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Transcript
```Next%Generation%Physical%Science%
and%Everyday%Thinking%
!
Interactions!!
and!Forces!
!Module!
!
Studio2style!Class
!
Next%Generation%Physical%Science%
and%Everyday%Thinking%
Interactions%and%
Forces%Module%
!
Unit!FM!
Force,based!Model!
for!Interactions!
!
!
Studio,style!Class!
!
Unit FM: Force-based Model for Interactions
Activity #
1
Activity (A) Title
Page
A1
Interactions, Force and Motion
FM-1
Ext A1
Force Diagrams
online
A2
Motion with a Continuous Force
FM-9
Ext B
Pushing a Skateboarder
online
A3
Pushes and Slowing Down
FM-21
Ext C
Connecting Force and Energy Models
online
A4
Forces and Friction
FM-29
Ext D
How Does Friction Work?
online
A5
Changing Force Strength and Mass
FM-41
Ext E
Changing Direction
online
A6
Falling Objects
FM-55
Extensions (Ext’s) are online homework activities.
UNIT FM
Developing Ideas
ACTIVITY 1: Interactions and Force
Purpose
In a previous unit you may have developed some
ideas about how to explain the effects of contact
push/pull interactions between objects in terms of
a model involving energy transfers and changes.
For example, for a soccer player kicking the ball,
previously we might have said:
“There is a contact push/pull interaction between the
player’s foot and the ball. During this interaction
energy is transferred from the foot to the ball”
However, scientists often use a different model when describing the same
interactions. Instead of ideas of energy, they use ideas about pushes and pulls
(which they call forces) that the objects apply to each other, and the effects
that they have. Using this model for the example above, we would say:
“There is a contact push/pull interaction between the player’s foot and the ball. The
foot pushes the ball.” or “The foot applies a force to the ball.”
In this unit you will be investigating ideas about forces and developing a
model connecting them to the motion of objects they are applied to. We will
start by examining how we can recognize when a force is acting on an object,
and when it is not.
When does a force stop pushing on an object?
FM-1
Unit FM
Initial Ideas
Think about a soccer player kicking a stationary
ball. As he interacts with it, by kicking it, the
ball starts to move. After the kick, the ball rolls
across the grass and gradually comes to a halt.
Sketch a speed-time graph for the motion
of the ball. Be sure to include both the
motion of the ball while the player’s foot
is touching it, and its motion after the
foot has lost contact with it until it stops.
Using a colored pencil, indicate the period on the graph during which
you think the foot was in contact with the ball and briefly explain your
reasoning.
Using a different colored pencil, indicate the period on the graph during
which you think there was a force pushing the ball forward. Again,
FM-2
Activity 1: Interactions and Force
Why do you think the ball gradually slows down and eventually stops
after it has been kicked?
Now draw two pictures of the ball and use arrows to show what forces
(if any) you think are acting on the ball at two different times during its
motion. Label your arrows to show where you think the forces come
from.
i) During the time foot was in contact with the ball
ii) After the foot has lost contact and the ball is rolling across the grass.
Briefly explain the reasoning behind your pictures.
Discuss your ideas with your group and try to agree on what the speed-time
graph and ‘force’ picture(s) should look like. Sketch your group’s graph and
two pictures on a large presentation board.
Participate in a whole class discussion about these questions. Make a
note of any ideas or reasoning that are different from those of your
group.
FM-3
Unit FM
Collecting and Interpreting Evidence
Exploration: When is there a force being applied to the cart?
You will need:
Low-friction cart and track
(Optional) Force sensor and instructions for set up and use
Computer with internet access
Color pencils
STEP 1: To start you will consider a situation that you already examined in a
previous unit. Place the cart at one end of the track and have one of your
team members give the cart a gentle push (or pull)
with their hand. While the cart is moving along the
track, give the cart two or three more pushes (or
pulls), in the same direction as the first push. (Stop
the cart when it reaches the other end of the track.)
If you did Unit EM, you already know that the speed-time graph for the cart
in this situation would be similar to that shown below. (The ‘stop’ occurred
after the data collection ended.)
Use a colored pencil to indicate the sections of this graph during which
you think the hand was in contact with the cart. Why did you choose
these particular sections?
FM-4
Activity 1: Interactions and Force
Discuss with your group what evidence you would look for on a speed-time
graph to tell you that a force is pushing the cart forward?
To illustrate your thinking, use a different colored pencil to indicate on
the graph the sections during which you think there is a force pushing
the cart forward. Briefly explain your reasoning below.
STEP 2. On the right is the
same speed-time graph
shown in STEP 1.
Imagine
you
could
measure the force pushing
the cart forward over the
same time period as this
speed-time graph.
On the blank forcetime graph shown
here, sketch what you
think a graph of force
versus time would
look like during the
same
time
period
shown on the speedtime graph.
Be sure to make any corresponding features in the two graphs line up.
(Note: It is only the shape of the graph that is important for now, so no
values for the strength of the force are shown.)
Explain the reasoning that led you to draw your force-time graph the
way you did.
FM-5
Unit FM
STEP 3: Your thinking can be
tested using a device called a
force probe. If one is available to
you, your instructor will give you
information on how to set it up
and use it. If not, you should
watch UFM–Act 1 - Movie 1 to
see
the
experiment
being
performed.
Sketch the speed-time
force-time graphs here.
and
Make sure that any significant
features that seem to occur at the
same time on both graphs also
Does the hand exert a force on
the cart while it is interacting
with it? How do you know?
During the periods in between the pushes, was there a force acting on
the cart? Again, what evidence from the graphs supports your idea?
FM-6
Activity 1: Interactions and Force
STEP 4: Three students are discussing the motion of the cart and the force
acting on it. They all agree that while the hand is pushing it there is a force
being applied to the cart, but have different ideas about what happens during
the periods when the hand is not in contact.
The force of the hand is
transferred to the cart
and is carried with it.
That’s why the cart keeps
moving forward after the
push.
Samantha
The force of the hand
stops when contact is
lost, but some other
force must take over to
keep the cart moving
Victor
After contact is lost
there are no longer any
forces being applied to
the cart. That’s why it
moves differently.
Amara
Do you agree with Samantha, Victor, Amara, or with none of them?
FM-7
Unit FM
Summarizing Questions
First discuss these questions with your group and note your ideas. Leave
space to add any different ideas that may emerge when the whole class
discusses their thinking.
S1: While the hand is applying a force to the cart, is the speed of the cat
increasing, decreasing, or staying constant? What evidence from this
S2: Do you think the force of the hand was transferred from the hand to the
cart during the interaction between them, and then continued to act on it
after contact was lost? What evidence supports your idea?
S3: At what moment do you think the force of the hand stopped pushing the
cart forwards?
S4: During a contact push/pull interaction, what do you think is transferred
from the giver to the receiver: energy, force, both, or neither? Explain
FM-8
UNIT FM
Developing Ideas
ACTIVITY 2: Motion with a Continuous Force
Purpose
In Activity 1 you saw the effect that quick pushes had on the motion of a cart.
This is like the situation in many sports, where the players move the ball (or
puck) around using quick pushes of their hands, feet, or a bat/racket of some
kind.
But what would the motion of an object
be like if it were involved in a single
contact push/pull interaction for a long
time; that is, if a constant strength push
were applied to it continuously? For
standing balanced on a well-lubricated
skateboard and you pushed, and kept on
pushing, with the same strength force, in
the same direction. What would his
motion be like?
How does an object move when a single force of
constant strength continuously acts on it?
Initial Ideas
Imagine you had a low-friction cart at rest at
one end of the track in front of you. Now,
suppose you were to interact with it by
pushing the cart continuously from behind
with a constant strength push until it
reached the other end of the track.
What do you think the motion of the cart would be like while it was
moving along the track under these circumstances?
FM-9
Unit FM
Sketch a speed-time graph to illustrate your idea.
Sketch your group’s speed-time graph on a presentation board and
participate in a short whole-class discussion about everyone’s ideas.
Make a note of any ideas, or reasoning, that are different from your own.
Collecting and Interpreting Evidence
Experiment: What happens to the cart when it is given a continuous
push?
You will need:
Low friction cart and track
Fan unit
FM-10
Activity 2: Motion with a Continuous Force
STEP 1: Place the cart near one end of the track
(or table). Each member of your team should try
using one finger to push the cart along the track.
(Make sure you push the cart from behind and
do not ‘grip’ it with your fingers.) Try to
maintain a constant strength push as the cart
moves.
How does the cart seem to behave as you push it?
How easy did it seem to maintain a continuous, constant-strength, push?
Why do you think this is?
Watch UFM-A2 - Movie 1, in which an experimenter will attempt to push a
low-friction cart along a track using a constant strength force. The strength of
the force he is applying will be measured using a force sensor and a graph of
this will be displayed (along with a speed-time graph).
Did the experimenter manage to apply a force with a constant strength
to the cart with his hand while it was moving along the track? How does
the force-time graph tell you this?
In reality, most people find it very difficult to maintain a continuous push of a
constant strength. We will now check to see if there is a better way to arrange
for such a force to act on the cart.
FM-11
Unit FM
STEP 2: In the past it has been suggested that a
fan unit applies a constant force to any object it
pushes on (or hence is attached to). To see
whether this is indeed the case watch UFM-A2 Movie 2, in which the same experimenter will
allow a cart with a fan unit attached to push
against a force sensor.
After he turns the fan unit on and it makes contact with the force sensor,
how does the push of the cart seem to behave while the fan is running?
Does the push seem to stay reasonably constant or does it seem to
increase or decrease significantly? How does the force-time graph tell
you this?
STEP 3: Having now established that a fan unit does indeed apply a constant
strength force, you will use such a fan to check what the motion of a cart is
like when such a force is applied to it. Place your group’s cart (with fan unit
attached) on the track at one end. Turn the fan unit on and then release the
cart. (Do not give it any sort of push or pull with your hand.)
Carefully stop the cart before it reaches the other end of the track and turn
the fan unit off.
Safety note: If the fan blades are exposed the person operating the fan may wish to
use a glove for protection.
How does the cart seem to move as the fan unit pushes it along the track
with a constant strength force? Does it seem to move at a reasonably
constant speed, or does it seem to speed up as it moves?
FM-12
Activity 2: Motion with a Continuous Force
If it is not already, place the motion sensor at one end of the track and open
the data collection file for this activity. Place the cart about 20 – 30 cm in front
of the motion sensor and collect data while the fan unit pushes the cart away
from the sensor.
Sketch the speedtime graph for
the motion of the
cart.
What does the speed-time graph tell you about the speed of the cart
while the fan unit was pushing it? Does this confirm your initial
impression?
STEP 4: Suppose you could repeat this experiment using a longer track. Do
you think the fan-cart would continue to speed up in this case, or do you
think something else would happen?
Suppose you could join three tracks together end-to-end and release the
fan cart from one end of this extended track. Do you think the fan-cart
would continue to speed-up as it moved along all three tracks, or do you
think something else would happen? Explain your thinking.
FM-13
Unit FM
You should now watch UMF-A2 - Movie 3. It shows a fan-cart running along
three tracks. On the replay, the amount of time (in seconds) it takes the cart to
move along each of the three tracks in succession will be displayed.
What does the video show? Does the speed of the cart keep increasing,
even over the length of three tracks? How do you know?
STEP 5: Answer the following questions based on the evidence you have
gathered in this activity.
What happens to the speed of an object while a single force is acting on
it in the same direction as its motion?
Look back at your initial ideas for the behavior of the speed of the cart at
the beginning of this activity. Do the results from these experiments
confirm your initial ideas, or not?
Summarizing Questions
First discuss these questions with your team and note your ideas. Leave
space to add any different ideas that may emerge when the whole class
discusses their thinking.
S1: If a cart is at rest and a single force acts on it, what happens? If the same
force continues to act on the cart what happens to the cart’s speed?
FM-14
Activity 2: Motion with a Continuous Force
S2: In general, during the time a single force with a constant strength acts
on a moving object, in the same direction as its motion, what is the
object’s motion like? Does it move at a constant speed, does its speed
continuously increase, or does the speed only increase at first and then
become constant after a short time? What evidence from this activity
S3: When you were using your finger to try to push the cart with a constant
strength force, you probably noticed the cart was ‘getting away’ from
you. (If not, try it again.) Why do you think the cart behaved in this
way?
S4: Suppose that, while the cart was being pushed along the track by the fan
unit, one of the fan blades jammed so that the fan unit immediately
stopped pushing on the cart. What do you think would happen to the
speed of the cart? Explain your reasoning.
S5: At the beginning of
Activity 1 of this unit
you sketched a speedtime graph for a soccer
ball that was given a
quick kick and then
slowed to a stop as it
rolled across the grass.
Sketch this graph again
on the following page,
with any changes from the original you wish to make.
FM-15
Unit FM
On the graph use different colored pencils to indicate:
a) The section (or sections) of the graph during which there was a
contact push/pull interaction between the foot and the ball
b) The section (or sections) of the graph during which a force acted
on the ball in the same direction as its motion
Explain your reasoning for choosing these sections.
S6. Two students in a previous class were discussing what they thought
would happen if they could join many, many tracks together and arrange
for a fan unit to push a cart along this extremely long track.
I think that as long as the fan
keeps pushing on it, no matter how
long the track is, the cart will keep
speeding up.
