers
Running on mains, they make 50 ticks each second.
Time between ticks is therefore 1/50 s = 0.02 s
14. A car is driven along a straight road. The graph shows how the
velocity of the car changes from the moment the driver sees a
very slow moving queue of traffic ahead.
Use the graph to calculate the distance the car travels while it is
slowing down.
Show clearly how you work out your answer.
Area under a v-t graph
15. Finding an average speed
1 If you are not already familiar with ticker timers, first
do the experiment Using the ticker-timer to measure
time
2 Do one of these two experiments.
Timing a trolley on a slope
Pupil speed
16. Naturally accelerated motion
Aristotle: objects fall at constant speed; the more
massive, the faster they fall.
Galileo’s thought experiment.
(Ignoring air resistance) All objects fall the same way,
getting faster and faster.
• a dramatic experimental test of this idea.
http://www.physics.ucla.edu/demoweb/demomanual/mechanics/gra
vitational_acceleration/guinea_and_feather_tube.html
17. Free fall
Galileo’s findings, modelled with chains.
If the time of fall is twice as long, how much further does
an object fall?
• the v–t graph gives the answer.
So what happens when an object is thrown vertically
upwards?
21. Equations of uniform motion
Two definitions:
Four relationships derived from these:
t
u
v
a
t
s
v
as
u
v
at
ut
s
t
v
u
s
at
u
v
2
2
1
2
2
2
2
22. Solving quantitative problems
A standard approach
1. Write down what you know, using conventional symbols.
2. Decide what equation to use and write it down.
3. Re-arrange the equation to make the unknown its subject.
4. Substitute values and find the unknown quantity.
5. Write answer to correct number of significant figures, with units.
24. Experiments about motion
In fours: do a few of these experiments:
Compensating for friction
Investigating free fall with a light gate
Measurement of g using an electronic timer
Finding average acceleration with a ticker-timer
Measurement of acceleration using light gates
Building a reaction tester
[from the Practical Physics website]
25. Using simulation software
Physlets: http://physics.bu.edu/~duffy/classroom.html
PhET: http://phet.colorado.edu/simulations/
Video analysis:
Multimedia Motion II, from Cambridge Science Media
Discuss, in small groups: What do you use?
28. Endpoints
In small groups:
Review the main ideas.
Identify anything that is not clear and clarify it by discussion.
Individually:
Decide what you need to do to consolidate any or all of this
material.