Download Motion - ICT for IST

ICT for Innovative Science Teachers
Leonardo da Vinci programme
2009-1-PL1- LEO05- 05046
Motion and Forces
Motion is a feature of everyday life,
whether it be walking, running,
cycling, or travelling by road, rail or
air, our daily experience is filled with
motion. Scientists and engineers have
devised numerous methods for
measuring motion in a wide variety of
contexts. To describe and calculate
motion and to understand its causes,
concepts of displacement, speed,
velocity, acceleration and force are
needed.
CC 2011 ICT for IST
This project has been funded with support from the European Commission under the Lifelong
Learning Programme. This publication reflects the views only of the author, and the Commission
cannot be held responsible for any use which may be made of the information contained therein.
A. Introduction
The theme of this module is the study of motion; how it may be measured,
analysed and understood using simple experiments and mathematical models.
To build an understanding, some basic concepts are required: displacement,
speed, velocity, acceleration and force. The activities exploit the use of ICT to
stimulate thinking about how these concepts are used to understand the
motion of objects due to various forces acting on them. There are four types
of activities:
1. Data logging: Four laboratory experiments:
To record and analyse walking motion using a distance-time
graph.
To investigate the relationship between velocity and distance
fallen for a card in free fall.
To investigate the acceleration of a small trolley and its
relationship with the force acting on it.
To investigate the motion of a trolley rolling down a slope and
rebounding due to the action of a spring buffer.
2. Video measurement: Four data-video activities:
To measure and analyse motion of a free falling ball.
To determine the acceleration due to the Moon gravity.
To measure and analyse the motion of an accelerated car and to
determine the force acting on the car.
To investigate the motion of a badminton shuttlecock falling in
the air and to determine its terminal velocity.
3. Simulation: Visual aids to assist understanding of the concepts of
velocity, acceleration and force and the interpretation of the datalogging experiments involving motion:
To study the motion of a ball moving in two dimensions.
To investigate the motion of a trolley rolling down a slope and
rebounding due to the action of a spring buffer.
To investigate terminal velocity of a bicycle when a steady
force is applied to the pedals.
4. Modelling:
Models to show the relationship between velocity,
acceleration and force in examples of uniform velocity, uniform
acceleration and terminal velocity.
Motion and Forces- 2
1. Background theory
1. BASIC CONCEPTS ABOUT MOTION
When objects move, the rate of
movement (described as the speed of
the object) is defined as the distance
moved per second. When the
movement is considered in one
direction in a straight line, the rate of
movement is described as the
velocity of the object. Thus:
speed =
distance travelled per
second
velocity = distance travelled in a
particular direction in a
straight line per second
Velocity must be regarded as a vector
quantity since it possesses both
magnitude and direction. When an
object travels at a steady (constant)
speed in a straight line, its motion is
described as uniform velocity. Any
change of magnitude or direction of
the velocity constitutes an
acceleration, defined as the rate of
change of velocity:
acceleration = change of velocity per
second
Each of these is a calculation of a rate
of change. They are „derived‟
quantities and, as such, are
essentially abstract concepts. Their
abstractness leads to difficulties for
many pupils. The most common
confusion is that between velocity
and acceleration; it is very tempting
to think that a fast moving object has
a high acceleration. In the particular
case of a swinging pendulum the
exact reverse is the case; at the
extremes of the swing where the
pendulum momentarily comes to rest,
the acceleration is a maximum;
conversely, at the moment that the
pendulum is moving at its fastest
velocity, through its vertical position,
the acceleration is actually zero. The
essential idea to grasp is that
acceleration is not about velocity, it is
about changes of velocity.
2. THE CONCEPT OF FORCE
Force is a fundamental concept in
science and is widely experienced,
however, it is very difficult to define.
The problem is that, although we can
personally feel forces when they
directly push or pull our bodies, for
bodies other than our own, we cannot
see or feel forces; we can only detect
them when we see their effects.
Forces are only observable by their
effects. A force can:
•
change the shape of an object, or
•
change the motion of an object, or
•
turn an object around
When any of these effects are
observed, we might conclude that
they signal the presence of one or
more forces.
In nature there appears a variety of
different types of force which are
observable across a range of physical
phenomena. The following names
describe forces which arise in
distinctive circumstances: elastic,
gravity (weight), impact, electric,
magnetic, nuclear, molecular, tension,
compression, buoyancy, hydrostatic,
friction, viscous, muscular. Although
their origins might be very different
physically, they are all capable of
producing the same effects identified
above.
3. BALANCED AND UNBALANCED FORCES
Forces rarely occur as single forces.
Pairs and multiples of forces are
much more common. Paradoxically
this often makes it difficult to detect
Motion and Forces- 3
forces. It is very common for several
forces to be acting on a body in a
state of balance so that no net effect
can be observed. For example, when
a person is sitting on a chair, their
body experiences a downward force
of gravity (weight) which is counterbalanced by the upward reaction
force of the seat which is supporting
the body. Since these two forces are
in a state of balance, there is no
resultant force on the body and the
normal effects produced by a force
are not observed. Clearly, if one
force is removed, (e.g. the chair is
kicked away) the remaining force
(weight) is unbalanced and the
normal consequence of a force
becomes painfully obvious! Thus the
very common occurrence of balanced
forces makes it often difficult to
appreciate their presence and
magnitude. Conversely, forces must
be unbalanced for their effects to be
observed.
When several forces act on a body
simultaneously, the total effect is
called the RESULTANT FORCE. It is
found by adding all the forces
vectorially (i.e. with due regard to
their direction as well as magnitude)
on the body. Unbalanced forces
imply a finite resultant force.
Resultant force is not a type of force;
it is simply the vector sum of the
forces acting on a body. In a state of
balance, the resultant force on a body
is zero. It is incorrect to say that
balanced forces cancel each other out.
For example, the upward force of the
seat does not cancel out my weight,
it simply counter-balances it. It is
preferable to speak of forces
counterbalancing rather than
cancelling each other out.
4. FORCE AND MOTION
Forces are profoundly connected with
the motion of objects. The absence
or presence of motion, the magnitude
of motion and the direction of motion
all depend upon the resultant force.
This connection is summarised in
Newton‟s first two Laws of Motion:
The First Law describes the situation
for balanced forces:
"When the resultant force on
an object is zero, the object is
either at rest or moving with a
uniform velocity."
The Second Law describes the
situation for unbalanced forces:
"An unbalanced force causes a
change in velocity
(acceleration) in proportion to
the resultant force on the
object"
This second relationship can be
expressed as an equation
a
F
m
where „a‟ is the acceleration produced
by a resultant force „F‟ acting on an
object of mass „m‟.
The equation always describes the
effect of the resultant force. If
several forces are acting on the body
concerned, it is essential that the
resultant force is derived or
calculated. Notice that the mass
appears in the equation in such a way
that it predicts the observation that
larger masses experience smaller
accelerations than smaller masses
subject to the same resultant force.
(The equation representing Newton's
Second Law is usually written as "F
= ma". This unfortunately tends to
obscure the identity of the cause and
Motion and Forces- 4
effect; the equation is better written
as above which expresses the idea
that acceleration is the effect of the
force which is the cause.)
5. AIR DRAG AND TERMINAL SPEED
As a free-falling object accelerates
(downwards due to gravity), the drag
force (caused by air resistance)
acting on the object increases and its
acceleration decreases. When the
upward drag force (Fd) equals the
downward force of gravity (Fg=mg),
the resultant force on the object
becomes zero and its acceleration
becomes zero. At this point the object
continues falling at a constant speed
called terminal velocity. Terminal
velocity varies directly with the ratio
of gravity force to drag force. More
drag means a lower terminal velocity,
while increased weight means a
higher terminal velocity.
In motion through air the drag force
is approximately proportional to the
square of velocity:
Fd
k v 2 where k is a drag constant.
The terminal speed for a human
skydiver varies from about the 150 to
200 km/h. A parachute greatly
increases the air resistance, so with
an open parachute, terminal speeds
can be cut down to 15-25 km/h which
is enough to land safely.
6 . MEASURING MOTION
Light gate method: A card of
known width is attached to the object
and the light gate is positioned so
that the card cuts the light beam as
the object moves. The computer
measures the interruption time and
uses this to calculate the velocity. If
a double segment card is used, the
computer can calculate the change of
velocity and hence the acceleration.
Motion sensor method: The sensor
is positioned to reflect ultrasound
pulses off a moving object. By
detecting the echoes of the pulses
from the object, the sensor enables
the computer to calculate the
distance of the object from the
sensor. By continuously monitoring
such distance measurements, a
distance-time graph is plotted on the
computer screen. Velocity and
acceleration values and graphs may
be derived from the plotted data.
7. GRAPHS OF MOTION
Graphs may be plotted using
measurements from a motion sensor.
The two main types of graph are
distance-time graphs (s-t) and
velocity-time graphs (v-t) and great
care is needed to distinguish which
type is being dealt with. The features
of the graph which convey physical
meaning are shape, steepness
(gradient), intercept, maxima,
minima, and area.
The basic measurements required for
calculating speed, velocity or
acceleration are those of distance and
time. The experiments in this
module use two types of sensor for
making such measurements: the light
gate (or photo gate) and the motion
sensor (or motion detector).
Motion and Forces- 5
s-t graph
v-t graph
A straight horizontal line represents a
body at rest.
A straight horizontal line represents a
body moving with uniform velocity.
A line sloping upwards represents a
body moving away from an origin.
A line sloping upwards represents a
body accelerating.
A line sloping downwards represents
a body moving towards an origin.
A line sloping downwards represents
a body decelerating.
A sloping straight line represents a
uniform (steady or constant) velocity.
A sloping straight line represents a
uniform acceleration.
A curve represents an acceleration.