Han
I agree that the cart will speed up for
a while, but I just don’t believe it could
keep speeding up forever. I think that
at some point its speed will become
constant.
Samantha
Do you agree with Han, Samantha, or neither of them? Explain your thinking.
Writing Explanations using a model of ‘Force and Motion’
As previously stated, the contact push/pull interactions you are examining in
this chapter are the same as those you were saw in a previous unit. In that
unit you used a model involving ideas about energy transfers and changes in
kinetic energy to explain the effects of such interactions. However, in this
chapter you are developing a model that involves ideas about forces and the
FM-16
Activity 2: Motion with a Continuous Force
effects they have on the motion of objects. This model
allows you to think about these same interactions in a
different way.
The process of writing explanations of phenomena
using force ideas is very similar to the process you
used when using the energy model. However, instead
of drawing an energy diagram, you should draw a
force diagram. (The procedure for drawing and
interpreting force diagrams was given in the previous
extension activity.) Also, instead of writing a narrative
that explains the behavior of an object in terms of
energy transfers and changes, you should do so in
terms of the forces acting on the object and the effect
they have on its motion (if any).
A general structure for explaining why an object
moves as it does in terms of the forces acting on it is
shown to the right.
When writing your scientific explanations you should keep in mind the same
criteria that were introduced at the beginning of the course:
•
and your narrative should be well written and easy to follow. Also, the
diagrams and narrative should be consistent with each other. Your
explanation should be relevant and focus on the phenomenon that is to be
explained. (For example, a cart may have been given a push to get it
started but you are asked to explain something that happened after the
push! In this case it would be OK to mention that the push got it started
but this need not be explained in detail.)
•
motion of objects that are supported by evidence and agreed upon by the
class.
•
Well-Reasoned: Reasons should be given for why the event happened as
it did in terms of the force(s) acting on the object. Usually this would be
based around a general statement (big idea) about the connection between
force and motion. For example, ‘When a single force acts on a stationary
FM-17
Unit FM
object it will start to move in the direction of that force.’ However, you
should also take care to establish why this ‘big idea’ is relevant to this
particular situation.
You should also use these criteria to evaluate the explanations written by
others. (As a reminder, if all the criteria are met, the explanation should be
considered good. If one or more of the criteria is not met, then the explanation
should be considered problematic and in need of revision.)
To illustrate the similarities between
energy-based
and
force-based
explanations, consider the following
two parallel explanations of why a
stationary cart begins to move when it is
given a quick push by someone’s hand.
Note: These explanations do not mention friction since we have not yet considered its
effect in developing our model of forces and their effects. However, since we are
dealing with a low-friction cart it can be assumed that the effects of friction can be
neglected during the push.
Explanation: Why does a stationary cart begin to move when it is
pushed?
Describe the interaction using a diagram:
Energy Diagram
Force Diagram
Contact Push/Pull Interaction
Energy
Cart
Increase in
kinetic
energy
FM-18
Force applied
to cart by hand
Activity 2: Motion with a Continuous Force
Write the narrative:
When the hand touches the cart there is a
When the hand touches the cart there is a
contact
contact
them.
push/pull
(We
this
the
push/pull
interaction
between
them during which the hand applies a force
interaction in which the cart is involved.)
to the cart. (We assume this is the only
During
is
interaction in which the cart is involved.)
transferred from the hand to the cart.
When a single force acts on an object at
Since there is no energy output from the
rest, the object starts to move in the
cart, this transfer of energy to it means its
direction of the force. Therefore, because
kinetic energy must increase. Because the
the cart is initially at rest when the force
the cart is initially at rest, this increase in
of the hand is applied to it, the cart starts
kinetic energy means that the cart starts
to move in the direction of the force
moving.
applied to it by the hand.
interaction,
is
between
only
this
assume
interaction
energy
So one explanation says that the cart starts to move because the idea of the
energy input to the cart results in an increase in its kinetic energy, while the
other says it moves because the hand applies a force to it during the
interaction between them. Which explanation is better? They are both good –
they are just two different ways of looking at the same interaction, one based
on a model of energy transfers and changes, the other on a model of how
forces affect motion. (As you have probably already inferred, though these
two sets of ideas are different, they are closely related.)
The previous explanation was meant to show you how both energy and force
models can be used to explain the same phenomenon. For the remaining
explanations in this unit you should consider, and use, only the force model.
The force-based explanation given above was intended to be good, and it
was probably evident to you that it was well-constructed and accurate, and
clear and consistent. However, you should now carefully consider the
elements that ensure it is well-reasoned.
Highlight or circle the general statement about force and motion around
which the explanation if based. (To be ‘general’, such a statement should
be able to be applied to any similar situation and not mention specific
objects.)
Using a different color, highlight or circle the part(s) of the narrative that
establishes that this is a situation to which this general statement can be
FM-19
Unit FM
applied. (This part of the narrative ‘sets the scene’, detailing the
information about the forces and motion (if any) for this particular case.)
Using yet another color, highlight or circle the part(s) of the narrative
that uses the general statement to explain the observable outcome (that
the cart beings to move).
Now it is your turn to practice constructing an explanation using our
developing model that connects force and motion.
In this activity you saw that a cart with a fan unit attached started to move
when the fan was turned on, and that its speed continued to increase as it
moved along the track. You should now write an explanation for why this
happened. (Use the ‘good’ force-based explanation given previously to guide
you.) You need not worry about how the fan works, just assume that it
applies a constant continuous force to the cart.
Explanation: Why did the cart with a fan-unit attached
continue to speed up as it moved along the track?
Describe the Situation using a diagram: (Draw a force diagram for the cart
for a moment in time while it is moving along the track and being pushed by
the fan unit.)
Write the narrative: (Make sure you base your narrative on the ‘big idea’ you
developed in this activity about what happens to the speed of a moving object
when a continuous force acts on it in the same direction as its motion.)
!
FM-20
UNIT FM
Developing Ideas
ACTIVITY 3: Pushes and Slowing Down
Purpose
In the first two activities of this unit you saw that,
when an object is moving, a force applied in the
same direction as the motion makes its speed
increase. But what if the force is applied in the
opposite direction to that in which the object is
moving?
For example, suppose that while your friend is
coasting along on his skateboard, you gave him a
quick gentle push in the opposite direction to that
in which he was moving. What do you think his
motion would be like during your push? What
Would something different happen if, instead of a quick push, you kept up a
continuous constant push on your friend?
What effect does a backward push have
on the motion of an object?
Collecting and Interpreting Evidence
You will need:
Low-friction cart and track
(Optional) Force sensor and instructions for set up and use
Fan unit
FM-21
Unit FM
Exploration #1: What effect does a short backward push have?
STEP 1: Let us again consider a situation
you likely first examined in Unit EM. Place
your cart at rest on the track Now one of
your team should give it a quick push, just
to get it started. As the cart is moving
someone else should give it two or three
very gentle taps in the direction opposite
to its motion.
Make sure that these taps are gentle enough that the cart does not stop
moving or reverse direction. After the tap, the cart should still be moving in
the same direction as it was beforehand
If you did Unit EM,
the speed-time graph
for the cart in this
situation would be
similar to that shown
here. (The final ‘stop’
occurred after the data
collection ended.)
Use a colored pencil to indicate the section(s) of this graph during which
you think the hand was in contact with the cart. Why did you choose
these particular sections?
Use a different colored pencil to indicate on the graph the section(s)
during which you think there is a force being applied to the cart in the
opposite direction to its motion. Briefly explain your reasoning below.
FM-22
Activity 3: Pushes and Slowing Down
STEP 2. On the right is
the same speed-time
graph shown in STEP 1.
Imagine
you
could
measure only the force
acting on the cart in the
opposite direction to its
motion over the same
time period.
On the blank forcetime graph shown
here, sketch what
you think such a
graph of force versus
time would look like
during the same time
period shown on the
speed-time graph.
Be sure to make any corresponding features in the two graphs line up.
(Note: It is only the shape of the graph that is important for now, so no
values for the strength of the force are shown.)
Explain the reasoning that led you to draw your force-time graph the
way you did.
STEP 3: As before, your thinking can be tested
using a device called a force probe. If one is
available to you your instructor will give you
information on how to set it up and use it. If
not, you should watch UFM–Act 3 – Movie 1
to see the experiment being performed.
FM-23
Unit FM
Sketch the speed-time and
force-time graphs here.
Make sure that any significant
features that seem to occur at
the same time on both graphs
also line up on your sketches.
Does the hand exert a force on
the cart while it is interacting
with it? How do you know?
What happens to the speed of the cart during each ‘backward’ push?
During the periods in between the pushes, was there a force acting on
the cart? Again, what evidence from the graphs supports your idea?
In between the backward pushes how does the speed of the cart behave?
Exploration #2: What effect does a continuous backward push have?
STEP 1: Now imagine that, after giving the cart a quick push to start it
moving, you applied a continuous, constant strength push in the opposite
direction to its motion (instead of applying gentle backward taps).
FM-24
Activity 3: Pushes and Slowing Down
What do you think the
motion of the cart would
be like in this case?
Sketch what you think
the speed-time graph
would look like and
STEP 2: Open the Motion Sensor data
collection file for this exploration. Mount
the fan unit on the cart. Place the cart at
rest on the track about 20 - 30 cm from the
Motion Sensor and so that the fan unit
will push TOWARD the sensor..
Turn the fan unit on and hold the cart still. Start the data collection and then
give the cart a quick push (or pull) AWAY FROM the sensor with your hand.
Allow the cart to return to the starting position before stopping it and turning
the fan off.
Sketch the speed-time
graph and describe the
motion of the cart.
FM-25
Unit FM
While the cart is moving away from its
starting position (after the initial push)
is its speed increasing, decreasing, or
staying reasonably constant? Use ideas
about forces to briefly explain why you
think this is?
While the cart is moving back toward
its starting position is its speed
increasing, decreasing, or staying
forces to briefly explain why you think
the cart is moving in this manner now?
Summarizing Questions
S1: If an object is already moving, what effect on its speed does a single
force applied in the direction opposite to its motion have? If such a force
continues to act, what else may happen?
FM-26
Activity 3: Pushes and Slowing Down
S2: At the beginning of this activity you gave a moving cart a very gentle
backward tap that was not strong enough to either stop it or reverse its
direction. Use the pictures below to draw three force diagrams
(including both force and speed arrows where appropriate) for the cart;
one for a moment before the tap (for which the speed arrow is already
included), one at the mid-point during the short time that you were
tapping it, and a third for a moment just after your tap. Briefly explain
any force and speed arrows you add.
Before the tap
During the tap
After the tap
S3: Shown below are two force diagrams for a moving cart upon which a
force (from a fan unit) is acting. What will the motion of the cart be like
in each case? (Increasing speed, decreasing speed, or constant speed.)
Explain how you know in each case.
Force applied to
cart by fan unit
Force applied to
cart by fan unit
S4: Push a cart so that it moves along the track and then give it a quick firm
tap with your hand to change its direction and send it back toward its
starting point. If you did this in Unit EM you would have seen from the
speed-time graph that during your tap the speed of the cart decreased
FM-27
Unit FM
quickly until it stopped for just a moment, and then its speed increased
quickly as it started to move back in the opposite direction.
Using the ideas you have developed in the first few activities of this unit,
you should now be able to explain this quick sequence of events in terms
of the force the hand applied to the cart and the effect it had on the cart’s
motion.
Explanation: Why did the cart reverse direction when it was
hit by the hand?
Describe the Situation using a diagram: (Complete the force diagrams below
that represent moments in time while the hand is contact with the cart, the
first while it is decreasing in speed, the second at the moment it is stopped,
and the third while it is increasing in speed in the opposite direction. On each
diagram draw a motion half-arrow as appropriate, and a labeled force arrow
representing the interaction with the hand.)
Decreasing speed
Stopped momentarily
Increasing speed
Write the narrative: (You will need to break your narrative into two parts.
First, explain why the cart slows down and stops. Then explain why it starts
moving again and speeds up. Remember to use ideas about forces, not
energy.)
FM-28
UNIT FM
Developing Ideas
ACTIVITY 4: Friction and Slowing
Purpose
In the previous activity you saw that when a force is applied to a moving
object in a direction opposite to that of its motion, the object’s speed
decreases. Is such a force always responsible when things slow and stop, or
would a moving object eventually slow and stop on its own?
In previous activities you have
probably noticed (from your
motion sensor speed-time graphs)
that the cart you were using in
slightly even when there was not
a hand or a fan unit pushing it
‘backwards’. Why do you think
this was?
Was some other force responsible for this slowing, or is it just something that
happens to all moving objects around us anyway?
Is friction a force and how does it work
to slow moving objects?
Initial Ideas
Three students discuss a simple experiment where someone gave a cart a
quick push and then let it move along the track on its own (before someone
else stopped it). They notice that their speed-time graph (shown above)
indicates that the cart was slowing down very gradually after the initial push,
and discuss why they think this was happening.
FM-29
Unit FM
I
think
a
friction-type
contact push/pull interaction
is slowing the cart down, but
since I can’t see anything
pushing on the cart I don’t
think a force is involved.
I agree that friction
is slowing the cart
down, but I do think
friction is a force. I
just don’t know how it
works
Daryl
Kristen
I know we learned earlier that
friction slows things down, but I’m
not sure in this case. Even without
friction, I think it would slow down
anyway, because the force of the
Samantha
Do you agree with Daryl, Kristen, Samantha or with none of them?
