Download Rolling downhill - Net Start Class

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ACTIVITY 7
Rolling downhill
M AT E R I A L S
What happens to the velocity of a ball while it is rolling down a hill,
instead of along a level track? Does its velocity change? Can you predict
how it changes?
For each group of 4 students
OV E RV I E W
A ball rolls down an incline. As it does so, its velocity changes. This
activity introduces the concept of acceleration. By measuring the
average speed of a ball rolling on an incline, students discover that the
ball’s velocity increases with time; the longer it’s on the hill the faster it
goes. Some students, who are ready to grasp proportional relationships,
will see that when the slope is constant, the rate of change of velocity
(the acceleration) is also constant. Graphs again are an effective way to
describe motion and changes in motion.
1 or more copies Student
Activity Sheet 7, Rolling
downhill
1 long ramp system (see
Appendix, item A-IV for
assembly) including:
1 tripod base (A)
1 half-meter stick
1 height marker (B)
1 support bar (C)
1 ramp box (E)
2 tracks
Students will:
1 large metal ball (3/4" diameter, approx. 2 cm)
• time a rolling ball over various distances on a ramp
1 measuring tape or meter stick
1 stopwatch
• calculate average velocity for four different segments of the ramp
2 sticky arrows or masking
tape
• graph velocity vs. time
(optional) for opening
demonstration: tennis ball,
2 one-meter sticks*
• discover a relationship between velocity and how long the object
has been accelerated
• interpret graphs of a variety of motions
* not in kit
TIME
2 (50-minute) class periods
This includes time for whole-class discussion on graphs at the
conclusion of the activity. Some teachers allow more than two class
periods to maximize the benefits of in-depth discussions and longer
reflection time for students.
B
C
FIGURE 7.1
E
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S C I E N C E B A C KG R O U N D
The physics of changing velocity. When velocity is not constant in time,
we say that acceleration is taking place. The quantitative definition of
acceleration is:
acceleration = (final velocity 2 initial velocity) / elapsed time
Acceleration is the rate of change of velocity; it’s an
indication of how quickly or slowly velocity is changing.
Like velocity, acceleration has a direction as well as a size.
Here are some examples:
before it
hits floor
after it
hits floor
• As a subway car pulls away from the station, its forward
speed is increasing. Its initial velocity is zero, and so the
car is accelerating forward. If it changes speed in a short
time, the acceleration is large.
• As a tired runner finishes the race and gradually slows
down, her forward speed is decreasing. Her forward
acceleration is negative; or we could say that the runner
is accelerating backward.
v
v
• When a basketball bounces off the floor, the direction of
motion changes from down to up. Even though the speed
might not change, there is a change in velocity that is
directed away from the floor (up). The bounce doesn’t
take very long, and so the acceleration is huge; it is also
upward.
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FIGURE 7.2
• A falling object accelerates downward. In each successive
interval of 0.1 second its speed is greater.
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When the direction of motion
changes suddenly, there is a
large acceleration, even if
speed stays constant.
0.0
0.2
Meters
Acceleration of falling objects. We all have a lot of experience with acceleration. A falling object is an interesting
special case, because the acceleration is constant—it’s
constantly increasing its speed.
Figure 7.3 shows how a ball falls. The black circles
represent the ball’s position every tenth of a second,
starting at 0 sec when it’s released. The positions cluster
together at the beginning, but then get farther and farther apart as it continues to accelerate. The light gray
circle shows where the ball would be after only half a
second—it has dropped more than a meter!
change in
velocity
0.4
0.6
0.8
FIGURE 7.3
1.0
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The black dots
show the position
of a falling object
every 1/10 second.
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Figure 7.4 graphs the motion of a ball
dropping about 5 meters straight down. It
takes only 1 second to fall about 5 meters.
4
The next graph, figure 7.5, shows a
ball’s motion when you throw it up in
3
the air nearly 5 meters, and then watch
it fall. The second half of this graph is
exactly like the one we just looked at in
2
figure 7.4. On the first half of the graph,
however, when the ball is on the way up,
it travels a smaller distance in each suc1
cessive time interval. It is slowing down.
On both parts of the ball’s trip, it is
accelerating downward. When its veloc0
0.5
ity is upward, the speed is decreasing;
Time (seconds)
when its velocity is downward, the
speed is increasing.
Unfortunately, the acceleration of a falling object is too large for us to
be able to study it with meter sticks and stopwatches. Your classroom ceiling is most likely less than 5 m (16 feet) high, and according to figure 7.4,
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FIGURE 7.4
Height (meters)
Falling objects
go farther in
each successive
time interval.
1
5
Height (meters)
4
3
FIGURE 7.5
2
When the ball is
moving upward, its
speed is decreasing;
as it moves downward, its speed is
increasing.
1
0.5
1.0
Time (seconds)
1.5
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any ball-dropping experiment you can do in the classroom would be over
in less than a second, which can’t be timed accurately with a stopwatch.
Although photogates or other kinds of electronic timers do get informative data with objects that fall only a few meters, we will, instead, study
a ball rolling on a slightly inclined track. It accelerates much more
slowly, enough so that we can measure it with a stopwatch.
This activity does not directly measure the acceleration, because all
we know is the average speed, which necessarily is less than the final
speed. Dividing the average speed by the time on the ramp gives an
2.0
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Calculating acceleration. Students are not asked to calculate acceleration in this module, but background information on how to do those calculations, and about the units of acceleration, is on the CD.