A curve represents a changing
acceleration
The area under a graph represents
distance travelled.
2. Pre-requisite
knowledge required
Definitions of speed, velocity
and acceleration
3. Science concepts
developed in the
module
Concepts of force and mass
Newton‟s Laws of Motion 1
and 2
Units for measuring all of the
above quantities
Fluid friction giving rise to
terminal velocity
Types of force: gravity
causing weight and tension in
string when stretched
Motion and Forces- 6
B. Didactical approach
1. Pedagogical context
The activities here concern basic concepts related to motion and its causes
through the application of forces. Since motion is a common everyday
experience, there are numerous contexts which may call upon basic concepts for
understanding. For example:
Walking
Cycling
Transport
Sport
2. Common student difficulties
Confusion between velocity and acceleration
Confusing the graphical representations and motion paths of real objects e.g.
plotting position and velocity as the path of motion
Distinguishing between slope and height of a graph
Interpreting changes in height and changes in slope (e.g. when is the object
slowing down, which motion is slowest)
Understanding the physical significance of the sign of a body's velocity
Understanding that it is possible to have zero velocity and non-zero
acceleration, or non zero velocity and zero acceleration
Understanding that the direction of acceleration relative to velocity
determines whether an object speeds up or slows down
Understanding that a body can have a positive velocity and negative
acceleration (or the reverse) simultaneously
Belief that the motion implies a force (so no movement means no forces)
Many students assume a linear relationship between force and velocity
Vectorial addition of forces
Using the concept of resultant force in the Laws of Motion
Acceleration in free fall is independent of mass
The presence of friction obscures evidence for the First Law of Motion
Motion and Forces- 7
REFERENCES:
1. Beichner, R. J., Testing student interpretation of kinematics graphs. American
Journal of Physics, 62, 750, (1994)
2. F. M. Goldberg and J. H. Anderson, Student difficulties with graphical
representations of negative values of velocity, Phys. Teach. 27, 254-260
(1989).
3. R. F. Gunstone, Student understanding in mechanics: A large population
survey, Am. J. Phys. 55, 691-696 (1987
4. A. Halloun and D. Hestenes, Common-sense concepts about motion, Am. J.
Phys. 53, 1056-1065 (1985).
5. McDermott, Lillian C., Mark L. Rosenquist, and Emily H. Van Zee. , American
Journal of Physics, 55, 503, (1987)
3. Evaluation of ICT
This section considers some of the practical arrangements for exploiting the use
of ICT to best effect, and discusses the qualities of the ICT methods which make
a special contribution to students‟ learning.
DATA-LOGGING
A previously described, there are two main types of sensors useful for measuring
motion; the light-gate and the ultrasonic motion sensor. The former gives
discrete measurements whilst the latter delivers a continuous stream of data
which may be immediately plotted on a distance-time graph in real time. Each
illustrates how data-logging enhances the value of practical experiments beyond
the limitations of conventional methods. The software program can perform
instant calculations to make available the derived quantities of velocity and
acceleration. It can also present graphs in real-time and offer a range of
analysis tools which assist the exploration and interpretation of the collected
data.
Activity 1. Analysing motion
This data-logging experiment introduces
the motion sensor in an informal manner
which has proved very successful with
younger and secondary age pupils. As
the pupil walks forwards and backwards
in front of the sensor, the immediate
display of the distance-time graph allows
the pupil to associate clearly the shape of
the graph with the type of motion. The
intimate connection between the personal
Motion and Forces- 8
movement and the data appearing on the screen provides a compelling
experience for the pupil, which has excellent potential for developing skills with
graphs: With suitable prompting from the teacher, the pupil may be led to
understand better how to interpret the shape of the graph. A valuable extension
activity consists of displaying a pre-set graph on the screen and then asking the
pupil to move in such a way that the data from the sensors produces a similar
graph.
Activity 2. Free fall
In this data-logging experiment a light gate is used which provides very accurate
time measurements. As a card passes through the gate, a light beam becomes
interrupted, and the time for the interruption may be used to calculate velocity
and acceleration. The calculation is done automatically by the program such
that values for velocity become instantly available. In effect the light gate
system becomes a „velocity meter‟ which is a great advance on methods that
employ manual calculation. Thus the thinking activity of the experiment can
clearly focus on a relationship between variables, rather than upon the
procedure of obtaining data. In the experiment on free fall, students can quickly
obtain a series of readings for the velocity of the card and relate these to the
height fallen in each case.
Activity 3A. Force and acceleration (using Insight ILOG)
In this experiment, the double segment card placed on the trolley allows the
calculation of two velocities in rapid succession so that acceleration may be
calculated. The activity of the experiment is then to investigate the relationship
between the acceleration of the trolley and the force causing the acceleration.
The expected results should match Newton‟s Second Law of Motion. In both
experiments, the prompt display of graphs and the use of curve fitting tools
allow trends to be evaluated and measured.
Motion and Forces- 9
Activity 3B. Force and acceleration (using Coach 6)
In this experiment the force sensor is attached to the trolley. The string runs
from the force sensor, over a pulley, to a hanging mass. The force sensor
measures the tension force. The motion detector records the motion of the
trolley as the string pulls it. Such set-up allows delivering a constant force to the
cart via the string and hanging mass. The experiment is then repeated for
different hanging masses. The activity of the experiment is then to investigate
the relationship between the acceleration of the trolley and the force causing the
acceleration. The expected results should match Newton‟s Second Law of Motion.
In both experiments, the prompt display of graphs and the use of curve fitting
tools allow trends to be evaluated and measured.
Activity 4. Rebounding trolley
In this data-logging experiment the motion sensor is used to monitor the motion
of a trolley. As in the first experiment, the distance data appears on the screen
as a continuous stream giving a smooth distance vs. time graph. For the
rebounding
trolley,
the
graph
shows
distinctive
features
which
can be
associated
with
motion
down and up the runway,
and points where the trolley
either comes to rest or
collides with the spring
buffer at the bottom of the
runway. At any point on the
graph the gradient indicates
the velocity which can be
measured using the gradient
tool. The program can also
calculate and plot a further
graph showing velocity vs.
time.
Motion and Forces- 10
Careful examination of this
shows that the velocity
after rebound is slightly
less than the velocity
before.
The gradient of
this
graph
indicates
acceleration
which
is
shown to be different for
motion
up
the
slope
compared
with
motion
down the slope.
The
difference
may
be
accounted
for
by
considering the role of
friction.
VIDEO MEASUREMENT
In the video-measurement activities students are able to consider events, which
happen outside the classroom. The position and time data are collected in the
selected video frames manually by clicking, or automatically, by tracking a
selected moving object e.g. a ball. The video data can be displayed in graphs
and tables and can be used for further analysis and processing. Graphs and
tables are synchronized with the video frames. When scanning the data in the
graph the corresponding video frames are shown. This helps students to bridge
the gap between the concrete visual display of a motion event and its abstract
graphical representation.
Activity 5. Falling ball
The video of the ball dropped
from a ladder allows analyzing
the motion of a free falling ball.
Before the measurement the
perspective distortion has to be
corrected and distance calibration
has to be performed. During the
measurement
the
vertical
position
data
are
plot
immediately and are used to
determine
the
velocity
and
acceleration of the falling ball.
In this measurement
measurement results.
the
manual
measurement
Motion and Forces- 11
gives
more
accurate
Activity 6. Moon jump
The events analysed via video
measurements can be more
unusual. In this activity such
example is used, the jump on the
Moon.
Based on the video
measurements students determine the acceleration due to the
Moon gravity.
Activity 7. Find a force
In this activity students measure
the position of the moving car.
They determine its acceleration
and the acting force.
Activity 8. Falling shuttlecock
This activity makes use of the video clip
recorded with a high-speed digital camera.
Such camera is useful in cases where
motion is too quick for recording with a
normal digital camera or webcam, e.g.,
data collection of human and animal
locomotion or motion in sports.
The video clip used in this activity shows
the motion of the free falling badminton
shuttlecock in which the effects of air
resistance are important and measurable.
Students investigate the motion and have
to explain how a constant terminal velocity
is reached.
The video clip reveals the small but for the
required accuracy substantial problem of
perspective distortion. In the prepared
video the perspective correction is already
applied.
Picture at the right shows the experimental setting after the correction of
perspective distortion.
Motion and Forces- 12
SIMULATION
The simulations presented here are best used as teacher demonstrations for
facilitating class discussions of the concepts involved. Their use needs to be
carefully managed and integrated with discussion in order to develop clear
logical thinking. Random clicking on the various program features is unlikely to
benefit thinking about subtle concepts, about which pupils often have very
confused ideas, so a structured approach is essential.
The simulations for this module have been chosen to illustrate the power of this
type of program to facilitate discussion leading to an understanding of abstract
concepts. They provide visualisations of examples of motion which may be
imagined in real life, but the software allows experimentation well beyond what
is feasible in reality.
Activity 9. Rolling ball
This simulation can promote thinking about the independence of the vertical and
horizontal components of motion when a body is moving in two dimensions. The
vertical acceleration of the ball is demonstrated to be the same irrespective of its
horizontal velocity, making the „fall time‟ always the same. Similarly, the ball‟s
horizontal velocity remains constant throughout the whole trajectory before
reaching the ground. The effect of the magnitude of horizontal velocity on „roll
time‟ may be studied by setting different initial values. When the bounce
condition is switched on it becomes harder to study time values but the graph of
vertical velocity shows the reversals and decay of velocity.
Activity 10. Rebounding trolley
This simulation is a virtual version of the data-logging experiment 4. The graph
initially shows the distance vs. time data. As with the experiment, the features
of the graph may be associated with the to-and-from motion of the trolley, but
with the additional visual aid in the Scene window. Dragging the cursor across
the graph shows very clearly the correspondence between the trolley motion and
the graph. Analysis of the graph can follow similar lines to that of the data
collected in the experiment: show derived graphs for velocity and acceleration
and think about how they are related to each other. The simulation also offers a
view of the variation of the friction force during the motion of the trolley.