Use the pictures below to draw force diagrams for the cart in the
experiment described above; the first while it is increasing speed during
the initial push, the second after the push, while the speed of the cart is
you did.
Speeding up during initial push
FM-30
Slowing down after initial push
Activity FM: Friction and Slowing
If you have examined friction-type contact push/pull interactions in Unit EM
of this course, you would have given a wooden block a push across the table
and saw it slow and stop. We said this was due to ‘friction’ but how do you
think friction actually works?
Whether you think friction is a force or not, explain what you think was
actually happening that slowed the block down.
!
Participate in a class discussion about these ideas. Make a note of any
ideas or reasoning that are different from those of your team.
Collecting and Interpreting Evidence
Experiment #1: Is friction a force?
You will need:
Low-friction cart with friction attachment
Track
Fan unit
Colored pencils
STEP 1: Examine the cart and note the
friction attachment that, when lowered,
allows a felt pad to touch whatever
surface the cart is placed on. (Your cart
may look different to the one shown in
the picture.) For now, make sure the pad
is raised so that it will not rub. Mount
the fan unit on the cart.
4-31
Unit FM
Place the cart at rest about 20 - 30 cm in front of
the Motion Sensor. Make sure that, when the cart
is given a quick push away from the sensor, the
fan unit will push on the cart in the opposite
direction to its motion.
Open the data collection file for this activity.
Hold the cart steady and turn the fan unit on.
After starting to collect data, give the cart a quick push away from the sensor.
Hold the cart with your hand at the moment it comes to a stop, before it
starts to move back toward the sensor.
Describe the motion of the cart from the moment just after you gave it
the quick push, to the moment you stopped it.
Sketch the speed-time graph for the motion of the cart and label it
‘FAN’.
FM-32
Activity FM: Friction and Slowing
STEP 2: Now remove the fan unit from the
cart and, using the adjustment screw, lower
the friction pad so that it rubs lightly on the
surface when the cart moves.
Adjust the level of the friction pad so that, after being given a similar quick
push, the cart comes to a stop in about the same place as the fan-cart did in
STEP 1.
When recording motion sensor data try to make the start and stop times on
the graph close to the same as the graph you drew in STEP 1, and also try to
match the initial pushes by having the graph rise to about the same
maximum value as it did in STEP 1.
When you are satisfied with the adjustment of the pad, use a different
color pencil to sketch the speed-time graph on the same set of axes you
used in STEP 1. Label the graph ‘FRICTION’.
How does the motion of the cart with the friction pad lowered compare
with the motion when the fan unit was pushing backward on it? (Are
the motions reasonably similar, or are they very different?)
Look at the graph you labeled ‘FAN’ above. What evidence does this
graph provide that, after the initial push, a force was being applied to
the cart in a direction opposite its motion? What force was this?
Now, look at the graph you labeled ‘FRICTION’ above. Does this graph
provide evidence that a force was being applied to the cart (after the
initial push)? If not, why not? If so, in what direction did the force act?
4-33
Unit FM
If your motion sensor graphs were not labeled, would it be possible for
someone who did not see the experiments to tell which one was
produced using the fan unit to slow the cart, and which was produced
friction is, or is not, a force that acts on moving objects in a direction
opposite their motion?
Experiment #2: What causes friction?
You will need:
Sticky notes
Wooden block
Launcher and clamp
Meter stick
2 sheets of sandpaper
Tape
Magnifying lens
STEP 1: Mount the launcher on the end of the
table (do not use a track for this experiment). Push
the wooden block against the rubber band, so it is
stretched back about 1 cm, and hold the block still
by pushing down on top of it. Release the block,
so that it slides across the table and stops.
Measure how far it travels. Do NOT enter this
value in the table on the next page!
FM-34
Activity FM: Friction and Slowing
Repeat the process from STEP 1, stretching the band back a little further each
time, until you reach a point where the block travels a distance of at least 50
cm on the table before stopping. Use a sticky note to mark how far back the
rubber band must be stretched to achieve this 50 cm travel distance.
This is how far back you will stretch the band in EVERY
step from now on. Do not remove this marker until you have
completed the whole activity.
STEP 2: Members of your team should now take turns launching the block
(stretching the rubber band back to the same marked point each time) and
measure how far the block travels.
Enter these measured values on the top row of the table below, and
calculate the average distance traveled by the block across the table.
Surface
Distance traveled (cm)
Trial 1
Trial 2
Trial 3
Average
Table
Top (STEP 2)
Sandpaper
(STEP 3)
Stickies
(STEP 4)
STEP 3: Now slide a sheet of sandpaper
under the launcher, so that the back
edge of the sheet lines up with your
launching mark.
Place a second sheet of sandpaper in
front of the first and slide its edge about
2 mm under the first sheet. Tape the
corners of the sheets of sandpaper to the
table.
4-35
Unit FM
Repeat the experiment from STEP 2, each time stretching the rubber band
back to the same previously marked point. (You do not need to determine a
new launching point.)
Complete the second line of the table.
How does the average distance the block travels on the sandpaper
compare with the distance it travels on the bare tabletop? Why do you
think this is?
STEP 4: Remove the sandpaper and place 15 sticky notes, about 4 cm apart, in
front of the launcher, so that they will be in the path of the block, when it is
launched, as shown below.
Now launch the block in the same way as you did before and measure how
far the block travels. (Make sure to ‘reset’ the sticky notes before each trial.)
Complete the last row of the table.
How does the average distance the block travels over the sticky notes
compare with the distance it travels on the bare tabletop?
FM-36
Activity FM: Friction and Slowing
Why do you think that the block does not travel as far before stopping
when the sticky notes are in the way? (Hint: During their interaction,
does a sticky note apply a force to the moving block? If so, in what
direction?)
be happening when the block slides across a surface. (An analogy in science is
when two situations or processes have certain characteristics in common.
visualize how the other operates also. For example, a test tube full of iron
filings can serve as an analogy for what happens inside a nail when it is
magnetized.)
STEP 5: Examine the surface of the sandpaper with the magnifying lens and
Describe what you see and feel.
The sticky notes slow the block down because each one applies a weak
force to the block in a direction opposite to its motion. How do you
think the sandpaper slows the block down?
Examine the surface of the table and the wooden block with the magnifying
Do the table and the block both look and feel perfectly smooth, or can
you see some imperfections? How would these affect the motion of the
block as it slides across the tabletop?
4-37
Unit FM
Students were comparing their ideas about how friction works with the first
experiment in the Activity 3, in which you applied several very gentle
‘backward’ taps to a moving cart, so slowing it down in several small ‘steps’.
One student made the following statement.
“When we slowed the cart down in Activity 3 we were applying several weak
‘backward’ forces to it. Each one of these forces made the cart slow down a
little, until eventually it stopped. But friction is different, there are no
backward forces acting on the block, it’s just the rubbing on the surface that
makes it slow down. ”
Do you agree or disagree with this student? Explain why.
Summarizing Questions
First discuss these questions with your team and note your ideas. Leave
space to add any different ideas that may emerge when the whole class
discusses their thinking.
S1: What evidence from this activity suggests that friction is a force that
opposes motion?1
S2: How does the row of sticky notes serve as an analogy to help
understand how friction works in slowing down a moving object? That
is, how does thinking about why the sticky notes slow the block down
sandpaper or the table?
1
Under certain circumstances the effects of friction can be taken to be negligible. In terms of
forces, you should make this decision based on whether or not there are much stronger forces
acting on an object, such that the friction force itself will have only a negligible effect.
FM-38
Activity FM: Friction and Slowing
S3: Why do you think the block slows down more rapidly on the sandpaper
than on the bare tabletop? Why does it slow down at all on the
apparently smooth tabletop?
S4: Why do you think the cart slows down very gradually, even when no
friction pad is used, but slows quickly when the pad is rubbing on the
track? Use the pictures below to draw force diagrams to illustrate the
difference between the two situations. Explain your reasoning below the
diagrams.
2
In this case the most important source of friction is the interaction between the wheel
bearings and the axles on the cart itself, not between the wheels and the track. However, this
still results in a ‘backwards’ force acting on the cart.
4-39
Unit FM
S5: Suppose you could start an object moving and then arrange for
absolutely no forces to act on it. How would it move from then on? To
Suppose a spacecraft is at rest in deep space, far
from any stars or planets, so that no form of
friction or gravity is acting on it. The main
engine, at the rear of the spacecraft, is fired for a
period of 2 seconds (to start the spacecraft
moving) and is then shut off.
What do you think the motion of the spacecraft would be like after the
engine is shut off? Explain your reasoning.
FM-40
UNIT FM
Developing Ideas
ACTIVITY 5: Changing Force-Strength and
Mass
Purpose
In the previous activities of this unit
you have seen that during a contact
push/pull interaction, when a single
force acts on an object, its speed either
increases or decreases, depending on
whether the force acts in the same
direction as its motion, or opposite to it.
Do you think a force of any strength
will produce the same effect on any
object, or will the motion of the object
depend on its mass and the strength of
the force?
If you were to continuously push your friend on his well-oiled skateboard,
would his motion depend on how hard you pushed? If so, how? Would his
motion depend on how much mass he has? How do you think these two
factors would affect his motion if you were to push against him in the
opposite direction to his motion as he moves?
When a force acts on an object, how is the
object’s motion affected by the strength of the
force and the object’s mass?
Initial Ideas
In Activity 2 of this unit you investigated the
motion of a cart while it is being pushed along the
track by a fan unit and saw that its speed
continuously increases. Suppose you were to
repeat the experiment again with two otherwise
identical carts, one of which has a fan-unit that
pushes with a stronger force than the other.
FM-41
Unit FM
Assuming the effects of friction are negligible, would the motion of the two
carts be exactly the same, or different in some way?
Sketch (and label)
two lines on the
blank
speed-time
graph for the two
otherwise identical
carts being pushed
by a ‘weaker’ and a
‘stronger’ force.
Briefly explain the
reasoning that led you to draw the graphs the way you did.
any ideas or reasoning different from those of your team.
Collecting and Interpreting Evidence
Exploration #1: How does force strength affect speeding up and slowing
down?
You will need:
Low-friction cart and track
Fan unit
Color pencils
Spare batteries and dummies (as needed)
FM-42
Activity 5: Changing Force-Strength and Mass
STEP 1: In Activity 2 you established that a fan-unit provides a constant
strength push on the cart. For this experiment you will need to have a way of
changing the strength of the fan-unit’s push on the cart. For some fan units
this can be accomplished with a built-in switch. For others you can change the
number of batteries that are used to power the fan unit. Your instructor will
tell you which method to use in your particular class.
Open the Motion sensor data collection file for this
experiment. Make sure the fan unit is set to provide
a ‘weaker’ force (by selecting the ‘low setting, or by
using only two real batteries to power it). Place the
cart about 20 - 30 cm from the motion sensor so
that the fan will push it away from the sensor. Turn
the fan unit on and hold the cart steady. Start the
data collection and then release the cart.
What happens to the speed of the cart as it moves? Why is this?
STEP 2: So that it is available for comparison you should now store the
current Motion Sensor data on the computer. (See the How to use the Motion
Sensor document for instructions on how to do this, or ask your instructor).
Now adjust the fan unit so it is set up for a ‘stronger’ force (either by selecting
the appropriate setting or by adding two more real batteries) and repeat the
experiment.
Using different color
pencils, sketch the
two speed-time
graphs. Label each
one according to
how strong the force
was.
FM-43
Unit FM
What is similar about how the speed of the cart behaves, even when
different strength forces are acting on it?
Which of the forces, stronger or weaker, caused the speed of the cart to
increase at a higher rate? Explain how the lines on the graph show this.
STEP 3: Clear all the Motion Sensor data on the computer. (See How to use the
Motion Sensor for instructions on how to do this, or ask your instructor.) Your
fan should currently be set to provide a ‘stronger’ force.
Now, place the cart about 20 - 30 cm from the
motion sensor, this time so that the fan unit will
push it toward the sensor. Turn the fan on and hold
the cart steady. Start the data collection and then
give the cart a quick push away from the sensor so
that the force of the fan slows it down.
Stop the cart just as it starts to move back toward the sensor.
How does the speed of the cart behave after your quick push? Why is
this?
STEP 4: Store the Motion Sensor data and then repeat this procedure using
only two batteries to power the fan unit. Try to make sure the speed of the
cart just after the push is about the same as it was in STEP 3. (To check this,
make sure both graphs rise to about the same maximum value at about the same
time.)
FM-44
Activity 5: Changing Force-Strength and Mass
Using different color
pencils, sketch the
two
speed-time
graphs. Label each
one according to
how strong the force
was.
What is similar about how the speed of the cart behaves after the initial
push, even when different strength forces are acting on it?
Which of the forces, stronger or weaker, caused the speed of the cart to
decrease at a higher rate? Explain how the lines on the graph show this.
STEP 6: You already saw earlier in this unit that when a single force is
applied to an object, its speed will change in some way. (It will increase if the
force is in the same direction as its motion, and decrease if the force is in the
opposite direction to its motion.) Now you have investigated how the
strength of the force affects the rate at which the object’s speed changes?
How does the rate at which the speed of the cart changes (increases or
decreases)1 depend on the strength of the force acting on it? Does the
1
Scientists use the term ‘acceleration’ to refer to any change in speed (increase or decrease)
and define an object’s acceleration to be the rate at which it’s speed changes. However, in
everyday use the word ‘acceleration’ is usually understood to mean only an increase in
speed. Therefore, to avoid confusion we will not use the term ‘acceleration’ in the PET
activities.
FM-45
Unit FM
speed change at a higher, or lower, rate when a stronger force is
applied? How can you tell this from the speed-time graphs?
Check your answers to this question with at least two other groups
and try to resolve any differences.
Exploration #2: How does mass affect the rate at which speed changes?
You will need (work with another group, if necessary):
2 Low-friction carts and 2 tracks
2 Fan units
Extra masses (metal bars)
Ruler
STEP 1: Place the two tracks side-by-side. Mount a fan unit on each of the
carts and place one on each track. Make sure you have two fan units that
provide about the same strength of push. To do this, turn on the fan units,
line up the carts side-by-side (on separate tracks), and let them go at the same
time.
Assuming the two carts are identical, what should happen if the fan
units are of about the same strength?
If the two fan units do not appear to have close to the same strength try
changing the number of batteries, or try different fan-units.
FM-46
Activity 5: Changing Force-Strength and Mass
STEP 2: Now, put two of the metal bars on one of
the carts. (Make sure they will not interfere with the
fan blade.) Again, hold the carts side-by-side, turn
on the fan units, and release both carts at the same
time.
Describe the motion of the two carts. If they were in a race, which one
would win? (After the experiment, leave the tracks and carts where they
are as you will need them again soon.)
When the same strength force acted to speed up the two carts, which
cart increased speed at a faster rate, the one with less mass, or the one
with more mass? How do you know?
STEP 3. In Activity 3 you also used a fancart, but this time gave it a quick push to
get it started and then used the fan unit to
exert a continuous force in the direction
opposite to its motion. This caused the
cart to slow down, stop momentarily, and
then move back toward its starting
position, speeding up as it did so.
Suppose you took your two carts, with equal strength fans and different
masses, and gave both carts a push away from you so that they start moving
side-by-side at the same speed (with the fan units pushing in the direction
opposite to that of their motion)
Which cart do you think would be the first to slow to a stop and start
moving back toward you – the one with less mass, or the one with more
mass, or would they both be the same? Explain your reasoning.
FM-47
Unit FM
STEP 4: Return the carts (one should still have its added mass) to the starting
point and turn them around so that the fan units will push them in the
opposite direction. Turn the fans on, and give both the carts a quick push,
against the fans, to start them moving at the same speed.
To have both carts
same speed, one
person can push
both of them, using
a ruler, as shown in
the top view here.
Repeat the experiment three times, using a different person to push for each
trial.
Which cart slows to a stop and reverses direction first, the one with less
mass, or the one with more mass? Does your observation agree with
When the same strength force acted to decrease the speed of the two
carts, which cart decreased at a faster rate, the one with less mass, or the
one with more mass? How do you know?
FM-48
Activity 5: Changing Force-Strength and Mass
In both cases you have seen in this exploration (speeding up and
slowing down) which cart’s speed changed at a higher rate when the
same strength force acted on them, the one with less mass, or the one
with more mass?
STEP 5: In STEP 2 you held a ‘race’ between two carts that had different
masses but the same strength force pushing on them. Now, suppose you
wanted to make such a race between the two carts end as a tie.
To make the race a tie, what would you have to do to the strength of the
fan unit pushing on the more massive cart? Explain your reasoning.
Now suppose that one of your carts had a total mass of 6 kg while the other
was only 2 kg, but that both fans applied a force of 20 N to them.
Watch UFM-A5 - Movie 1, which shows a simulation of this arrangement in
which both fans have the same force strength of 20 N.
Which simulator cart (Cart 1 or Cart 2) has a mass of 6 kg and which has
a mass of 2 kg? How do you know?
To make both carts increase speed at the same rate, and hence make the
race a tie, what strength force should the fan acting on the 6 kg cart push
with? (Remember, its mass is three times greater than the lighter cart.)
FM-49
Unit FM
Now watch UFM-A5 - Movie 2, in which the simulation will be run four
times. Each time the strength of the fan force being applied to the 6 kg cart
will be set to a different value. (The force strength on the 2 kg cart will be kept
at 20 N throughout.)
For which value of the force strength on the 6 kg cart does the race
between the two carts end in a tie? Does this agree with your prediction
above?
When the carts increased speed at the same rate their masses were not the
same, so it cannot be just mass that determines the rate at which speed
changes. Similarly, the force strengths were not the same, so it cannot be just
the force strength that determines the rate at which speed changes.
How you could combine the values of mass and force strength for each
cart, such that you would get the same calculated final value for each of
them, indicating that something about them was the same? (In effect you
are trying to develop an equation involving force strength and mass that
gives the same final result for each cart.)
Summarizing Questions
First discuss these questions with your group and note your ideas. Leave
space to add any different ideas that may emerge when the whole class
discusses their thinking.
S1: When a single force acts on an object, how does the rate at which its
speed changes depend on the strength of that force? Is this true for both
FM-50
Activity 5: Changing Force-Strength and Mass
S2: To the right is a speed-time
graph for a cart that was given a
quick push along the track and
Which force do you think was
stronger, the initial push, or the
one that slowed it down? How
do you know?
S3: How does the mass of an object affect the rate at which its speed
changes, while a force acts on it? What evidence supports your answer?
S4: At a practice session a soccer goalie is practicing rolling a soccer ball
along the ground. To improve his strength he also practices rolling a
bowling ball. The coach measures the speed of both balls and sees that,
when the goalie pushes as hard as he can, the soccer ball has a speed of
15 m/s just after it leaves the goalies’ hands, but the bowling ball has a
speed of only 2 m/s.
Write an explanation for why the bowling ball’s speed is much less than
the soccer ball’s speed, just after they left the goalie’s hands. Assume the
goalie applied the same strength force to both balls, for the same
amount of time,
FM-51
Unit FM
Explanation: Why was the bowling ball’s speed much less
than the soccer ball’s speed just after the goalie had pushed
them both with the same strength force, for the same amount
of time?
Describe the Situation using a diagram: (Draw two separate force diagrams,
one for each ball at a moment in time during the push.)
Write the narrative: (Use the idea you developed in this activity about how
the effect of a force on an object depends on the object’s mass.)
S5: In this unit you considered mostly cases in which you compared the
motion of two objects for which only the force strength or the mass was
different. But what if you had two objects that both had different
masses, and were both acted on by forces of different strengths? How
could you predict which object’s speed would change at a faster rate
under these circumstances?
Two students were discussing their ideas about a relationship that they
could use to help them decide:
FM-52
Activity 5: Changing Force-Strength and Mass
We saw that the greater the force strength, the
faster the speed changes. I also think that the
more mass an object has, the faster it slows down,
so increases in the force strength and mass both
produce a faster change in speed. That makes me
think the rate at which the speed of an object
changes depends on the force strength multiplied
by the mass
I agree with what you say about the
force strength, but the speed of the
cart with more mass increased at a
slower rate, not a faster one. I think
you have to divide the force strength
by the mass to find out about the rate
at which the speed will change.
Amara
Han
In terms of a mathematical relationship, Amara thinks:
Rate of change in speed = Strength of force × Mass of object ,
while Han thinks:
€
Rate of change in speed =
Strength of force
Mass of object
Do you agree with Amara, Han, or neither of them? What evidence from
FM-53
Unit FM
S6: Some students have a race between two different fan carts. Cart A has a
mass of 0.5 kg and a fan strength of 0.3 N. Cart B has a mass of 0.7 kg
and a fan strength of 0.4 N. Which cart will win the race, and why2?
Participate in a class discussion to go over the summarizing questions.
2
When the force strength is measured in units of newtons (N) and the mass is measured in
kilograms (kg), the units of ‘rate of change of speed’ will be (meters per second) per second
[(m/s)/s]. These units tell us how quickly the speed (in m/s) will change during one second.
For example a ‘rate of change of speed’ of 5 (m/s)/s means the speed will change by 5 m/s
for every second that the force is being applied.
FM-54
UNIT FM
Applying Ideas
ACTIVITY 6: Falling Objects
Purpose and Key Question
In the previous activities, you used objects that move horizontally to develop
your ideas about how the motion of an object is related to the forces acting on
it. However, it can be shown that exactly the same ideas apply to objects that
move vertically (up and down). You know that if you hold an object up and
then release it, it will fall to the floor. This behavior can be explained using
the idea that there is a gravitational interaction between the object and Earth.
In this activity, you will explore how different objects fall and, in particular,
how their mass affects how they fall. You will also consider how the results
For example, suppose you dropped a soccer ball and a
bowling ball from the same height at the same time.
Which one would reach the ground first and, why?
The key question for this lesson is:
How does the mass of an object affect how it
falls?
Initial Ideas
If you were to drop a bowling ball and a soccer ball from the same
height, at the same time, which one do you think would reach the floor
FM-55
Unit FM
To help illustrate your thinking about the force(s) acting on each ball,
sketch a force diagram for both balls at the same moment in time as
they are falling. (Remember, they are released at the same time from
the same height.) Be sure to include arrows representing the
gravitational force acting on each ball, as well as any speed arrows you
think appropriate, paying attention to the relative lengths of both.
Do you think that the strength of the gravitational force acting on each
ball would remain constant as it falls or do you think these force
strengths would change as the balls get nearer to the ground? Explain
why you think so.
!
FM-56
Draw your group’s force diagrams on a whiteboard. Participate in a
class discussion about everyone’s ideas and make a note of any ideas or
Activity 6: Falling Objects
Collecting and Interpreting Evidence
You will need:
•
•
•
•
Computer with internet connection
Two objects with very different masses (e.g. a 1 kg and a 100 g mass)
Several objects with different masses (but similar size and shape)
Hard board such as a whiteboard (to drop balls onto)
Exploration #1: How do falling objects move?
STEP 1. If you did Activity 4 of Unit PEF, you will have seen that when a ball is
dropped from a height of about 2 meters its speed increases as it falls.
Suppose a small ball were dropped from the top of a tall building. Do you
think its speed would continue to increase all the time it is falling? Why do
you think so? (You may assume the effects of the air are negligible.)
To check your thinking, watch UFM-A6 - Movie 1. It shows
a simulation of a young man at the top of a building, holding
a baseball in his hand. When you play the movie, he will
release the ball and a speed-time graph for the falling ball
will be plotted. When you are ready, run the simulation.
While the ball was falling, was a force acting on it the
whole time? How do you know?
CF-57
Unit FM
Did the strength of the force acting on the ball change significantly as it fell,
or did its strength remain approximately constant? How do you know?
(Hint: Consider whether the rate at which the speed increases stays the
same or not.) 1
STEP 2. Now, imagine you were to hold two
spheres of a similar size, but different mass, at
the same height above the ground and
released them at the same time.
Which sphere do you think would hit the ground first (if either)? Explain
your thinking in terms of the strength of the gravitational force acting on
each of the two spheres.
STEP 3: Lay the hard board on the floor. From those available to you, select two
similarly sized spheres of different mass and hold them at the same height
(about head high) above the board. Release them at the same time.
1
Actually, the strength of the gravitational force exerted on an object depends on its distance
from the center of the Earth. Thus, even when an object falls to the ground from a great height,
such as an aircraft, its distance from the Earth’s center changes by only a very small relative
amount and so the gravitational force has about the same strength throughout its fall.
FM-58
Activity 6: Falling Objects
ALL of your group members should watch and LISTEN carefully as the spheres
hit the board. Listen to see if they hit the board at the same time (single ‘plunk’),
or at different times (‘plunk . . . plunk’). Be aware that some of the spheres have
a tendency to bounce once they hit the board so you may want to have one group
member be in charge of watching to see if one of the spheres bounced. You need
to be able to distinguish between a ‘soft plunk . . . soft plunk’ (each sphere hitting
the board at a different time) and a ‘loud plunk . . . soft plunk, plunk’ due to both
spheres hitting the board at the same time and then one of the spheres bouncing.
You may need to repeat the experiment a few times to check. Make sure that
everyone in your group agrees on what you saw and heard.
Does the more or the less massive sphere CLEARLY hit the board first or do
they both appear to hit at the same time?
STEP 4. Now repeat the experiment using different pairs of spheres of varying
masses.
Describe your observations about which object hits the board first (if either).
Based on your observations, when you drop two spheres of different mass,
do they increase speed at the same rate as they fall or at different rates
depending on their mass? What evidence supports your conclusion?
Mass and Weight
In everyday conversation we tend to use the terms ‘mass’ and ‘weight’ to
mean the same thing. However, scientists have very different meanings for
these terms, and it is important that you appreciate the difference.
CF-59
Unit FM
The mass of an object is a measure of the amount of matter it contains and would be
the same no matter where in the universe the object was. The unit of mass is the
kilogram (kg). For example, a person with mass of 60 kg here on the Earth would also
have a mass of 60 kg on Mars.
The weight of an object is a name we give to the strength of a planet’s
gravitational force acting on an object and so could be different depending on
where in the universe an object is. Since weight is a force, its unit is the newton (N),
just as it is for all other forces. (You are probably more familiar with the imperial
unit, the pound (lb)). For example, a person with a mass of 60 kg would have a weight
of 590 N (~130 lb) here on Earth but only 220 N (~49 lb) on Mars.