When the model for the simulation is visible, the physical basis for the
calculations may be explored and further investigations are possible through
varying the slope angle and friction constant. These activities will be discussed
in the „Modelling‟ Activity 14 below.
Activity 11. Terminal velocity
This simulation can be a useful tool for discussing the validity of Newton‟s laws
of Motion which seem to be contradicted in many natural situations in everyday
life, largely due to the invisible presence of friction. In this example of pedalling
a bicycle, it is clear that, having obtained some speed, if the cyclist stops
pedalling, motion does not continue with uniform velocity, as predicted by the
First Law. Of course this is a false conclusion because the force of friction has
Motion and Forces- 13
been ignored; the law requires thinking about the resultant of all forces acting
on the cyclist in the direction of motion.
Similarly, when pedalling with a steady force, the bicycle does not experience a
steady acceleration as predicted by the Second Law. Again, this is a false
conclusion due to the neglect of friction. The simulation shows that, for a given
pedalling force, there is an initial period of acceleration as predicted by the
Second Law, but the rate of acceleration diminishes as the opposing friction
force reaches parity with the pedalling force making the resultant force zero. At
this stage the bicycle reaches a steady velocity as predicted by the First Law.
This steady velocity is usually called „terminal velocity‟. The dynamic character
of the frictional force, increasing with velocity, is well illustrated using the
simulation; graphs of velocity, acceleration, pedalling force and friction force
may be readily compared.
MODELLING
The purpose of the modelling activities is to give pupils an insight into the
physical and mathematical basis of the calculations performed by the model.
The essence of modelling is to experiment with adjusting the model so that it
gives results which best match data from real experiments. The results from the
models may be compared directly with those obtained from the data-logging
activities and simulations.
Activity 12. Free fall
The model is based upon the simple assumption that the acceleration of an
object freely falling due to gravity is constant. From this, calculations are made
of velocity and vertical distance using the basic definitions of their relationships
with time.
In the Insight modelling system the first formula calculates the change of
velocity Δv during the time interval Δt:
v
where
a
t
a is the acceleration (due to gravity)
The second formula calculates the change of vertical distance Δs during the time
interval Δt:
s
where
v
t
v is the current value of velocity.
Motion and Forces- 14
The Insight calculates these changes in repeated cycles and automatically
updates the values of v, s and t in each cycle by summing the respective
changes. As the model runs, velocity increases linearly, but the distance
increases non-linearly. The graphs may be explored by finding gradients: the
gradient of the velocity-time graph indicates acceleration; the gradient of the
distance-time graph indicates velocity. Use of the cursors allows values to be
conveniently compared.
In the Coach 6 modeling system the change of vertical position y and the change
of velocity v of a moving object are found by numerical integration of equations:
v
dy
dv
and a=
dt
dt
By using the acceleration due to the moon‟s gravity (which can be determine
experimentally in the Activity 6) model can be modified to observe a fall on the
moon.
In both systems the data generated by the model is usefully compared with the
results for the falling card in Activity 2 or with the results for the falling ball in
Activity 5.
The relationships represented in the model illustrate the physical principles
which govern the motion of falling objects. This is an example of how the
methods of data-logging, video measurements and modelling can provide
complementary learning experiences.
Activity 13. Force and acceleration
This model builds upon the previous model for free fall, but in this case the
acceleration „a‟ is not assumed to be constant but is calculated from the
resultant force „F‟ acting on the object of mass „m‟:
a
F
m
This is no less than Newton‟s Second Law of Motion.
The model generates data in a similar way to the previous model, except that in
this case the mass of the object and the resultant force acting on it may be
specified freely. Again the model invites comparison with data collected in a real
Motion and Forces- 15
experiment, in this case Activity 3a and 3b where a trolley is pulled by a
constant force in the string.
Activity 14. Rebounding trolley
This model is yet a further development of the previous models. The newly
introduced factor here is a second force, that of friction, in addition to the
component of gravity causing the trolley to roll down the slope. There are two
interesting features of the frictional force: it varies with the speed of the trolley
and its direction changes, always opposing the motion of the trolley. Both of
these features are implicit in the formula for calculating the force of friction „Ff‟:
Ff
where
c v
c is a constant representing the degree of friction
v is the velocity of the trolley
The component of gravity down the slope is calculated thus:
Fs
where
mg sin(b)
m is the mass of the trolley
g is the strength of gravity
b is the angle of the slope
To calculate acceleration, the Resultant force must be calculated as Fs + Ff.
This model complements the data-logging experiment in Activity 4 and the
simulation in Activity 10 and similar activities for investigating the data may be
used. Those activities become extended by exploiting the possibility of choosing
different values for the angle of slope, the strength of gravity and the mass of
the trolley. As with previous models, this model illustrates the physics principles
involved in the motion of the trolley; a complex problem is broken down into
simple stages.
Activity 15. Terminal velocity
As with the previous model, two forces are applied to the object requiring the
resultant force to be calculated before calculating the acceleration.
In Insight the model is similar to the one employed in the simulation of the
bicycle Activity 11 in which a constant force is applied to the pedals and is
opposed by the force of air resistance (fluid friction).
The latter force (Ff) is assumed to depend upon the square of velocity:
Ff
k v 2 where k is a drag constant
As with activity 11, both the acceleration phase and terminal velocity phase may
be explored by studying the graphs. The resultant force is seen to follow the
same pattern as the acceleration, becoming zero when terminal velocity is
established and negative when velocity reduces. The frictional force increases
and decreases according to the velocity, but changes are amplified compared
with changes in velocity, a result to be expected as the force depends upon the
square of velocity.
Motion and Forces- 16
The Coach 6 model can be used to compare theoretical predicted data with
experimental data from Activity 8 in which the motion of the free falling
shuttlecock, where the effects of air resistance are important, is recorded.
During the fall of the shuttlecock two forces act on it: the gravitational force and
the drag force depending on the shuttlecock‟s velocity. There are two types of
drag possible:
-
linear drag Fdrag
-
quadratic drag Fdrag
k v , or
k sign(v ) v 2 where k is a drag constant.
Students investigate which model better match the experimental data.
Once again, the modelling activity complements the data-logging and simulation
activities, each method providing different insights and opportunities for learning.
4. Teaching approaches
The three groups of activities
presented here offer distinctive but
complementary insights into the
science involved in this topic. For the
activities to be effective for teaching
and learning, it is helpful for teachers
to consider two types of skills in
using the software tools:
Operational skills which concern
the manipulation of the computer
hardware and knowledge of the
features in the software.
Procedural skills which concern
the manner in which the software
tools are employed in the lesson
context for the purpose of
achieving learning benefits. A
dominant aspect of these skills is
the development of an inquiring
approach to the analysis and
interpretation of data and to
making links with previous
knowledge.
Such skills are important for the
preparation of pupils for the activities,
and the activity sheets below each
contain indications of the skills
needed for the particular activity.
For the teacher, there are further
pedagogical skills which contribute to
the effectiveness of the activities:
1. Clarity of learning objectives for
each activity.
2. Understanding of the special value
of the ICT method and exploiting
its full potential in purposeful
ways.
3. To manage the activity in a way
which promotes „appropriate‟
rather than „indiscriminate‟ use of
ICT.
4. To integrate the learning from
each activity to develop pupils‟
understanding of the topic.
The development of the last of these
is a particular aim of the ICT for IST
Project, and the activities presented
below have been specially selected to
illustrate how integration might be
achieved. The different types of
activities are intended to be
complementary both to each other
and to further practical activities
away from the computer. Teachers
Motion and Forces- 17
will usually have their preferred
sequence of teaching themes
involving, demonstrations,
explanations, class experiments, but
the table below suggests a suitable
Teaching sequence
sequence exemplifying a logical
development of concepts. The right
hand column shows how the activities
in this module may be chosen to
enhance the teaching sequence
ICT for IST Activities
Define concepts of speed and velocity
from distance and time
* Experiments measuring distance and
time to calculate speed
D-Logging:1 Record walking motion
Define acceleration
Discuss gravity and free fall
* Observe independence of vertical and
horizontal components of motion
Simulation: 9 Rolling ball
D-Logging: 2 Investigate free fall
Model: 12 Uniform acceleration
*Experiment to investigate the
relationship between the force on an
object and the resulting acceleration.
Introduce concept of mass and inertia
D-Logging: 3 Force acting on a
trolley
Model: 13 Force, mass and
acceleration
*Experiment to study the effect of an
object‟s mass on its acceleration
Introduce the effect of frictional forces
Define Resultant force
* Experiments with runways to
compensate for friction
Introduce concept of terminal velocity
D-Logging: 4 Rebounding trolley
Simulation: 10 Rebounding trolley
Model: 14 Rebounding trolley
Video measurement: 10 Terminal
velocity
Simulation: 11 Terminal velocity
Model: 15 Terminal velocity
The non-computer experiments (*) are not described here, since their details
are well established in conventional teaching schemes and text books.
Motion and Forces- 18
Comparisons of the observations
and results of each activity form a
central role in this integration
process. For example:
Compare the graphs obtained in
the data-logging experiments; a
velocity-time graph may be
derived from the slope of a
distance-time graph; acceleration
is indicated by the slope of a
velocity-time graph;
Compare the results from the
simulations and data logging
experiments
to
make
links
between
the
results
of
experiments and their theoretical
explanation.
In these, the graph is a key tool in
facilitating
comparisons
and
interpretations and skills with graphs
generally provide a common thread
in exploiting ICT for IST activities.