Exploration #2: How does mass affect the strength of the gravitational force?
Having now seen how objects with different masses fall, we will consider
how the strengths of the gravitational forces acting on them (more commonly
called their weights) compare.
Objects fall (and speed up as they do so) because a gravitational force exerted
on them by the Earth (their weight) pulls downward on them. One way to
estimate the strength of the gravitational force acting on an object is to see
how much effort it takes to stop the object from falling. (That is, how strong a
force it takes to hold it up.) The harder it is to stop an object falling, the
stronger the gravitational force that is pulling it downward.
STEP 1. Hold out one of you hands, palm upward, place a low-mass object
(e.g. a 100 gram mass) on your palm and leave it there so it does not move.
Now stretch out your other hand and have someone place an object with
significantly more mass on it (e.g. a 1 kilogram mass). Again, do not let the
object move while you are holding it up.
Now focus on the effort you have to exert to hold each object steady, to stop it
from falling.
How does the effort you have to exert for the two objects compare? Does
it take the same effort to support each one, or does it take more effort for
one or the other? If so, which one?
FM-60
Activity 6: Falling Objects
strength of the gravitational force acting on these two objects?
For which of the two objects is the gravitational force pulling downward
stronger, or is it the same for both? Explain briefly how your answer to
the previous question supports your thinking.
!
resolve any differences.
STEP 2. You have now seen that, regardless of their masses, similarly shaped
spheres increase speed at the same rate as they fall. However, you have now
seen that the strength of the gravitational force that pulls downward on all
objects (their weight) does depend on their mass.
Consider the following questions about some races between fan-carts, which
Imagine you had a race between two low-friction
fan-carts on side-by-side tracks, like those shown
here. These carts have different masses (6 kg and
2 kg) but the same strength force (20 N) acting on
each of them.
Would these two carts increase speed at the same rate, so making the
race end in a tie? If so, why? If not, why not and what could you do to
make the race end in a tie? Carefully explain your reasoning.
Suppose you had a race between two different mass fan-carts that did
end in a tie. Would this be evidence that the strength of the fans was the
same, or that it was different, and if so which one was stronger? Explain
CF-61
Unit FM
You have seen that objects of different mass all fall at the same rate of
increasing speed. (Essentially, the race ‘downward’ ends in a tie.)
Does this evidence support the idea that the strength of the gravitational
force acting on them has the same strength, regardless of their mass, or
does it support the idea that the strength of the gravitational force acting
on an object depends on its mass?
Recall that in the previous activity you saw that the rate at which an object’s
speed increases when a force acts on it is given by the relationship:
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Explain, in terms of this relationship and the force strengths and masses
involved, how it is that all objects can fall at the same rate of increasing
speed2.
Exploration #3: Does the shape of an object affect how it falls?
You will need:
A sheet of paper (notebook size)
A pencil
2
Close to the surface of the Earth, and in the absence of any other effects, the rate at which all
objects increase speed as they fall can be measured to be approximately 9.8 (m/s)/s. This
means their speed increases by 9.8 m/s for every second that they are falling. This value is
sometimes called the ‘acceleration due to gravity’ and is determined by the mass of the Earth
(and how far we are from its center). Close to the surface of Mars the acceleration due to
gravity is only 3.7 (m/s)/s because Mars’ mass is much less than that of the Earth.
FM-62
Activity 6: Falling Objects
STEP 1: Do all objects really fall together? Suppose you were to drop a
bowling ball and a feather from the same height, at the same time.
Which one do you think would reach the ground first? Explain your
reasoning.
Hold the sheet of paper and the pencil (one in each hand) at the same height
(about head high) above the ground. Release them at the same time and all
your team members should watch carefully as they fall.
Does the pencil or the paper hit the floor first? Describe the behavior of
the pencil and the paper as they fall.
Why do you think the result of this experiment is different from what
you observed earlier when dropping the spheres?
STEP 2: Now ‘scrunch’ the sheet of paper up into a small ball and repeat the
experiment.
Now, does the pencil or the paper hit the floor first, or do they hit at
approximately the same time? Why do you think this result is different
from that in STEP 1 when you dropped the same two objects?
Do you think any other force, apart from the gravitational force of the
Earth, acts on objects as they fall? If so, does this force affect all objects
equally, or does it affect some more than others?
CF-63
Unit FM
STEP 3: Suppose you were to drop a bowling ball and a bird’s feather from
the same height, at the same time.
Which do you think would reach the floor first? Briefly explain your
reasoning.
Suppose you could drop the ball and feather in a situation in which
where there was no air. Would your answer to the previous question be
the same, or different? Again, explain your reasoning?
Watch UFM-A6 - Movie 2, which shows a ball and a feather falling from the
top of a large chamber, first in air and then when there is no air.
Does what happens in the movie agree with your predictions? If not, try
to explain it.
In the next unit you will consider the effects of the air on falling objects
further. For the Summarizing Questions on the following pages, assume these
effects can be ignored.
FM-64
Activity 6: Falling Objects
Summarizing Questions
S1: Does the strength of the gravitational force of the Earth pulling an object
toward the ground depend on the object’s mass? What evidence
S2: Your observations in this activity suggest that if the 6 kg and 2 kg carts
were dropped from the same height at the same time, they would reach
the ground together. In other words the race to the ground would end in
a tie.
a) How could you explain such a result in terms of their masses and the
relative strengths of the gravitational forces pulling the carts
downward?
b) Draw force diagrams for both carts as they are falling side-by-side.
Be sure to include both force and speed arrows of appropriate
lengths?
CF-65
Unit FM
S3: It is common for people to explain that objects of different mass fall
together because the gravitational force acting on them is the same
strength3. If the gravitational forces acting on a bowling ball and a soccer
ball were truly the same strength as they fell, which one would actually
reach the ground first? Explain your reasoning.
3
Because all objects fall with the same rate of increasing speed people often say that ‘gravity
pulls the same on everything’, but we have seen that this is not true. It would be more
appropriate to say that the pull of gravity on an object depends on its mass, but that the effect
it causes (rate of change of speed) is the same for all objects.
FM-66
Next%Generation%Physical%Science%
and%Everyday%Thinking%
Interactions%and%
Forces%Module%
!
!
Unit!CF!
Combinations!of!!
Forces!
!!!!
!
!
Studio4style!Class!
!
Unit CF: Combinations of Forces
Activity #
1
Activity (A) Title
Page
A1
Combinations of Forces
CF-1
Ext A1
Newton’s Second Law
online
A2
Balanced Forces
CF-13
Ext B
More on Balanced Forces
online
Ext C
Balanced and Unbalanced Forces
online
A3
Comparing Forces During Interactions
CF-25
Ext F
Newton’s Third Law and Balanced Forces
online
A4
Explaining Phenomena Using Force Ideas
CF-35
Ext D
More on Vertical Motion (includes air drag)
online
A5 ED
Engineering Design: Inspiration from
Nature
CF-45
Extensions (Ext’s) are online homework activities.
Unit CF: Combinations of Forces
Activity #
1
Activity (A) Title
Page
A1
Combinations of Forces
CF-1
Ext A1
Newton’s Second Law
online
A2
Balanced Forces
CF-13
Ext B
More on Balanced Forces
online
Ext C
Balanced and Unbalanced Forces
online
A3
Comparing Forces During Interactions
CF-25
Ext F
Newton’s Third Law and Balanced Forces
online
A4
Explaining Phenomena Using Force Ideas
CF-35
Ext D
More on Vertical Motion (includes air drag)
online
A5 ED
Engineering Design: Inspiration from
Nature—The ‘Whirligig’ Challenge
CF-45
A6 ED
Engineering Design: Safety on the Docks
(forthcoming Summer 2016)
CF-53
Extensions (Ext’s) are online homework activities.
UNIT CF
Developing Ideas
ACTIVITY 1: Combinations of Forces
Purpose
In the previous unit you considered situations in which only a single
horizontal force was applied to an object. But what if there is more than one
force? For example, suppose two hockey players try to hit a puck at the same
time? How should we treat the forces acting on the puck to understand its
motion? In this unit you will extend your thinking to include how multiple
forces combine to affect the motion of objects.
How do objects behave when more than
one force acts on them?
Initial Ideas
with two fan units
mounted on it that push
on the cart in opposite
directions
and
with
different strengths.
Force applied
to cart by
stronger fan
Force applied
to cart by
weaker fan
Now suppose you turned both the fan units on and gave the cart a quick
shove along the track in the same direction that the stronger fan is pushing.
The force diagram above represents the situation just after your hand has lost
contact with the cart.
What do you think the motion of the cart would be like just after your
push? Would its speed increase, decrease or remain reasonably
constant? Why do you think so?
.
CF-1
Unit CF
Suppose that you repeated
the experiment, but this
time gave the stationary
cart a quick shove in the
same direction that the Force applied
to cart by
weaker fan is pushing. stronger fan
Again, the force diagram
represents the situation
just after your hand has lost contact with the cart.
Force applied
to cart by
weaker fan
How do you think the speed of the cart would behave now, just after
your push? Again, why do you think so?
Collecting and Interpreting Evidence
You will need:
Computer with internet access
Exploration #1. What effect do combinations of forces have on an object
at rest?
In this exploration, you will use the simulator model to examine scientists’
ideas about the effect that a combination of two forces has on an object that is
initially at rest. You will also consider whether a single force, acting on an
otherwise identical cart, could have exactly the same effect.
STEP 1: Suppose you had a low-friction cart that
has two fan units mounted on it that both push in
the same direction, with individual force strengths
of 30 N and 20 N. (Cart 1)
If this cart was initially held at rest with the
fans turned on and then released, what
would happen?
CF-2
Activity 1: Combinations of Forces
Do you think Cart 1 would start to move or not, and if it did what do
you think would happen to its speed as it did so (increase, decrease, or
remain constant)? Why do you think so?
Imagine you had a second, identical, low friction cart
(with the same total mass), but with only one fan unit
mounted on it (Cart 2). Suppose you wanted Cart 2 to
behave in the same manner as Cart 1. (That is, you want
them to remain side by side after you release them.)
If you could vary the strength of the force
the single fan unit applies to Cart 2, what
?
value do you think it should have to
make Cart 2 behave in exactly the same
manner as Cart 1? Why do you think this force strength would work?
the strength and/or direction of the single force being applied to Cart 2,
NOT adding any other forces, or adjusting the forces being applied to
Cart 1.)
STEP 2. You can check your thinking by watching UCF-A1 - Movie 1. It
shows a simulation of this situation being run several times. In each run, the
strengths of the two forces acting on Cart 1 will be kept at 20 N and 30 N,
while the strength of the single force acting on Cart 2 will be changed to
different values.
Does Cart 1 start to move or not and, if so,
how does its speed behave? Does this agree
CF-3
Unit CF
Which value for the strength of the single force being applied to Cart 2
made it move in exactly the same manner as Cart 1? Is this what you
predicted?
When more than one force acts on an object at rest, but they all
push/pull in the same direction, how can you determine the strength of
a single force that would have exactly the same effect?
STEP 3: Now consider a different situation in which
the two fan units mounted on Cart 1 push in opposite
directions. The fan unit pushing to the right (30 N) is
stronger than the one pushing to the left (20 N).
How do you think Cart 1 will move
now, if at all, when released? (Not
move, increase or decrease in speed, or
move at a constant speed.) Explain
Do you think the weaker 20 N force will have any effect on the motion of
the cart or, will it behave in exactly the same manner as if only the 30 N
force were acting on it? Explain your thinking.
CF-4
Activity 1: Combinations of Forces
What value do you think the strength of the single force on Cart 2
should have now, so that its motion will exactly match that of Cart 1
with the two opposing forces? Again, explain your reasoning.
You can check your thinking by watching UCF-A1 - Movie 2. It shows a
simulation of this situation being run several times, with the strength of the
single force acting on Cart 2 changed to different values.
Does the speed of Cart 1 behave in the way you predicted?
Which value for the strength of the single force being applied to Cart 2
made it move in exactly the same manner as Cart 1? Is this what you
predicted?
When more than one force acts on an object at rest, but they push/pull
in opposite directions, how can you determine the strength of a single
force that would have exactly the same effect?
Unbalanced Combinations of Forces
When more than one force acts on an object, the effect they cause is due to the
combination of all the forces together. When the total strength of all the forces
being applied in one direction is bigger than the total strength being applied
in the opposite direction (as shown below) we say that the forces are
unbalanced.
300 N
500 N
400 N
CF-5
Unit CF
(When the total strength of all the forces being applied in one direction is
exactly the same as the total strength being applied in the opposite direction,
we say that the forces on the object are balanced. You will examine the effect
of a balanced combination of forces on an object in the next activity.)
In the first part of this activity, you examined the effect that an unbalanced
combination of forces has on an object that is initially at rest.
When unbalanced forces are applied to an object that is initially at rest,
what effect does the simulator model suggest they have on it? After it
has started moving, does its speed increase, decrease, or remain
constant?
Does the simulator model suggest that a single force can have exactly
the same effect on a stationary object as an unbalanced combination of
forces? If so, describe how you would calculate the strength of that
single force.
You should also note that when a single force acts on an
object this is just the simplest case of an unbalanced
combination of forces.
Exploration #2: What effect does an unbalanced combination of forces
have on an object that is already moving?
In this second exploration you will use the simulator model to examine
scientists’ ideas about the effect that an unbalanced combination of two forces
has on an object that is already moving. (How the object started moving is
not important here, just that it is already moving.)
CF-6
Activity 1: Combinations of Forces
STEP 1: Consider two identical carts
that are moving to the right at the same
speed, as shown by the equal-length
speed arrows.
?
Cart 1 has a fan unit pushing on it in
the same direction as its motion with a
force strength of 30 N, while a second
fan unit pushes on it in the opposite direction to its motion with a force
strength of 20 N.
When the simulator is run, what effect do you think this unbalanced
combination of forces will have on the motion of Cart 1? Will its speed
increase, decrease, or remain constant? Explain why you think so.
(Remember, it will already be moving to the right with a certain speed at
the moment the simulator starts!)
What value do you think the strength of the single force being applied to
Cart 2 should have to make the two carts move side-by-side? Explain
To check your thinking, watch UCF-A1 Movie 3. As usual, the simulation will
be run several times with different force strengths being applied to Cart 2.
Does the speed of Cart 1 increase, decrease, or remain constant? Is this
what you predicted above?
CF-7
Unit CF
Which value for the strength of the single force being applied to Cart 2
made it move in exactly the same manner as Cart 1? Why does this make
sense?
STEP 2: Now suppose the strength of
the two forces being applied to Cart 1
were changed such that the force in
the opposite direction to its motion
(30 N) was stronger than the force in
the same direction as its motion (20
N), as shown to the right.
What effect do you think this unbalanced combination of forces would
have on the motion of the Cart 1? Do you think it its speed would
increase, decrease, remain constant, or would something else happen?
What do you think you would have to do to the direction and strength
of the single force being applied to Cart 2 to make the two carts continue
to move side-by-side? Explain your reasoning.
Again, check your ideas by watching UCF-A1 - Movie 4 and record the
results below.
CF-8
Activity 1: Combinations of Forces
Suppose the simulator were to run for several seconds longer. What do
you think would happen to the carts? Explain your thinking.
Watch UCF-A1 Movie 5. Do the carts behave as you predicted?
STEP 3: Use your results from this exploration to answer the following
questions.
If an object is already moving, what effect (if any) does the simulator
model suggest an unbalanced combination of forces has on its speed?
Does the speed change, or does it remain constant? Why does this make
sense?
What happens to the speed of a moving object if the force being applied
in the same direction as its motion is stronger than the force being
applied in the direction opposite its motion?
What if the stronger force is applied in the direction opposite to the
motion?
Does the simulator model suggest that a single force can have exactly
the same effect on a moving object as an unbalanced combination of
forces? If so, describe how you would calculate the strength of that
single force.
CF-9
Unit CF
Net Force
You have seen in this activity that when an unbalanced combination of forces
acts on an object, you can also find a single force that would make the object
move in exactly the same manner. Further, you have seen that the strength
and direction of this single equivalent force can be found by adding and/or
subtracting the strengths of the individual forces, depending on the direction
in which they are applied.
Scientists call the result of such a calculation the net force acting on the object.
For example, consider the box below. The total force pushing to the right is
700 N, while the force pushing to the left is 500 N. Thus the net force on the
box would be 200 N pushing to the right. This means that an identical box
would move in exactly the same manner if a single 200 N force were pushing
it to the right.
Unbalanced
combination of
forces
300 N
500 N
400 N
Net force
200 N
In a situation in which a single force acts on an
object the net force is simply the same as that
single force. For example, for the cart shown here
the net force is simply 30 N pushing it to the right.
Summarizing Questions
S1: a) When an unbalanced combination of forces acts on an object (either at
rest or in motion), does the speed of the object change, or does it remain
constant?
b) Why does it make sense that this is the same as the effect of a single
force?
CF-10
Activity 1: Combinations of Forces
S2: Shown below are two force diagrams for a cart that is already moving.
What would the motion of each cart be like? Explain your reasoning.
S3: In a previous class a student made the following statement:
“When more than one force acts on an object only the strongest force
matters. It’s as if the weaker forces were not there and the object moves in
the same way as if only the strongest force were acting on it.”
Do you agree or disagree with this student? What evidence from this
S4: Two fan units of strength 30 N and 40 N push on a moving cart in the
same direction as its motion, while a 65 N frictional force acts in the
opposite direction.
What is the net force (strength and direction) acting on this cart? What
will happen to its speed if these forces continue to act on it?
CF-11
Unit CF
S5: In the Initial Ideas section of this activity you
fan units of unequal strength attached. Students
in a previous class performed this experiment
and noticed that, after their initial push, the
speed of the cart steadily decreased.
The students were not sure at first which of the two fans was the
strongest and so their instructor asked them to determine this (based on
their observation) and construct an explanation for how they know.
Explanation: Which of the two fans was the strongest while
the cart was decreasing in speed.?
Describe the Situation using a diagram:
Force applied to cart by
Force applied to cart by
Fan #1
Fan #2
Write the narrative:
The initial push gets the cart started moving to the right, but after the hand
loses contact the only forces acting on the cart are from the contact push/pull
interactions with the two fan units. When a weaker force opposes a stronger
force, an object will move in the direction of the stronger force, but will slow
down as it does so. Since the cart is decreasing in speed after the initial push,
this means the force in the direction of motion must be stronger than the force in
the opposite direction, so Fan #1 (in the direction of motion) must be stronger
than Fan #2 (in the opposite direction to the motion).
Evaluate this Explanation:
Is this explanation good or problematic? (Remember, it should be wellconstructed, accurate, and well-reasoned.) If you find this explanation to be
good, give your reasons below. If you find it to be problematic, again give
your reasons and also correct it.
CF-12
UNIT CF
Developing Ideas
ACTIVITY 2: Motion with Balanced Forces
Purpose
In the previous activity you saw
that
when
an
unbalanced
combination of forces acts on an
object, the speed of the object
changes, which is the same what
happens when a single force acts
on it.
But what if the combined strength of the forces pushing (and/or pulling) in
one direction is exactly equal to the combined strength of the forces pushing
(and/or pulling) in the opposite direction? In this case we say the forces are
balanced. If such a balanced combination of forces acted on an object at rest
would it start to move? If it were already moving when the forces acting on it
became balanced, what would its motion be like from then on?
For example, suppose the two men above push the box with a force of 200 N
each, while a frictional force of 400 N opposes them. What would the motion
of the box be like in this case? Would your answer depend on whether it
started at rest, or was already moving?
?
200 N
400 N
200 N
How does an object behave when the
forces acting on it are balanced?
CF-13
Unit CF
Initial Ideas
Imagine having a low-friction cart with two
fan units mounted on it. Further, when
operating, these fan units push on the cart in
opposite directions with exactly the same
strength.
Suppose you held this cart stationary on a
level surface, turned both fans on, and then
simply let go.
How do you think the cart would move (if at all)? Briefly explain your
reasoning.
Now, suppose you were to give the cart a quick push with your hand (in one
direction or the other) to start it moving.
How do you think the cart would move after your push? (Speed up,
slow down, or maintain a reasonably constant speed, or immediately
stop?) Why do you think it would behave in this manner?
!
CF-14
Participate in a class discussion about these ideas. Make a note of any
ideas or reasoning that are different from those of your team.
Activity 2: Motion with Balanced Forces
Collecting and Interpreting Evidence
Experiment #1: How do balanced forces affect motion?
STEP 1: Your instructor will show you a cart
with two fan units mounted on it. These fan
units have been adjusted so that, when
turned on, they push in opposite directions
with the same strength force. Your
instructor will hold the cart at rest, turn on
both fans, and then release the cart.
Describe the behavior of the cart.
Why do you think the cart behaves in this way?
In general, if balanced forces act on an object that is at rest, what do you
think happens to it?
STEP 2: With the fans still running, your instructor will give the cart a quick
push in one direction to start it moving.
Describe the motion of the cart after the quick push. Does its speed
rapidly increase or decrease, or does its speed seem to stay about the
same?
CF-15
Unit CF
STEP 3: Now your instructor will turn the fans off and repeat STEP 2.
Describe the motion of the cart after the quick push.
Compare the motion of the cart with the fans running to its motion with
them turned off. Does there seem to be any significant difference? Why
do you think this is?
STEP 4: You can compare your ideas
with those of scientists by watching
UCF-A2 - Movie 1. At first the
simulator shows a cart at rest with two 50 N forces acting on it, in opposite
directions. Answer the following questions as you watch the movie. (Pause
and rewind the movie as necessary.)
For the first few seconds of the movie, the pair of balanced 50 N forces
act on the cart it while it is at rest. What is its speed during this period
and does the speed change or does it remain constant?
Why do you think the cart behaves in this manner, even though two
forces are acting on it?
After a few seconds the simulation will then be rewound and run again. This
time, the cart will be given an initial push for about one second.
Sketch the speed-time graph for the cart on the next page, on the blank
graph titled ‘BALANCED FORCES’. (You will use the other blank graph
later.)
CF-16
Activity 2: Motion with Balanced Forces
BALANCED FORCES
NO FORCES
After the initial push, when only the balanced 50 N forces act on the
cart, does the speed of the cart change or does it remain constant?
Next, the simulator will be run with different strengths of the two opposing
forces, but keeping the values the same so that the forces are still balanced.
Does the motion of the cart after the initial push depend on the strength
of the balanced forces? Why do you think this is?
Finally, the two opposing forces will be deleted, and the simulator will be run
one more time (with an initial push applied as usual).
Sketch the speed-time graph for the cart on the blank graph above
labeled ‘NO FORCES’.
After the initial push, when no forces act on the cart, does the speed of
the cart change or does it remain constant?
CF-17
Unit CF
Is the motion of an object with balanced forces acting on it similar to, or
different from, an object with no forces acting on it? Why do you think
this is?
How could you explain the results of these investigations in terms of the
net force acting on the cart?
Experiment #2: Are the forces balanced or unbalanced?
You will need:
Low-friction cart with friction pad and track
Fan unit
STEP 1: Make sure the friction pad on the
cart is raised up so that it will not rub on the
surface when the cart moves. Mount the fan
unit on the cart and place it on the track
about 20 cm from the motion sensor, so that
the fan unit will push the cart away from the
sensor.
Open the data collection file for this activity. Turn the fan on, start the data
collection, and then release the cart.
Look at the speed-time graph on the computer. Do you think the forces
acting on the cart after you released it were balanced or unbalanced?
How can you tell from the graph?
CF-18
Activity 2: Motion with Balanced Forces
Use this picture to draw a force diagram for the cart while it is moving
along the track. Be sure to label any force arrows you add.
STEP 2: Now, lower the friction pad very slightly, so that it rubs lightly on
the surface, and repeat the experiment. (If the cart does not move after you
lower the pad and turn the fan on, you have lowered it too much!)
Do you think the forces acting on the cart now are balanced, or
unbalanced? How can you tell from the speed-time graph?
What forces do you think were acting on the cart while it was moving
along the track? Which force do you think was strongest? Again, explain
your reasoning and draw a force diagram.
STEP 3: Keep lowering the pad in very small steps, until you get to a point
where the cart will not move when you turn the fan on and release it.
Do you think the forces acting on the cart now are balanced, or
unbalanced? How can you tell?
Again, what forces do you think were acting on the cart? Which force do
you think was strongest? As usual, explain your reasoning and draw a
force diagram.
CF-19
Unit CF
STEP 4: Finally, with the fan still running, very carefully adjust the friction
pad until you get to a point where, after being given a quick push to get it
started, the cart moves at a fairly constant speed. (You can use the Motion
Sensor to collect data to check whether the speed is constant.)
Assuming the cart did move at a constant speed after the push, do you
think the forces acting on the cart (after the push has ended) were
balanced, or unbalanced? How can you tell?
What forces do you think were acting on the cart while it was moving
along the track? Which force do you think was strongest? Explain your
reasoning and draw a force diagram.
CF-20
Activity 2: Motion with Balanced Forces
Summarizing Questions
S1: a) When the forces acting on an object are balanced does its speed
change or does it remain constant? What evidence supports your idea?
b) How does your answer to part a) apply to an object at rest, with
balanced forces acting on it?
S2: Explain your answer to the previous question in terms of the net force
acting on such an object and how this would affect its speed.
S3: Use the pictures below to draw three force diagrams for the cart with
balanced forces of a fan and friction acting on it (STEP 4 of Exploration
#2); one before the initial push, one during the initial push, and one
after the push. Explain your diagrams below the pictures.
Before the push
During the push
After the push
CF-21
Unit CF
S4: Two students were discussing their ideas about balanced forces:
I just can’t see how an object with
balanced forces acting on it can be
moving at a constant speed. Surely, if
it’s moving in any way, the force in the
direction of motion must be stronger
than the opposing force.
What I can’t understand is how an
object with balanced forces can be
moving at all. After all, didn’t we learn
that an object at rest, with balanced
forces acting on it, will stay at rest?
Dave
Luisa
How would you respond to Dave’s and Luisa’s concerns?