In several cases, the graph is a key
tool in facilitating comparisons and
interpretations and skills with graphs
generally provide a common thread
Activity
Data-logging
1 & 3B, 4. Motion
sensor graphs
2 & 3A. Light gate
measurements
Video
measurement
in exploiting ICT for IST activities.
The management of the classroom
setting also has an important
influence
on
the
successful
integration of activities.
For this
module, in view of the fact that an
understanding of motion requires
clear thinking about several interrelated concepts, we suggest that
the teacher needs to provide a
strong guidance structure in the use
of the activities. Most teachers will
achieve
this
through
didactic
demonstrations linked with whole
class discussion. However, there are
still opportunities for follow-up work
(reinforcement, extension, revision
etc.) by pupils working individually
or in pairs or in groups. Again, it is
usually advisable to provide a
structure for activities using some of
the worksheet suggestions. In both
planning
and
teaching,
it
is
important to have clear learning
objectives for the use of the
activities, and to assist this, the
table
below
summarises
their
distinctive potential learning benefits.
Potential learning benefits, ‘ICT value’
Graph of distance vs. time is displayed during experiment
Changes are observable immediately.
Graph analysis tools facilitate detailed investigation of data.
Instant calculations of velocity and acceleration
Allows detailed analysis of the motion of moving objects.
6. Moon jump
A graph of position versus time is created during the
measurement. This graph can be used for calculating the
velocity and the acceleration.
7. Find a force
Graph analysis tools facilitate detailed investigation of data.
8. Falling
shuttlecock
The motion of a moving object can be easily compared with
its graphical representations.
5. Falling ball
Motion and Forces- 19
Simulation
9. Vertical &
horizontal motion
10. Rebounding
trolley
Animated graphics provide visualisation of the abstract
concepts involved in analysing motion:
- Independence of vertical and horizontal components of
motion in two dimensions
- Relating graph features to motion events
11. Terminal
velocity
- The distinction between velocity and acceleration
Modelling
The models demonstrate how the relevant physical
principles can be expressed in simple stages using
mathematical formulae. They help to break down complex
physical phenomena into simple understandable stages.
12. Free fall
13. Force and
acceleration
- The role of friction in interpreting the Laws of Motion
14. Rebounding
trolley
The models calculate data which may be compared with
data obtained from the real experiments (data-logging) with
circuits.
15. Terminal
velocity
The effect of altering parameters such as air resistance,
gravitational field strength, friction may be investigated.
Model 1 shows how basic definitions of velocity and
acceleration can be related to experimental data.
Model 2 illustrates how Newton‟s Second Law of Motion can
be used for predicting motion.
Models 3 and 4 illustrate the role of dynamic friction in
motion.
Motion and Forces- 20
5. Resources for Student Activities
USING INSIGHT SOFTWARE
Activity
1. Data-logging
Software
program
Insight iLOG
Files available
1. walking set up
1. walking data (sample data)
2. Data-logging
Insight iLOG
2. free fall set up
2. free fall data (sample data)
3. Data-logging
Insight iLOG
3. acceleration set up
3. acceleration data (sample data)
4. Data-logging
Insight iLOG
4. rebounding set up
4. rebounding data (sample data)
9. Simulation
Simulation Insight
9. rolling ball simulation
10. Simulation
Simulation Insight
10. rebounding simulation
11. Simulation
Simulation Insight
11. terminal simulation
12. Modelling
Simulation Insight
12. free fall model
or Insight iLOG
13. Modelling
Simulation Insight
13. acceleration model
or Insight iLOG
14. Modelling
Simulation Insight
14. rebounding model
or Insight iLOG
15. Modelling
Simulation Insight
15. terminal model
or Insight iLOG
Motion and Forces- 21
USING COACH SOFTWARE
Activity
Software
program
1. Data-logging
Coach 6
Files available
01.Analysing motion.cma (activity file)
01.Analysing motion.cmr (result file)
2. Data-logging
Coach 6
02.Relation between velocity and distance fallen
for a card in free fall.cma (activity file)
3. Data-logging
Coach 6
03.Force causes acceleration.cma (activity file)
03.Force causes acceleration.cmr (result file)
4. Data-logging
Coach 6
04.Rebounding trolley.cma (activity file)
04.Rebounding trolley.cmr (result file)
5. Video
measurement
Coach 6
05.Falling ball.cma (activity file)
6. Video
measurement
Coach 6
7. Video
measurement
Coach 6
8. Video
measurement
Coach 6
12. Modelling
Coach 6
13. Modelling
Coach 6
13.Model of force and acceleration.cma (activity
file)
14. Modelling
Coach 6
14.Model of a rebounding trolley.cma (activity
file)
15. Modelling
Coach 6
15.Model of terminal velocity.cma (activity file)
05.Falling ball.cmr (result file)
06.Moon jump.cma (activity file)
06.Moon jump.cmr (result file)
07.Find a force.cma (activity file)
07.Find a force.cmr (result file)
08.Falling shuttlecock.cma (activity file)
08.Falling shuttlecock.cmr (result file)
12.Model of free fall.cma (activity file)
15.Model of terminal velocity - linear.cmr
(result file with experimental data)
15.Model of terminal velocity - quadratic.cmr
(result file with experimental data)
Motion and Forces- 22
EQUIPMENT AND MATERIALS FOR DATA-LOGGING ACTIVITIES
Computer
Software – See table above
Interface (data-logger)
Light gate. motion sensors, force sensor
Dynamics trolley
Runway
Adjustable masses, string, pulley in clamp
Black card and scissors
Clamps and stands
Low voltage fan and power supply
Motion and Forces- 23
C. Student Activities
ACTIVITY 1. ANALYSING MOTION
Learning Objectives:
1.
To obtain distance-graphs of pupils‟ motion as they
walk in front of a motion sensor.
APPLIED ICT TECHNOLOGY:
DATA LOGGING
2.
To relate the shape of the graphs to the motion
which produced them.
STUDENT LEVEL:
AGE 14-17
3.
To obtain measurements for finding velocity from
the graph.
4.
To derive a velocity-time graph from data for
distance.
RECOMMENDED SETTINGS:
STUDENT ACTIVITY IF
ENOUGH EQUIPMENT IS
AVAILABLE, OTHERWISE
TEACHER DEMONSTRATION
Operational Skills:
Connecting sensors and interfaces
Choosing logging parameters
Starting and finishing real-time logging
Using the cursor tools for obtaining measurements from the graph
Changing the designation of the graph axes
Deriving secondary data by calculation
Procedural Skills:
Evaluating measurement quality
Analysing data using graph
Reading values/slopes
Materials:
Interface (data-logger)
Motion sensor
Stand and clamp
Motion and Forces- 24
Activity method:
1.
Set up the motion sensor clamped to
a stand at chest height as shown.
Take care that there is an open path
at least 2 metres wide and 3 metres
long in front of it.
2.
Set the data logging software to
record distance for about 30 seconds.
3.
Starting from about 30 cm from the
sensor, start recording data. The
motion sensor is taking readings
when you hear it “ticking” fast. First
stand still then move forwards and
backwards.
4.
Observe the graph and relate it to the original motion.
5.
Obtain other graphs which represent different types of motion such as
steady speed and acceleration.
Analysing activities (using Insight iLOG):
1.
Sweeping cursors
After the experiment, the real-time experience can be re-lived to a certain
extent using the graph cursors and bar display: Drag the X cursor slowly
across the screen, and note how the bars grow and shrink in the same
manner as the changes of the values recorded during the experiment,
creating an „action replay‟ effect.
2. Taking measurements from the graph
Use the cursor to find the furthest distance recorded by the sensor. Then
take measurements to find the distance moved in 1 second at different
places on the graph.
3.
Calculate speed
Measure the gradient of the graph line to find the speed of movement at
different times during the experiment.
Questions and Assignments (using Coach 6):
Describe how the distance between you and the sensor changes with time.
Read out the initial, smallest and the greatest distance from the sensor.
Describe the motion graph shape.
Explain the significance of the slope of the distance-time graph.
How does the slope change during the motion of the cart?
Motion and Forces- 25
What does this tell you about its motion?
Measure the slope of the graph line (use the Slope option) to find the
velocity of movement at different times during the experiment?
Create a motion graph which looks like a letter M?
Write down which steps (in time intervals) were necessary to create your
'M' – shape motion graph. Use words like: stand still, move
forward/backward, move slow/fast.
Analysing activities (using Coach 6):
Students walk in front of the motion sensor and a graph of distance vs. time is
being plotted real-time on the computer screen during their motion. Students
are asked to interpret resulting graphs.
In the second part of the
activity students are asked to
walk to create a motion
graph which looks like a
letter M, like the graph at the
right.
It is recommended that
students save their data after
each measurement.
The default behaviour of
Coach is that when a
measurement run is followed by another run, the data of the previous run is
overwritten, and its graph becomes gray (it is only displayed on the screen).
To keep previous runs active the option Copy Column should be used. This
option is available after a measurement run, by right clicking the diagram or
table.
Further work:
Use the software to derive a graph of speed against time.
Record a graph for walking at a steady speed, then look carefully at the
speed graph for evidence of your reciprocating leg movement whilst
walking.
Motion and Forces- 26
ACTIVITY 2. RELATIONSHIP BETWEEN VELOCITY
AND DISTANCE IN FREE FALL
Learning Objectives:
1. To obtain a graphs of velocity against height fallen
for a weighted card falling vertically.
2. To interpret the graphs so as to describe the
relationship between the velocity of the card and
the height fallen.
3. To investigate the effect of the mass or the shape
of the card on the final velocity.