S5: Imagine you want to push a heavy sofa
across a carpeted floor, on which a frictional
force opposes any movement, or attempt at
a) If the sofa were at rest, what would you have to do to start it
moving? Push with a force strength less than, equal to, or greater
than the frictional force resisting the movement of the sofa? Briefly
CF-22
Activity 2: Motion with Balanced Forces
b) After you start the sofa moving, what would you have to do now to
keep it moving across the floor at a constant speed? Push with a
force strength less than, equal to, or greater than the frictional force
resisting the movement of the sofa? This time, write a scientific
Explanation: Why does the sofa move across the floor at a
constant speed?
Describe the Situation using a diagram: (Draw a force diagram for the sofa
while it is moving across the floor at a constant speed.)
Write the narrative: (Use the idea you developed in this activity about
motion at a constant speed to explain why you think the strength of your
push should be equal to or greater than the frictional force.)
CF-23
Unit CF
S6: You have seen that once an object is moving, if absolutely no forces act
on it, it will continue to move at a constant speed. However, based on
their real-world experiences, many people hold the idea that a
continuous constant force is needed in order to maintain a constant
speed. Why do you think this is such a common idea? (Hint: Think
about what you have learned in this activity about motion at a constant
speed, together with the forces that act on an object when you push it in
the real world.)
Newton’s First Law of Motion
You have already seen Newton’s Second Law of Motion, which tells us how
the rate of change of speed of an object is related to the strength of the net
force acting on it.
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From this, you can see that if the strength of the net force acting on an object
is exactly zero, then the rate of change of its speed will also be zero,
regardless of its mass. A rate of change of zero means that the speed will not
change, so the object’s speed will remain constant. This is the situation when
the forces acting on an object are exactly balanced, so the idea you developed
in this activity makes sense in terms of Newton’s Second Law.
However, Newton thought that this idea was so important that he made it a
‘Law’ on its own, which we call Newton’s First Law of Motion. Using our
terminology, we can state this law as:
“When the forces acting on an object are balanced, its speed (and direction)
will remain constant.”
Hopefully, it is evident that this applies equally to a situation in which no
forces act on an object, because that is just the simplest case of a ‘balanced’
combination of forces. (Just like a single force is the simplest case of an
‘unbalanced’ combination of forces.)
CF-24
UNIT CF
Developing Ideas
ACTIVITY 3: Comparing Forces during
Interactions
Purpose
In all previous activities in this module you have used ideas about forces to
examine what happens to only one of the objects involved in a contact
push/pull interaction. For example, when a
stationary low-friction cart is given a push,
we say a force is applied to the cart and the
effect of this force is to start the cart
moving. However, there is another object
involved – the hand! Does the cart also
exert a force on the hand while they interact? If so, how do these forces
compare?
In this activity you will examine the forces that two objects exert on each
other during a contact push/pull interaction between them, to see if there is a
general rule that can be applied to any such situation.
When two objects interact in a contact
push/pull interaction, how do the forces they
exert on each other compare?
Initial Ideas
A small, empty, pick-up truck
and a large, fully loaded, box van
are about to collide. The box van
has a greater mass, but the pickup has a higher speed. What
forces do you think they will exert on each other while they are colliding, and
how do you think those forces will compare?
During the short period of the collision, do you think both vehicles will
apply a force to the other? How would you know if they did?
CF-25
Unit CF
How do you think these forces would compare? To show your thinking,
use the pictures below to draw two separate force diagrams, one for
each of the two vehicles at a moment in time during the collision.
Briefly explain why you drew any force arrows as you did.
!
Draw your two force diagrams on a presentation board and participate
in a class discussion about your ideas. Make a note of any ideas or
reasoning that differs from those of your group.
Collecting and Interpreting Evidence
Exploration #1: Do both objects in an interaction apply forces?
You will need:
2 low friction carts (share with another group if necessary)
STEP 1. Place both carts at rest on the track about 50 cm apart. Give one
(Cart A) a quick
push toward the
other (Cart B) and
let them collide.
Describe what happens to both carts during the collision.
CF-26
Activity 3: Comparing Forces during Interactions
Did a force act on Cart A during the collision? What is about the motion
Did a force act on Cart B during the collision? What is about the motion
Did the forces applied to each cart (one on each) both act in the same
direction, or in opposite directions? How do you know?
Draw speed and force arrows (with appropriate labels) on the pictures
of the two carts below to show the forces they applied to each other for a
moment in time during the brief period that they are in contact with
each other. (Only the directions of the forces are important, we will deal
with the relative force strengths in the rest of the activity.)
Explain how your diagrams are consistent with the observation that,
during the collision, Cart A decreased in speed, while at the same time
Cart B increased in speed.
CF-27
Unit CF
Exploration #2: How do the forces applied to each other by objects at
rest compare?
You will need:
(Optional) 2 force plates (you may have to work with another group), and
instructions for set up and use
STEP 1. In a football game, very often players
from opposite teams will block by pushing on
each other in opposite directions, while neither of
them moves.
When two people apply forces to each other in this way, which person
do you think will exert the stronger force on the other, or will the forces
be equal in strength? Briefly explain your thinking.
STEP 2. Your thinking can be checked using
devices called force plates to measure the
forces people apply as they push against
each other. The plates are rather like
bathroom scales, but can be connected to a
computer to measure the force being applied
to them. If the equipment is available to you,
your instructor will give you a separate
sheet on how to set it up and use it.
If you do not have the equipment, you should watch UCF-A3 - Movie 1,
which shows the same experiments being performed.
The forces with which people push on each other will be measured by having
two people each hold a force plate vertically, and push them against each
other, without either of them moving. Note that in order to be able to tell
them apart, one person’s force strength will register as a positive value, while
the other person’s force will register as a negative value.
CF-28
Activity 3: Comparing Forces during Interactions
By using the equipment, or noting what happens in the movie, answer the
following questions.
When different pairs of people pushed on each other, how did the
relative force strengths compare? (Remember, you are comparing the
strengths of the two forces exerted between each pair of people, not from
one pair to the next.)
Did the relative masses of the two people involved make a difference as
to who exerted the stronger force?
Did it make a difference as to who exerted the stronger force whether a
person was actively pushing, or just ‘resisting’?
Exploration #3: How do the forces applied to each other compare when
two objects collide?
You will need:
(Optional) 2 carts, track, 2 force probes, metal blocks
STEP 1: In Exploration #2 the interacting objects (people with force plates)
were not moving, but would the results be different if one or both of the
objects were moving when they interacted? What if the colliding objects had
different masses?
To investigate this question, in this experiment you will examine the forces
that two colliding carts exert on each other.
CF-29
Unit CF
When two objects of different masses, moving at different speeds, collide
together, which do you think will apply the stronger force to the other,
or will they both be the same strength?
Which do you think will be the most important factor, mass or speed, or
will neither of them matter?
STEP 2. Your thinking can be checked using force sensors to measure the
forces involved in a collision between two carts. If the equipment is available
to you, your instructor will give you a separate sheet on how to set it up and
use it. If you do not have the equipment, you should watch UCF-A3 - Movie
2, which shows the same experiments being performed.
By using the equipment, or noting what happens in the movie, try to answer
the following questions.
When two carts with the same mass collide with each other, how do the
forces they exert on each other compare? Does it matter what their
motion is like before the collision?
When two carts with different masses collide with each other, how do
the forces they exert on each other compare? Does it matter what their
motion is like before the collision?
CF-30
Activity 3: Comparing Forces during Interactions
Exploration #4: How do the forces applied to each other compare when
one object pushes another continuously?
You will need:
Computer with internet connection
STEP 1. Finally, we will consider the case of one object
pushing another continuously, so that they move
along together.
For example, when you push a loaded shopping cart
around the store, how does the force it exerts on you
compare to the force you are exerting on it?
In this situation do you think you always exert a stronger force on the
shopping cart than it exerts on you, or would it depend on whether the
speed is changing or is constant, or would the relative force strengths be
equal? Why do you think so?
STEP 2. Watch UCF-A3 – Movie 3 in which a fan cart pushes another cart
along a track. The strengths of the forces that the carts exert on each other are
measured using force sensors. This will be done both while the carts are
increasing speed and also while they are moving at a constant speed.
In both cases, how did the relative force strengths compare? Were they
very different or about the same?
Summarizing Questions
S1. For each of the situations you explored in this lesson, how did the
strength and direction of the force that one object exerts on the other
during an interaction compare with that of the force that the second
CF-31
Unit CF
object exerts on the first? Did any factors, such as relative mass or relative
speed, seem to make a difference to the results?
S2: A man pushes a crate across the floor
by applying a 135 N force to it. As a
result, the crate gradually increases in
speed as it moves. What is the strength
of the force that the crate applies to the
man, less than, equal to, or greater than 135 N? Explain how you know.
S3: Now reconsider the situation from the Initial Ideas section of this activity,
in which pick-up truck and box van collide. The box van has the greater
mass, but the pick-up has a higher speed. How would the forces they
exert on each other during the collision compare?
a) To show your thinking, use the pictures below to draw separate force
diagrams for each vehicle during the collision. Briefly explain your
diagrams.
b) Why does the collision have a greater effect on the pick-up truck than
it does on the box van? (Hint Consider what you have learned about
what determines the effect a force has on object of a particular mass.)
CF-32
Activity 3: Comparing Forces during Interactions
Newton’s Third Law
The idea you have been developing in this activity was first proposed by Sir
Isaac Newton and is now known as Newton’s Third Law. It can be stated as:
If Object A exerts a force on Object B, then Object B exerts a force on
Object A that is equal in strength and opposite in direction.
(However, Newton originally stated this idea in a way you may be more
familiar with: “To every action there is an equal an opposite reaction.” Note that
to Newton the words ‘action’ and ‘reaction’ referred specifically to what we
now call forces.)
It is important to realize that this law does not allow us to say what the actual
strength of this pair of forces is, just that they will always have the same
strength, no matter what the details of a particular situation are.
Thus, during any contact push/pull interaction, there are two equal strength
forces involved, only one of which acts on each object involved. We will call
these two forces an interaction pair. For example, in a collision between two
carts (A and B) the interaction pair of forces would be represented on two
force diagrams as shown below.
Force exerted on
Cart A by Cart B
Cart A
Force exerted on
Cart B by Cart A
Cart B
It is important to realize that these two forces act on two separate objects, one
on each cart. Thus, when considering what effect such an interaction has on
the objects, for each object we consider only one force. (For example, if you
want to know what happens to Cart A, you could cover the diagram for Cart
B with your hand and only look at the diagram for Cart A, and vice versa.)
CF-33
Unit CF
Interaction Pairs are NOT Balanced Forces
It is important not to confuse an interaction pair of forces with what we have
come to call balanced forces.
In an interaction pair, there are always ever only two objects involved and
one force acts on each of them separately. For example, imagine pushing a
You know that you are exerting a
force on the cart, but Newton’s
Third Law tells us that the cart is
also exerting a force on you. It is
this pair of forces that is an
interaction pair and they are
always
equal
in
strength,
regardless of whether the objects
involved are changing speed or not.
Interaction pairs of forces act on two
separate objects
However, when we refer to balanced forces we are referring to two or more
forces that all act on the same object. For example if the grocery cart is
moving at a constant speed, then the forward force exerted on it by you and
the backward frictional force exerted on it by the ground are exactly equal in
strength and we say the forces acting on
the cart are balanced.
Note that, while these two forces have
the same strength under these particular
circumstances (the speed is constant), it
does not always have to be so. For
example, if the cart were increasing in
Balanced forces act on the
speed these two forces would not be equal
same object
in strength. (Indeed, it would be this
unbalanced combination of forces that would cause the cart’s speed to
increase.)
CF-34
UNIT CF
Applying Ideas
ACTIVITY 4: Explaining Phenomena using
Force Ideas
During this module you have developed ideas about how the forces acting on
an object affect its motion. By now the class should have reached consensus
on a model of how the motion of an object is determine by the forces that are
being applied to it. Your instructor may make a summary of the ideas
developed by the class available to you. You will likely find that these ideas
are very similar to those developed by scientists and summarized in
Newton’s three Laws of Motion.
Explanations using force ideas
In this module you have already been practicing writing and evaluating
explanations using your developing model of force and motion. In this
activity you will apply the class consensus model to explain some more
‘everyday’ phenomena.
Remember, to construct a scientific explanation using ideas about forces you
should first draw one or more force diagrams that show all the relevant forces
acting on the object of interest at particular moments in time, and also a speed
arrow, if it is relevant. When writing your narrative, you should keep in mind
that it should satisfy the usual criteria:
•
should be clear and easy to read and your narrative should be well
written and easy to follow. Also, the diagrams and narrative should be
consistent with each other. Your explanation should be relevant and
focus on the phenomenon that is to be explained. (For example, a cart
may have been given a push to get it started but you are asked to
explain something that happened after the push! In this case it would
be OK to mention that the push got it started but this need not be
explained in detail.)
•
Your explanation should be accurate. The narrative should use one or
more relevant ideas that are consistent with those we have established
from the evidence gathered in class. (In other words they should be
consistent with Newton’s Laws.)
CF-35
Unit CF
•
Your explanation should be well reasoned. Reasons should be given
for why the event happened as it did in terms of the force(s) acting on
the object. Usually this would be based around a relevant general
statement (big idea) about the connection between force and motion.
For example, ‘When a single force acts on a moving object in the same
direction as its motion, its speed will increase.’ However, you should
also take care to establish why this ‘big idea’ is relevant for this
particular situation.
Role of Friction
It is also very important to state explicitly in your narrative if you are taking
the effects of friction to be negligible (too small to make a significant
difference). This may be the case if you are dealing with situations that
involve a vehicle with well-lubricated wheels or an object sliding across a
very smooth surface (such as ice), especially if other forces acting on the
object are much stronger than any friction forces. For example, when pushing
a low-friction cart with your hand you might include a statement such as:
“We can ignore the effects of friction because the force of the hand is much stronger
than the very weak frictional force acting on the cart.”
However, if you decide the effects of friction are not negligible, then the force
of friction should play a part in the explanation. For example, if the task is to
explain why a soccer ball decreases in speed as it rolls across the grass, then it
is a frictional force that is responsible for this behavior and so it cannot be
ignored.
Your first task is to evaluate some explanations written by previous students.
Explaining the motion of an ice-hockey puck
After a hockey player gives a puck a quick ‘hit’ with his stick, the puck slides
across the ice, decreasing in speed very gradually. (Note: this could also
apply to a well-lubricated cart that is given a quick shove along the track!)
Some students in a previous class offered the following force diagrams and
explanations for this behavior in terms of the forces acting on the puck.
CF-36
Activity 4: Explaining Phenomena using Force Ideas
Explanation #1: Why does the puck gradually slow down as it moves
across the ice?
Here are three different students’ force diagrams for the puck.
Student A
Student B
Student C
Force of
Force of
Force of
stick
friction
friction
decreasing
force of stick
Which of these force diagrams do you think would be most appropriate
to use in this explanation? Explain your thinking.
Here are three different students’ narratives for this explanation.
Student D
Student E
The initial hit is what starts
After
the puck moving. After the
contact with the puck, only a
between them, the force of
frictional force acts on it, so
the stick was transferred to
because no forces are acting
it slows down.
on it.
the
stick
has
Student F
lost
During
the
interaction
runs out as it moves. Because
the force pushing it forward
speed decreases.
Each of these is problematic in at least one way. Work with your group
to identify the problems.
Student D:
CF-37
Unit CF
Student E:
Student F:
based on the force diagram you chose on the previous page.
!
Participate in a class discussion about these explanations and make any
notes you think necessary.
Taxiing a Plane
When taxiing a plane around an airport (before takeoff or after landing) the
pilots use the engines to push the plane along the ground. (The engines work
in the same way that the fan units push on the carts you have used.) When
the aircraft is standing still, with the engines running slowly, the pilot
increases the power of the engines to start the plane moving, but when the
plane reaches the desired taxiing speed, he reduces the engine power again
(but not to zero.) Why is this? (If you have never noticed this, next time you
are on a plane listen to the engine noise while it is taxiing along level ground.)
Your task is to explain why the pilot reduces the engine power once the plane
has reached the desired taxiing speed. Answering the following questions
Do you think a frictional force plays a significant role in this situation or
CF-38
Activity 4: Explaining Phenomena using Force Ideas
To start the plane moving and make it speed up, do the forces acting on
it need to be balanced or unbalanced?
Once the speed of the plane has increased to the desired taxiing speed,
to maintain that speed do the forces acting on it need to be balanced or
unbalanced?
force needed to start the plane moving and increase its speed, versus the
force strength needed to maintain a constant speed?
Explanation #2: Why does the pilot reduce the engine power when the
plane has reached the desired taxiing speed?
Represent the situation using a diagram:
(Draw two separate force diagrams, one while the plane is increasing speed,
the other while it is taxiing at a constant speed.)
Write the narrative:
(Remember to connect the ideas about forces you use to the actual question
CF-39
Unit CF
Why does the bug get ‘squished’?
As you are driving down the highway, you hit a bug with your windshield.
How can you explain that the bug suffers more ’damage’ than your car does?
Explanation #3: When a bug hits the windshield of a moving car why
does the bug get ‘squished’ while the car suffers no significant damage?
To answer this question, assume your windshield exerts a force of 1 N on the
bug in the direction that the car is moving. What is the strength and direction
of the force that the bug exerts on the car? Why does the bug suffer more
‘damage’ than the car does?
Representing the model using diagrams: (Draw separate force diagrams for
both the car and the bug during the collision between them.)
Write the narrative: (Explain your reasoning about the forces acting on the
car and the bug and why this results in much more damage to the bug!)
CF-40
Activity 4: Explaining Phenomena using Force Ideas
You are the expert witness
You will need
Low-friction cart and track
Small block (to represent a case)
A passenger is suing a bus
company for injuries she claims
were sustained when the bus had
to brake sharply to avoid hitting
The passenger was seated in the row of seats
behind the luggage rack. She claims that when
the driver braked sharply, this caused a case to
fly backwards off a luggage rack in front of her
and hit her head. As an expert in Newton’s
Laws you have been called to testify whether
this story is credible or not.
As part of your testimony you will do a live demonstration in the courtroom,
but you need to practice it and explain the results before you ‘take the stand’.
Use the small block to represent the case and
the top of the cart to represent the luggage rack
in the bus. Devise a way to demonstrate what
happens to the case when it is in the middle of
the luggage rack at the moment the bus stops
suddenly.
Describe how you will conduct your courtroom demonstration.
CF-41
Unit CF
When you perform your demonstration, what happens to the block
DURING the very short period of time that the cart is coming to a stop?
Does this support or refute the passenger’s claim?
It is possible that someone in the court will ask you some questions about
your demonstration similar to those below. Use ideas that connect force and
When an object is already moving, what is needed to make it slow
quickly and stop?
When you have two objects moving together (like the cart and the block)
what would happen if a strong force acted on one of them in the
opposite direction to its motion, but no such force acted on the other?
Did a strong force act on the cart to slow and stop it quickly? If so, how
was that force exerted on the cart?
During the very short period of time while the cart was stopping
suddenly, did a strong force also act on the block to slow and stop it? If
so, what object exerted that force on the block? If no such force acted on
the block, what would happen to its speed?
CF-42
Activity 4: Explaining Phenomena using Force Ideas
Lawyers sometimes try to clarify/summarize a witness’s statements for the
benefit of the jury. Suppose two lawyers said the following to you in court.
Lawyer 1: “So what you are saying is that a ‘backward’ force acts on the cart so it
stops moving, but as it does so a ‘forward’ force also acts on the block so it is
pushed to the front of the cart.”
Lawyer 2: “I disagree with my colleague. I think that what you are saying is that
a ‘backward’ force acts on the cart, but no force acts on the block so it just keeps
moving forward at the same speed while the cart stops.”
Which lawyer do you agree with, or neither of them?
Finally, the block does stop when it reaches the front lip of the already
stopped cart.
Why is it that the block now stops, rather than stopping at the same time
as the cart?
Finally, you should write a scientific explanation for why the case would slide
forward, not backward, when the bus stopped suddenly. Copies of this
explanation will be given to the jury who must decide the case.
First think about the case and the bus separately, drawing separate force diagrams for
each. Then combine your ideas in the written narrative to answer the question.
Explanation #4: Why would the case slide toward the front of the bus
when the bus is stopped suddenly?
Represent the situation using a diagram:
(On the next page, draw two separate force diagrams, one for the case and
one for the bus, for the same moment in time while the bus is in the process
of stopping but before the case hit anything in front of it.)
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Unit CF
Bus:
Case:
Write the narrative:
(Use general ideas about the connection between the forces acting on an
object and its motion to explain why the bus and the case behave as they do.)
Suggest some circumstance under which the passenger’s claim might be
credible? Briefly explain why.
Participate in a class discussion about all these explanations.
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UNIT CF
Engineering Design
ACTIVITY 5: Inspiration from Nature
The Whirligig Challenge
Landing a spacecraft on another planet is not a simple procedure. To see how
complex it can be watch UCF-A5 – Movie 1 (a 5-minute NASA video “Seven
Minutes of Terror”) which describes how engineers designed the landing
sequence for the robotic spacecraft that landed the Curiosity rover on Mars in
August of 2012. In this activity you will design an alternative landing
mechanism for a robot spacecraft that is to land on another world.
For a source of creative ideas, engineers often turn to biomimetics—the
practice of studying natural systems in order to solve engineering problems.
Activities involving biomimetics provides opportunities to learn biology,
physics, and engineering at the same time.
The Whirligig
The Whirligig is an excellent example of biomimetics, since its function is
similar to a maple seed.
The “Whirligig” (left) is an example of biomimetics. Images by Cary Sneider
Watch UCF-A5 – Movie 2 to see how maple seeds act as tiny helicopters,
enabling them to drop slowly to the ground, often some distance away from
their parent tree.
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Unit CF
The Challenge
Imagine you are part of a team of scientists and engineers that are planning to
land a robot craft on Titan, a moon of Saturn that has a dense atmosphere (the
surface air pressure is about 50% greater than Earth’s).
Since Titan has a dense atmosphere, the team has decided that a whirligig
type mechanism would be a good way to land the craft. However, some team
members are worried that, with the current design, the craft will still be
traveling too quickly when it lands, damaging the onboard computer. Your
job is to improve the current model of the craft (whirligig), by changing its
shape so that it falls more slowly, but stays upright as it falls. Because of an
upcoming team meeting you have 30 minutes to improve the model design to
everyone’s satisfaction, using only paper, scissors, paperclips, a ruler, and a
stopwatch.
Recall that the engineering design process can be broken into three stages:
1. Define the problem, goals, and constraints
Problem:
Describe the problem are you trying to solve. (Note that your team has already
chosen to use a whirligig mechanism, so your problem statement should
address that mechanism, not whether to choose any other way to do it.)
Goals:
How will you know if your redesigned whirligig system is successful?
Constraints:
What are the limitations you will place on your redesign?
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Engineering Design: Inspiration from Nature
2. Develop solutions
Start by making a whirligig as currently designed. Use the diagram on the
last page of this activity. Cut along solid lines and fold along dotted lines.
Bend the “wings” in opposite directions. Add a paperclip at the bottom if
needed for stability.
Drop your whirligig and note how it behaves.
Suggest at least two changes to the design you think might solve the problem.
and use them to plan and carry out an investigation to determine which
model best solves the problem. Be sure that your investigation is a fair test of
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Unit CF
Draw force diagrams for the original model and for your ‘best’ model as they
are falling. Using these diagrams write a brief explanation for why your ‘best’
model functions differently from the original design.
3. Optimize the most promising solution
Consider the explanations and evidence provided by all of the teams in your
class to determine a model that best solves the problem. (This could
incorporate more than one change from the original design!)
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Engineering Design: Inspiration from Nature
What’s the physics?
This particular problem could have been addressed using a ‘trial and error’
approach. However, it is important for engineers to understand the scientific
principles behind their designs in order to know what changes are likely to
have the desired effect. Understanding of the Whirligig Challenge involves
analyzing the forces acting on the whirligig after it is dropped.
After it is dropped, the only forces acting on a whirligig are the gravitational
force of the Earth pulling it downward and a drag force (air resistance)
opposing its motion.
Immediately after it is released, for a short period of time the speed of the
whirligig increases. What does that tell you about which of the two forces
acting on it is stronger during this period? Explain how you know.
The strength of the drag force acting on the whirligig depends on its speed.
This means that as its speed increases, the strength of this force increases.
However, after increasing in speed for a short period, the whirligig falls the
rest of the way at a constant speed (called its ‘terminal velocity’). What does
that tell you about the strengths of the two forces acting on it now? Explain
how you know.
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Unit CF
Assuming your ‘best’ model fell more slowly, this means its terminal velocity
was lower than that of the original model. This, in turn, means that the forces
acting on your ‘best’ model must have become balanced more quickly after
being released. What was it about your redesign that you think was
responsible for this?
In your experiments the effect of the drag force was to stop the speed of the
whirligig increasing beyond at certain value (its terminal velocity). However,
when the spacecraft enters the atmosphere of Titan it will likely be very going
very fast, much faster than its terminal velocity. The effect of the drag force
on the whirligig will then be to actually slow it down as it falls. Explain why
this happens.
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Engineering Design: Inspiration from Nature
Science Meets Engineering in the NGSS
One of the most radical features of new science standards being adopted in
many states is the idea that engineering design should be taught at the same
level as science inquiry. However, that does not mean commonly presented
activities such as bridge building and egg drop contests necessarily qualify.
To meet Next Generation Science Standards, it is important that the
engineering design activities be supported by science concepts.
The Whirligig Challenge is designed to provide the kinds of experiences that
students will need to achieve two performance expectations at the middle
school level in the NGSS:
Motion and Stability: Forces and Actions MS-PS2-2. Plan an
investigation to provide evidence that the change in an object’s motion
depends on the sum of the forces on the object and the mass of the
object.
Engineering Design: MS-ETS1-4. Develop a model to generate data for
iterative testing and modification of a proposed object, tool, or process
such that an optimal design is achieved.
There are many versions of this activity on the Internet. It requires very few
materials, engages students in engineering design, and is a lot of fun for
upper elementary and middle school students. Engaging students in such
activities helps them deepen their learning of science concepts, models, and
theories, while providing opportunities for them to be creative, leading to
increased enjoyment, interest, and for some at least, motivation to continue
learning science and engineering, and considering a career in a STEM field.
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Unit CF
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