APPLIED ICT TECHNOLOGY:
DATA LOGGING
STUDENT LEVEL:
AGE 14-17
RECOMMENDED SETTINGS:
STUDENT ACTIVITY IF
ENOUGH EQUIPMENT IS
AVAILABLE, OTHERWISE
TEACHER DEMONSTRATION
Operational Skills:
Connecting sensors and interfaces
Choosing logging parameters
Managing the collection of timing data
Using the cursor tools for obtaining measurements from the graph
Procedural Skills:
Evaluating measurement quality
Analysing data using graph
Reading values/slopes
Materials:
Interface (data-logger)
Light gate sensor
Black card weighted with two blobs of plasticine
Ruler (1 metre)
Stand and clamp
Motion and Forces- 27
Activity method:
1. Assemble the apparatus so that the lightgate sensor is about 20cm above the
bench.
2. Hold the card 10 cm above the sensor, set
the software to record velocity and release
the card. Note the velocity and enter the
height fallen against this value in the table.
Repeat this four times for the same starting
height.
3. Repeat the whole process several times,
dropping the card from different heights.
4. Observe the graph of velocity against
height fallen.
Analysing activities (using Insight iLOG):
1. Observe the graph
Use the cursor to study how the values vary from one point to the next. Is
there a simple pattern in the results?
2. Fit a line to the points
Use a best-fit line to pass through all the points and identify the formula
which describes this line.
3. Search for a pattern in the results
Theory predicts that velocity varies according to the square root of height.
Test this by building a formula to calculate the square root of height and
plot these values on a new graph against velocity. A straight line confirms
the theoretical prediction.
Questions and Assignments (using Coach 6):
Use the Scan option to study how the values vary from one point to the
next. Is there a simple pattern in the results?
Does the card fall twice as fast if you drop it from twice the height?
What is the relationship between the velocity and the height fallen? Use a
best-fit line to pass through all the points and identify the formula which
describes this line.
Theory predicts that velocity varies according to the square root of height.
Test this by building a formula to calculate the square root of height and
plot these values on a new graph against velocity. A straight line confirms
the theoretical prediction.
Motion and Forces- 28
Analysing activities (using Coach 6):
In this activity the time interval of the black card passing along the light gate
is measured. The velocity is calculated based on this measured interval and
the length of the card. In Coach Activity it is assumed that the card has 10 cm
length. The respective dropping height has to be typed in. Students
investigate how the velocity of the card depends upon the height it falls.
Motion and Forces- 29
Activity 3A. INVESTIGATING FORCE AND
ACCELERATION (USING INSIGHT iLOG)
Learning Objectives:
1. To obtain a graph of acceleration against force
for a trolley pulled by string attached to a falling
mass.
2. To interpret the graphs so as to describe the
relationship between the acceleration and the
force causing it.
3. To investigate the effect of the mass on the
acceleration.
APPLIED ICT TECHNOLOGY:
DATA LOGGING
STUDENT LEVEL:
AGE 14-17
RECOMMENDED SETTINGS:
STUDENT ACTIVITY IF
ENOUGH EQUIPMENT IS
AVAILABLE, OTHERWISE
TEACHER DEMONSTRATION
Operational Skills:
Connecting sensors and interfaces
Choosing logging parameters
Managing the collection of timing data
Using the cursor tools for obtaining measurements from the graph
Changing the designation of the graph axes
Procedural Skills:
Evaluating measurement quality
Analysing data using graph
Reading values/slopes
Materials:
Interface (data-logger)
Light gate sensor clamped on a stand
Trolley fitted with double segment black card
String and pulley
Stackable masses: 4 x 50g
Motion and Forces- 30
Activity method:
1. Prepare the card
with two
accurately cut
vertical segments
and attach it to
the trolley.
2. Clamp the lightgate sensor so
that the card
passes through
the beam when
the trolley moves along the bench.
3. Clamp the pulley on the edge of the bench, tie one end of the string to the
slotted mass holder, run the string over the pulley and attach the other end
to trolley.
4. Begin with a falling mass of 100g giving a tension of 1 newton.
Place the
spare 300g mass on the trolley.
5. Pull the trolley away from the pulley so that the slotted mass is raised to a
point just below the pulley. Start logging and release the trolley, allowing
the mass to fall and the trolley to move along the bench
6. Repeat the measurement several times, each time recording the force of 1
newton in the table.
7. Take one of the 100g masses from the trolley and add it to the falling
mass, making the tension force 2 newton. Pull back and release the trolley
to make more measurements.
8. Repeat the process to obtain measurements for 3 and 4 newtons. Each
time you release the trolley, record the string tension in the 'Force' column
of the table.
Analysing activities (using Insight iLOG):
1. Look at the bar chart
In the Table, click on the heading of the 'Acceleration' column to highlight
all the acceleration values and click on the 'Chart' button.
What does the shape of the chart tell you about the range of results for acceleration?
2. Look at the graph of acceleration vs. force
Move the cursor across the graph, and observe the bar display which shows how the
Motion and Forces- 31
acceleration varied during the experiment.
Think about the connection between the acceleration and the force.
3.
Find out what sort of line fits the graph:
Use the „Trial Fit‟ option to find a formula which gives the best fit straight
line through the data.
Theory predicts that the acceleration varies in proportion to the applied force. Do your
results indicate this?
Further work:
Find out how the graphs are affected by the mass of the trolley: Add mass
to the trolley, repeat the measurements and compare the results with the
first set.
Motion and Forces- 32
Activity 3B. INVESTIGATING FORCE AND
ACCELERATION (WITH COACH 6)
Learning Objectives:
1. To obtain a graph of acceleration against force
for a trolley pulled by string attached to a falling
mass.
2. To interpret the graphs so as to describe the
relationship between the acceleration and the
force causing it.
3. To investigate the effect of the mass on the
acceleration.
APPLIED ICT TECHNOLOGY:
DATA LOGGING
STUDENT LEVEL:
AGE 14-17
RECOMMENDED SETTINGS:
STUDENT ACTIVITY IF
ENOUGH EQUIPMENT IS
AVAILABLE, OTHERWISE
TEACHER DEMONSTRATION
Operational Skills:
Connecting sensors and interfaces
Choosing logging parameters
Managing the collection of timing data
Using the cursor tools for obtaining measurements from the graph
Changing the designation of the graph axes
Procedural Skills:
Evaluating measurement quality
Analysing data using graph
Reading values/slopes
Materials:
Interface (data-logger)
Force sensor
Motion sensor
String and (low-friction) pulley
Track system with a low friction trolley
Hanging mass set
Motion and Forces- 33
Activity method:
1. Mount the pulley to the edge of the table or at the end of the Dynamics
Track, allowing the string to hang over the edge.
2. Place the motion detector (default 0664) at the other side of the table or
the track, allowing for the 20 cm minimum distance between the motion
detector and the cart.
3. Attach the force sensor to the top of the cart, oriented so that the
horizontal tension on the string will be detected.
4. Run the string from the force sensor, over a pulley, and to a hanging mass.
Initially use about 20 g.
5. Start your measurement and at the same time release the cart. Let the car
roll toward the pulley. Be sure that the mass is free to fall for the entire
distance the cart travels and the cables are not hindering motion. Catch the
cart before it hits the pulley.
6. Measure the combined mass of your cart and the force sensor.
7. Repeat the experiment for 3 additional hanging masses.
8. Perform assignments given in the Data Analysis.
Questions and assignments:
Look at the recorded data. What kind of motion do you observed? What
does a slope of velocity represent?
Determine the average acceleration during the cart's rolling time.
Determine the average force applied during the cart's rolling time.
Repeat the experiment for 3 additional hanging masses (every time add 20
g extra).
Note: You can keep all runs in the same diagram by using the 'Copy
Motion and Forces- 34
column' option available in the Tool menu of the Diagram window.
Now you have several data runs. What was the effect of adding masses?
Can you see a pattern in the data over the course of several runs?
Write down the force and acceleration values for each trial. Are force and
acceleration related?
Analysing activities:
The force sensor is attached to the trolley. The string runs from the force
sensor, over a pulley, to a hanging mass. The force sensor measures the
tension force. The motion detector records the motion of the trolley as the
string pulls it. Such set-up allows delivering a constant force to the cart via the
string and hanging mass. The experiment is then repeated for different
hanging masses. Students should discover first that the constant force causes
constant accelerated motion and second that larger force produces higher
acceleration; the force is proportional to the acceleration.
Further work:
Find out how the graphs are affected by the mass of the trolley:
Add mass to the trolley, repeat the measurements and compare the
results with the first set.
Motion and Forces- 35
ACTIVITY 4. INVESTIGATING THE MOTION OF A
REBOUNDING TROLLEY
Learning Objectives:
1. To obtain graphs of distance against time and
velocity against time for a trolley rolling up and
down a slope.
2. To associate the features of the graphs with the
observed motion.
3. To interpret the shapes of the graphs in terms of
the forces acting on the trolley.
APPLIED ICT TECHNOLOGY:
DATA LOGGING
STUDENT LEVEL:
AGE 14-17
RECOMMENDED SETTINGS:
STUDENT ACTIVITY IF
ENOUGH EQUIPMENT IS
AVAILABLE, OTHERWISE
TEACHER DEMONSTRATION
Operational Skills:
Connecting sensors and interfaces
Choosing logging parameters
Starting and finishing real-time logging
Using the cursor tools for obtaining measurements from the graph
Changing the designation of the graph axes
Deriving secondary data by calculation
Procedural Skills:
Evaluating measurement quality
Analysing data using graph
Reading values/slopes
Materials:
Interface (data-logger)
Motion sensor
Stand and clamp
Trolley
Runway
Spring buffer attached to a trolley or to a runway
Motion and Forces- 36
Activity method:
1. Assemble the apparatus so that the trolley can move up and down the
sloping runway (exemplary setup shown on the picture below).
2. Set the data logging software to record data and plot a graph of distance
against time.
3. Move the trolley by hand up and down the runway in the following different
ways and observe the shape of the graph in each case:
-
a constant velocity away from the sensor,
a faster or slower constant velocity,
an acceleration,
a deceleration,
an oscillation.
4. Reset the software to record a new set of data, release the trolley from the
top and allow it to roll down and bounce off the block at the lower end.
5. Observe the graph showing the forwards and backwards motion.
Analysing activities (using Insight iLOG):
1. Sweeping cursors
After the experiment, the real-time experience can be regenerated using
the graph cursors and bar display: Drag the X cursor slowly across the
screen, and note how the bars grow and shrink in the same manner as the
changes of the values recorded during the experiment, creating an „action
replay‟ effect.
What parts of the graph are associated with the collisions with the barrier?
What parts of the graph are associated with the trolley at rest?
2. Taking distance measurements from the graph
Select „Change‟ and use the cursor to find the distances moved by the
trolley after each rebound.
Describe the pattern of results for successive oscillations.
3. Taking time measurements from the graph
Select „Interval‟ and find the time intervals between the successive
Motion and Forces- 37
collisions with the barrier.
Describe the pattern of results between successive collisions.
4. Calculate velocity
Measure the gradient of the graph line to find and compare the velocities
before and after each collision with the barrier.
What does this tell you about the type of collisions with the barrier?
5.
Use the software to derive a graph of velocity against time.
What does the graph indicate about the acceleration of the trolley?
Questions (using Coach 6):
What parts of the graph are associated with the collisions with the barrier?
What parts of the graph are associated with the trolley at rest?
Describe the pattern of results for successive oscillations.
Find the time intervals between the successive collisions with the barrier.
Find and compare the velocities before and after each collision with the
barrier. What does this tell you about the type of collisions with the barrier?
Use the software to derive a graph of velocity against time.
What does the graph indicate about the acceleration of the trolley?
Further work:
The basic experiment can be applied to several investigations:
Find out how the slope of the runway affects the graph.
Find out the effect of increasing the mass of the trolley by attaching
further masses.
Add a wind brake to the trolley to increase air friction.
Replace the spring buffer with a cardboard „crumple zone‟.
Motion and Forces- 38
ACTIVITY 5. FALLING BALL
Learning Objectives:
1. To obtain graphs of height versus time and velocity
versus time for a free falling ball
2. To interpret the motion graphs
3. To determine the acceleration of a freely falling ball
APPLIED ICT TECHNOLOGY:
VIDEO MEASUREMENT
STUDENT LEVEL:
AGE 14 - 17
RECOMMENDED SETTINGS:
STUDENT ACTIVITY
Operational Skills:
Making measurements on the Video Screen
Using the Perspective correction, Function fit and Derivative options
Procedural Skills:
Analysing data using a graph
Reading values/slopes
Evaluating measurement quality
Materials:
Video film which shows a person standing on a ladder and dropping a ball.
Activity method:
1. In the Data-Video Window you see a video clip of a person standing on a
ladder and dropping a ball. Watch the video clip.
2. In this video you are going to measure the height of the falling ball. To
perform correct measurement first you need to correct the perspective
distortion.
3. Right click the Data-Video window and select the menu option Perspective
correction. A red perspective rectangle is placed on the top of the video
screen. Drag the corners of the rectangle one by one to the corners of an
object in the video clip which has rectangle form. Every time a corner of
the perspective rectangle is moved the video screen is distorted. After
mapping all four corners the distorted rectangle is transformed. Now
deselect the menu item Perspective correction and the red rectangle
disappears.
4. Now you are going to scale your video. Right click the Data-Video window
and select the Change Scale... option. Move the origin of the coordinate
Motion and Forces- 39
system to a convenient position. Each tile on the wall has height of 2.2 m.
Move the scale-ruler to match the tile height and fill in the scale length 2.2
m.
5. Carry out measurements on the position of the ball. Start the measurement
by clicking the green Start button. Collect points by clicking on the ball.
6. The collected data appears on the graph of the height of the ball versus
time.
Questions:
Describe the height versus time graph.
What was the initial height of the ball?
How long was the motion?
What can you deduce about the ball's speed?
What can you deduce about the ball's acceleration?
Create a graph of the horizontal velocity versus time.
What was the initial velocity of the ball?
What was the final velocity of the ball?
What can you deduce about the ball's acceleration?
Determine the acceleration of the ball. How did you find it?
Compare this experimental value with the theoretical value of the Earth‟s
gravity. How close is you measured value to the theoretical value?
Lists some reasons why your values of the ball‟s acceleration may be
different from the accepted value for g.
Analysing activities:
Students measure the position of the falling ball, the height versus time graph
appears simultaneously. Students create velocity versus height graph and
analyse both graphs. They determine the ball‟s acceleration; different ways
are possible e.g. by using the Function fit, Derivative, or Slope options.
Motion and Forces- 40
The height versus time and the velocity versus time graphs of the falling ball.
Coach 6 Activity:
05. Falling ball
Motion and Forces- 41
ACTIVITY 6. MOON JUMP
Learning Objectives:
4. To measure a position of an astronaut during its jump
on the moon
5. To interpret position versus time graph with respect
to the visualized motion of the astronaut
APPLIED ICT TECHNOLOGY:
VIDEO MEASUREMENT
STUDENT LEVEL:
AGE 14 - 17
RECOMMENDED SETTINGS:
STUDENT ACTIVITY
6. To determine the acceleration due to the moon
gravity
7. To calculate the astronaut‟s weight on the moon
Operational Skills:
Making measurements on the Video Screen
Using the Scan, Function fit and Derivative options
Procedural Skills:
Analysing data using a graph
Reading values/slopes
Materials:
NASA Video film which shows the astronaut‟s jump on the moon (taken from
NASA web site)
Activity method:
1. In the Data-Video Window you see the first frame of the movie Moon jump.
This movie shows an astronaut jumps and salutes the American flag. Watch
the movie.
2. Carry out measurements on the position of the astronaut.
The movie is already scaled and the graph of position versus time is
prepared. It is assumed that the astronaut's height is 2 m. Notice how the
coordinates system is positioned in the Video screen.
3. From the position versus time graph determine the acceleration due to the
moon's gravity?
Questions:
What is the acceleration due to the moon's gravity?
Motion and Forces- 42
Compare this experimental value with the theoretical value of the moon‟s
gravity.
Assume that the astronaut mass is 95 kg. What is the weight of the
astronaut on the moon?
How did his mass and weight on the moon compare to his mass and weight
on Earth?
What would be your weight on the moon?
Analysing activities:
The video clip shows a jump of an astronaut on the moon. Students measure
the position of the jumping astronaut on the video and determine the
acceleration of the astronaut due to the moon's gravity, for example by using
the „Function-fit‟ option.
The measured data, the estimated acceleration due to the moon's gravity is
-1.6 m/s2.
Coach 6 Activity:
06. Moon jump
Motion and Forces- 43
ACTIVITY 7. FIND A FORCE
Learning Objectives:
1. To obtain graphs of position versus time and velocity
versus time for a moving car
2. To interpret the motion graphs
3. To explain how force, acceleration and mass are
APPLIED ICT TECHNOLOGY:
VIDEO MEASUREMENT
STUDENT LEVEL:
AGE 14 - 17
RECOMMENDED SETTINGS:
STUDENT ACTIVITY
related
4. To be able to state Newton‟s second law of motion
Operational Skills:
Making measurements on the Video Screen
Using the Scan, Function fit and Derivative options
Procedural Skills:
Analysing data using a graph
Reading values/slopes
Evaluating measurement quality
Materials:
The movie „Motion of the car‟ was taken from the web site http://itsserver.tamu.edu/bryan/ITS_project/phys_video_sim.htm (free for educational
purposes)
Activity method:
1. In the Data-Video Window you see the first frame of the movie „Motion of
the car‟. The small car is being pulled by a hanging mass. Watch the
movie.
2. Carry out measurements on the position of the car. The movie is already
scaled and the graph of position versus time is prepared.
3. The horizontal position versus time graph of your measurements appears
on the screen.
Questions:
Describe the motion of the car.
- What was the initial position of the car?
Motion and Forces- 44
- What was the final position of the car?
- How long was the motion?
- What can you deduce about the car's speed?
Create a graph of the horizontal velocity versus time (use the Derivative
option).
What was the initial velocity of the car?
What was the final velocity of the car?
What can you deduce about the car's acceleration?
Determine the acceleration of the car. How did you find it?
What is the net force that causes motion of the car? How did you find it?
Tip: Information about the masses used in the experiment is given on the
first frame of the video clip.
Analysing activities:
On the video students measure the position of the car, the horizontal position
versus time graph appears simultaneously. Students create velocity versus
time graph and analyse both graphs. They determine the car‟s acceleration;
different ways are possible e.g. by using the Function fit, Derivative, or Slope
options.
The determined car‟s acceleration is circa a = 0.26 m/s2.
Using the Second Newton‟s law students can calculate the force acting on the
car. The total mass = mass car + mass in car + mass hanger = 0.575 kg
The calculated force is: F= m*a = 0.575 kg * 0.26 m/s2 = 0.1495 N
Coach 6 Activity:
07. Find a force
Motion and Forces- 45
ACTIVITY 8. FALLING SHUTTLECOCK
Learning Objectives:
1. To obtain graphs of position versus time and velocity
versus time for the falling badminton shuttlecock
2. To interpret the motion graphs
3. To observe the effect air resistance
APPLIED ICT TECHNOLOGY:
VIDEO MEASUREMENT
STUDENT LEVEL:
AGE 14 - 17
RECOMMENDED SETTINGS:
STUDENT ACTIVITY
4. To determine the terminal velocity of the falling shuttlecock
Operational Skills:
Making measurements on the Video Screen
Using the Scan, Function fit and Derivative options
Procedural Skills:
Analysing data using a graph
Reading values/slopes
Evaluating measurement quality
Materials:
The motion of the falling shuttlecock was
recorded with a digital camera at a resolution
of 384 512 and a frame rate of 300 fps.
A commonly available synthetic badminton
shuttlecock of brand name “Angel Sports”,
weighing 3.28 g and having a maximum skirt
diameter of 6.5 cm was used. The picture
shows the experimental setting. The annotation points at the shuttlecock and it is above
the meter stick that was positioned on a little
cart for calibrating distance.
The video is already corrected for the
perspective distortion on the basis of a known
rectangle shape in the scene.
Activity method:
1. In the Data-Video Window you see a video clip of a person dropping a
badminton shuttlecock. Watch the video clip.
Motion and Forces- 46
2. You are going to measure the vertical position of the falling shuttlecock.
The video is already scaled; 1 meter stick that is positioned on a little cart
is used for calibrating distance and the rate of 400 frames per second for
calibrating time. Also the perspective distortion is corrected. The original
video is shown in the Video pane.
3. Carry out measurements on the position of the shuttlecock. Because there
are many frames in this video you are going to use point tracking. Right
click the Data-Video window and select Point Tracking. Move the tracking
are (P1) on the tracking frame over the white shuttlecock. Start measuring
by clicking the green Start button.
4. The collected data appears on the graph of the vertical position versus
time.
Questions:
Describe the motion of the shuttlecock.
Describe the vertical position versus time graph:
- What was the initial position of the shuttlecock?
- How long was the motion?
- What can you deduce about the shuttlecock‟s speed during its motion?
Create a graph of the vertical velocity versus time. Describe the resulting
graph.
- How the velocity of the shuttlecock changes in time?
- Determine the terminal velocity of the shuttlecock.
Explain why the velocity of the shuttlecock does not change after some
time.
What forces are acting on the falling shuttlecock?
Analysing activities:
In this activity students investigate the motion of the falling badminton in
which the effects of air resistance are important and measurable. Students
interpret the resulting vertical position versus time graph of the falling
shuttlecock and create the velocity versus time graph.
Motion and Forces- 47
In the position versus time graph the position curve straightens out and linear
function fit of the position-time graph shows the approach to linear motion
after about 0.8 second.
The velocity-time graph indicates that the falling shuttlecock reached after a
short time a constant velocity.
Students should interpret the motions graphs, discuss the forces acting on the
falling shuttlecock and estimate the terminal velocity of the shuttlecock.
Coach 6 Activity:
08. Falling shuttlecock
Motion and Forces- 48
ACTIVITY 9. STUDYING THE MOTION OF A BALL
MOVING IN TWO DIMENSIONS
Learning Objectives:
1.
2.
3.
To understand the concepts of uniform velocity
and uniform acceleration
To understand that the vertical motion of a body
is independent of the horizontal motion.
APPLIED ICT TECHNOLOGY:
SIMULATION
STUDENT LEVEL:
AGE 14-17
RECOMMENDED SETTINGS:
TEACHER DEMONSTRATION
To understand that when a ball bounces, the velocity AND CLASS DISCUSSION
becomes reversed.
Operational Skills:
Using the software controls for running the simulation
Procedural Skills:
Describe observations and link these with theoretical explanation
Activity method (using Simulation Insight):
1.
Open the Insight file „5. Rolling ball simulation‟.
2.
Click 'Roll' to begin.
3.
Observe the ball rolling along the shelf and then falling to the ground.
Discuss the main differences between the motion on the shelf and the
motion as the ball falls.
4.
Reset and roll the ball again, but this time note the times taken to
(a) reach the end of the shelf
(b) fall to the ground.
5.
Reset the ball on the shelf, set the horizontal velocity to a new value and
repeat the observations.
6.
Repeat this for a series of different values for horizontal velocity.
7.
Tick the 'Bounce' checkbox and compare the motion resulting from different
values of horizontal velocity.
Motion and Forces- 49
Discussion:
Use the results to discuss the effect of the horizontal motion on the time to fall
to the ground.
Discuss the effect of the horizontal velocity on the time to reach the end of the
shelf.
Thinking about your observations, discuss the correctness of the following
statements:
As the ball rolls along the shelf it experiences no acceleration.
The time for the ball to fall to the ground depends upon the acceleration due
to gravity and the height of the shelf above the floor.
When the ball bounces on the floor or the wall, its horizontal component of
velocity does not change.
After the ball bounces, its velocity only changes in direction.
Motion and Forces- 50
ACTIVITY 10. INVESTIGATING THE MOTION OF A
REBOUNDING TROLLEY
Learning Objectives:
1. To associate the features of the graph with the
observed motion of the trolley.
2. To understand how the forces acting on the trolley
are combined to calculate the resultant force.
3.
APPLIED ICT TECHNOLOGY:
SIMULATION
STUDENT LEVEL:
AGE 14-17
RECOMMENDED SETTINGS:
TEACHER DEMONSTRATION
To understand the relationship between the distance AND CLASS DISCUSSION
moved, the velocity and the acceleration of the trolley.
Operational Skills:
Using the software controls for running the simulation
Procedural Skills:
Describe observations and link them with theoretical explanation
Activity method (using Simulation Insight):
1. Open the Insight file „6 Rebounding simulation‟
2. Run the simulation and observe the shape of the distance vs. time graph.
3. On the graph, identify the points where the trolley hit the fixed barrier.
Identify also the points where the trolley came to rest after rolling up the
runway.
4. Select „Gradient‟ and move the cursor across the graph to show how the
gradient changes. The gradient indicates the velocity of the trolley. Find
the point on the runway where the trolley reached its maximum velocity.
5. What happens to the velocity when the trolley hits the fixed block?
6. On the Control panel, click the data button to show the velocity data on the
second graph. Review your answers to (4) and (5) above.
7. In a similar way show the graph of data for acceleration.
Compare this
with the previous graphs for distance and velocity.
8. Show the graphs of the force down the slope, the force of friction and the
resultant force on the trolley. Use the cursors to take some measurements
to show that the resultant force is equal to the sum of the slope force and
friction force.
Motion and Forces- 51
Discussion:
Thinking about your observations, discuss the correctness of the following
statements:
The force of gravity on the trolley remains constant throughout the
motion.
The force of gravity has a component down the slope in the direction of
motion.
The force of friction depends upon the velocity of the trolley.
The resultant force is always in the direction of motion of the trolley.
The acceleration is always in the direction down the slope.
Motion and Forces- 52
ACTIVITY 11. INVESTIGATING THE TERMINAL
VELOCITY OF A BICYCLE
Learning Objectives:
1. To associate the features of the graph with the
observed motion of the bicycle.
2. To understand how the forces acting on the bicycle
are combined to calculate the resultant force.
3. To understand why the velocity of the bicycle
becomes constant when the resultant force
becomes zero.
APPLIED ICT TECHNOLOGY:
SIMULATION
STUDENT LEVEL:
AGE 14-17
RECOMMENDED SETTINGS:
TEACHER DEMONSTRATION
AND CLASS DISCUSSION
Operational Skills:
Using the software controls for running the simulation
Procedural Skills:
Describe observations and link these with theoretical explanation
Activity method (using Simulation Insight):
1. Open the Insight file „7. Terminal simulation‟.
2. Adjust the pushing force to 100 newton and start the simulation running.
Observe the graph of velocity against time.
3. Repeat your observations with smaller and larger pushing forces.
4. Vary the size of the pushing force and observe the effect on the velocity.
Motion and Forces- 53
Discussion:
Thinking about your observations, discuss your answers to the following
questions:
When a constant pushing force is applied, why is the increase in velocity
limited?
Why does the force of friction (air resistance) increase as the velocity
increases?
What happens to the friction force and resultant force when the velocity
reaches a steady value (terminal velocity)?
What happens to the acceleration while the velocity increases?
Motion and Forces- 54
ACTIVITY 12. FREE FALL
Learning Objectives:
1.
To use a model to obtain and analyse graphs of
velocity and acceleration for an object falling due
to gravity.
2.
To interpret the properties of linear and non-linear
graphs for indicating rate of change.
3.
To understand the relationships between distance
moved, velocity and acceleration.
APPLIED ICT TECHNOLOGY:
MODELLING
STUDENT LEVEL:
AGE 14-17
RECOMMENDED SETTINGS:
STUDENT ACTIVITY OR
TEACHER-LED CLASS
DISCUSSION
Operational Skills:
Using the software controls for using the model
Using the cursor tools for obtaining readings from the graph
Procedural Skills:
Use the shape of the distance vs. time graph to make predictions about
the velocity of the object
To relate the shape of the graph with the formulae in the model
Activities (using Simulation Insight or Insight iLOG)
1.
Open the Insight file „12. free fall model‟.
2.
Click on the START button to see the model run.
3.
Click on the SPACE bar to show calculated values. The time increases for
each press of the space bar. If the space bar is held down, a continuous
stream of values is calculated.
4.
Observe the differences and similarities between the graphs for distance
and velocity.
5.
Stop the model and select „Change‟ („Analyse‟ menu). Use the cursors to
measure the change in distance moved during 2 second intervals at
different starting points on the graph. Explain the pattern in the results.
6.
Compare the results for similar measurements of „Change‟ on the velocity
vs. time graph. Explain why the results are different from those for the
distance vs. time graph.
7.
Select „Gradient‟ from the „Analyse‟ menu. Measure the gradient on the
Motion and Forces- 55
distance vs. time graph at 5, 10, 15 and 20 seconds. Describe the pattern
in the results.
8.
Describe how the velocity vs. time graph may be predicted from the
measurements of gradient.
Questions and Assignment (using Coach 6):
Click the Start button to run the model.
What are the similarities and differences between the graphs for height
and velocity?
Measure the slope (by using the Slope option) of the height vs. time graph
at different times 0.3, 0.6, 0.9 and 1.2 seconds. Describe the pattern in
the results.
What is the meaning of these values?
Compare the displacement of a falling ball in equal time intervals.
Look also on the animation Free Fall 1 available under the yellow button
Animation. In this animation the falling ball “leaves” its picture in equal
time intervals.
Describe how the velocity of the ball changes in time?
- What is the initial velocity of the ball?
- What is the final velocity of the ball?
- Compare the changes of velocity in equal time intervals.
- What is the average velocity of the ball?
Measure the slope of the velocity vs. time. What is the meaning of this
value?
Find in the model the value of the acceleration due to gravity on the
Earth?
Simulate the motion of the ball on the Moon? Describe the similarities and
differences between the motion on the Moon and on the Earth.
Analysing activities (using Coach 6)
The model calculates the height and the velocity of an object in free fall due to
Earth's gravity. The activity is enriched with an animation showing a free
falling ball which motion is controlled by the model variable y.
Motion and Forces- 56
Students analyse the resulting motion graphs.
Coach 6 model and animation with trace turned on
(each 35 time steps)
Motion and Forces- 57
ACTIVITY 13. FORCE AND ACCELERATION
Learning Objectives:
1. To use a model to obtain and analyse graphs of
velocity and acceleration for an object to which a
constant force is applied.
2. To understand the relationship between the
acceleration of the object and, its mass and the
force applied to it.
APPLIED ICT TECHNOLOGY:
MODELLING
STUDENT LEVEL:
AGE 14-17
RECOMMENDED SETTINGS:
STUDENT ACTIVITY OR
TEACHER-LED CLASS
DISCUSSION
Operational Skills:
Using the software controls for using the model
Using the cursor tools for obtaining readings from the graph
Procedural Skills:
Explaining the physical basis of each formula employed in the model
Activities (using Simulation Insight or Insight iLOG)
1. Open the Insight file „13. acceleration model‟.
2. Click on the START button to set the model to run and note the values of
force and mass.
3. Hold down the SPACE bar to calculate a series of values and observe the
graphs which are colour coded to show distance, velocity and acceleration
against time.
4. Compare the shapes of the graphs and think about what these indicate
about the three variables.
5. Stop the model and use „Duplicate‟ („Data‟ menu) to copy the data for
distance and velocity.
6. Run the model again, set the force to 10 newtons and obtain another set of
data.
7. Comparing the new graphs with the first set, describe the main differences.
8. Repeat step 6, but this time change the mass.
9. Summarise the effects of force and mass on the acceleration of the object.
Motion and Forces- 58
Questions and Assignment (using Coach 6):
Look at the model and notice that in the model the acceleration variable is
not defined, shows question mark. Which model variables influence the
acceleration? How do you know?
Double-click the acceleration variable and define its formula.
Click on the Start button to run the model.
Describe distance vs. time graph.
Describe velocity vs. time graph.
Measure the slope of the velocity vs. time. What is the meaning of this
value?
What is the calculated value of the acceleration?
Investigate (by using the Simulate option) what is the effect of
bigger/smaller resultant forces on the object‟s motion.
In similar way investigate what is the effect of more heavy/less heavy
objects.
Summarise the effects of force and mass on the acceleration of the object.
Analysing Activities (using Coach 6)
The model in this activity has to calculate the distance moved, velocity and
acceleration of an object caused to accelerate by a steady resultant force.
Students first have to finish model by defining the formula for the acceleration
variable. They analyse the resulting motion graphs and investigate the effects
of force and mass on the acceleration.
Motion and Forces- 59
ACTIVITY 14. REBOUNDING TROLLEY
Learning Objectives:
1. To use a model to obtain and analyse graphs of
velocity and acceleration for a trolley rolling down
a slope and rebounding against a spring buffer.
2. To understand the relationship between the
acceleration of the trolley and, its mass and the
force applied to it.
APPLIED ICT TECHNOLOGY:
MODELLING
STUDENT LEVEL:
AGE 14-17
RECOMMENDED SETTINGS:
STUDENT ACTIVITY OR
TEACHER-LED CLASS
DISCUSSION
Operational Skills:
Using the software controls for using the model
Using the cursor tools for obtaining readings from the graph
Procedural Skills:
Explaining the physical basis of each formula employed in the model
Comparing the graphs obtained for different values of force and mass
Activities (using Simulation Insight or Insight iLOG)
1. Open the Insight file „14. rebounding model‟.
2. Click on the START button to set the model running and observe the shape
of the distance vs. time graph.
3. On the graph, identify the points where the trolley hit the fixed barrier.
Identify also the points where the trolley came to rest after rolling up the
runway.
4. Select „Gradient‟ and move the cursor across the graph to show how the
gradient changes. The gradient indicates the velocity of the trolley. Find
the point on the runway where the trolley reached its maximum velocity.
5. What happens to the velocity when the trolley hits the fixed block?
6. On the Control panel, click the data button to show the velocity data on the
second graph. Review your answers to (4) and (5) above.
7. In a similar way show the graph of data for acceleration.
Compare this
with the previous graphs for distance and velocity.
8. Show the graphs of the force down the slope, the force of friction and the
resultant force on the trolley. Use the cursors to take some measurements
to verify that the resultant force is equal to the vector sum of the slope
Motion and Forces- 60
force and friction force.
Questions and Assignment (using Coach 6):
Click on START to see the model run.
On the Distance vs. Time graph, which points show where the trolley hit
the buffer?
Which points show where the trolley came to rest after rolling up the
runway?
Which points show where the trolley came to rest after rolling up the
runway?
At what point on the runway did the trolley reach a maximum velocity?
What happens to the velocity when the trolley hits the buffer?
Think about the connection between the velocity graph and the distance
graph. Use the Scan option to analyse both graphs simultaneously.
Show the graph of acceleration. Click the Diagram button and select User
defined < Acceleration versus time.
Think about the connection between the acceleration graph and the
previous graphs.
Look at the model. Move the mouse pointer over each of the variables in
turn to see how they are calculated. In particular notice how the forces are
calculated.
The force down the slope is calculated from the strength of gravity and the
angle of the slope.
The force of friction depends upon the velocity of the trolley.
Investigate the effect on the graphs of (use the Simulate option):
- altering the angle of the slope;
- making the friction constant zero;
- altering the mass.
Motion and Forces- 61
Analysing Activities (using Coach 6)
The model calculates the forces on the rebounding trolley, its distance moved,
velocity and acceleration as it moves down and up after bouncing a spring
buffer at the bottom of a runway.
Motion and Forces- 62
ACTIVITY 15. TERMINAL VELOCITY
Learning Objectives:
APPLIED ICT TECHNOLOGY:
MODELLING
1. To use a model to obtain and analyse graphs of
STUDENT
LEVEL:to the
velocity and acceleration for a bicycle when a steady force
is applied
A
GE
14-17
pedals.
2. To understand how the forces acting on the bicycle
are calculated and combined to calculate the velocity
and acceleration.
RECOMMENDED SETTINGS:
STUDENT ACTIVITY OR
TEACHER-LED CLASS
DISCUSSION
3. To understand why the velocity of the bicycle
becomes constant when the resultant force becomes zero.
Operational Skills:
Using the software controls for using the model
Using the tools for altering the graph display
Procedural Skills:
Explaining the physical basis of each formula employed in the model
Interpreting the graphs to describe relationships between variables
Activities (using Simulation Insight or Insight iLOG)
1. Open the Insight file ‟11. terminal model‟.
2. Click the START button to set the model running.
Note that the pushing
force is steady at 100 newton.
3. Observe the graph of velocity against time.
When the velocity reaches a
steady value, adjust the pushing force to 200 newton. (Right click on the
„pushing force‟ box.)
4. Observe the effect on the velocity of increasing the pushing force.
5. Show the graph of acceleration and explain how it may be predicted from
the velocity graph.
6. Show the graphs of all the force variables against time.
Describe how they
are related to each other.
7. Show the graphs of velocity and resultant force against time and explain
the relationship between these variables.
Motion and Forces- 63
Questions and Assignment (using Coach 6):
Play the video “Falling shuttlecock” to see the experiment..
In the model is assumed that during an object‟s fall the two forces are
acting on the object. Look at the model and indicate which forces are
acting on the object?
Move the mouse pointer over the drag force variable. As you can see this
force is not defined. How would you define this force?
The drag force (also called air resistance) depends on the velocity of the
falling object. Theoretically there are 2 models which can be used to
describe the drag force:
- linear model – the drag force is proportional to velocity Fdrag = - kv, and
- quadratic model - the drag force is proportional to the square velocity
Fdrag = - k*sign(v)*v2.
Investigate which model, linear or quadratic, better match the
experimental video-data. The experimental data are already placed in the
distance vs. time and velocity vs. time graphs as the pink background
graphs.
To define the drag force double-click the drag force variable symbol in the
model and type it the formula.
Which model is better? Why?
What is the terminal velocity reached by the falling shuttlecock? How do
you know?
Activities (using Coach 6)
The model in this activity calculates the forces acting on a falling object, its
distance moved, velocity and acceleration as it falls down. The video “Falling
shuttlecock” shows such an experiment in which the falling object is a
badminton shuttlecock.
Motion and Forces- 64
The drag force is not defined in the model. Students have to fill in the formula
describing this force. They investigate which formula, linear Fdrag = - k*v or
quadratic Fdrag = - k*sign(v)*v2 better match the experimental data given as
the background graphs. For the investigation students need to adjust the
values of mass, initial height y, and constant k.
The experimental data are taken from the video measurement of activity
08.Falling shuttlecock.
Motion and Forces- 65