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“acceleration” that is too small by a factor of 2. The data will show, however, that the average velocity increases in proportion to the time on the
ramp, which implies that the acceleration is constant.
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FIGURE 7.6
In uniform motion,
an object travels equal
distances in equal time
intervals.
40 cm
0
40 cm
40 cm
1.0
0.5
1.5
SCIENCE IN EVERYDAY LIFE. A car has a pedal called “the
accelerator.” You “step on the gas” to go faster. A car, however,
is not quite an isolated system, especially at high speeds where
0 0.5
it becomes hard to push the air out of the way fast enough, at
which point “put the pedal to the metal” just means go fast,
rather than accelerate constantly. Much more consistently we
could call the brake pedal “the decelerator.”
A practical application of acceleration is in the timing of your tennis
serve. The ball should be thrown upward so that its highest point is right
at the height where you can hit it, because that point is where it is moving
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Visualizing motion. Let’s compare visualizations of accelerated motion
and uniform motion for systems like the ones you are using in these
activities. Figure 7.6, which was also in the introduction to Activity 5,
represents uniform motion. It shows the ball at fixed time
intervals (every 0.5 second). Unlike the accelerating falling
ball in figures 7.4 and 7.5, the uniformly moving ball covered
equal distances in each time interval. In the present activity
students will measure accelerated motion on an incline, as
shown in figure 7.7. Again the ball is shown at equal time
intervals (every 0.5 sec), but it covers more distance for each
successive interval. Accelerated motion is not uniform motion.
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Time (seconds)
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1.0
1.5
Time (seconds)
FIGURE 7.7
In accelerated motion,
an object covers different
distances in each equal
time intervals.
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1.5
height (meters)
its slowest. As shown in figure 7.8, the ball spends 0.2
seconds within 5 cm of the turn-around point—plenty of
time to hit it. Throwing the ball too high sends it through
the target region faster, and now you must time your
swing more precisely.
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1.0
0.5
G E T T I N G R E A DY
The concluding discussion for this activity includes
0
several graphs for class interpretation. Look ahead
0.5
1.0
now to that discussion, and plan on devoting more
time (seconds)
time to it than you did for the conclusion of most of
FIGURE 7.8
the previous activities.
Hitting a tennis ball at the top of its
Five parts in your kit (in addition to two sections of track)
arc—where it is moving slowest—makes
make up the long ramp system. See Appendix A, Item A-IV
it easier to hit.
for complete assembly instructions. Notice that the two tracks
used in this activity are connected end to end to make the ramp. You
G L O S S A RY
will use no horizontal track. Figure 7.9 is the assembly diagram from the
acceleration
appendix. Students have used all but one of the pieces earlier. The new
item is a small box labelled ‘E’ that supports the joint between the two
balanced forces
tracks. The track clips nestle in between the posts on the box. Notice that
distance
the top surface of the box (the top is where the 4 prongs point up) has a
slight angle. This angle matches the ramp angle when the upper ramp
median
end is set at 6.5 cm.
position
Decide how you want to share the
setup instructions with your stuspeed, average speed
C
dents (from Appendix A, item AB
system
IV). They can be distributed in
print form to each group,
time
shown on the overhead projecuniform motion
tor, or described as part of
your activity introvelocity
duction for the class.
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taller side of box
faces uphill
FIGURE 7.9
FIGURE 7.10
Assembly of the long
ramp system
When properly placed, the support
box posts fit around the track joint
where the two track sections connect
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To have a constant acceleration to measure, it’s very important that the
inclines of the coupled track pieces are identical.
A
FIGURE 7.11
B
To ensure that the inclines of the two ramp pieces are the same, set
the height marker that supports the upper end of the higher track at
6.5 cm (be sure the half-meter stick is pushed all the way to the bottom
of the tripod). The bottom end of the lower track must rest on the tabletop and not hang over the edge. The joint between the two tracks is supported by the box that fits exactly at the joint. These conditions produce a
shallow and consistent incline angle that leads to good stopwatch data.
Your students will likely want to experiment with steeper slopes. This
can go on the question board for later open investigations, or on hold
until Activity 9 when they will specifically look at the effect that steepness of the slope has on acceleration.
As part of the concluding discussion you could include the visualizations comparing uniform to non-uniform motion (figures 7.6 and 7.7 on
page 110). These figures offer a different way to visualize the same
motions that students will be studying graphically. Showing this representation of uniform and non-uniform motion will be helpful for some
students, but may overload others.
I NTRODUCI NG TH E ACTIVITY
Ask students why we used the ramp in the previous activities. Possible
responses would be: “We wanted to get the ball going” or “It was speeding
up on the ramp.” When students start saying “speeding up” or “go faster,”
you can begin discussing the words accelerate, which means “to change
velocity,” and acceleration, which is the rate of change of velocity (how
quickly or slowly velocity changes).
Below are two optional demonstrations. Kept brief, these can help the
students shift from thinking about motion on a horizontal surface to
motion on an incline, without reproducing the investigation they will do.
In a place visible to the whole class, roll a tennis ball so that it moves
uniformly across a few meters of a horizontal surface. Ask the students to
tell you about the important features of its motion: Because it has constant speed and direction, it is moving uniformly.
Now make a shallow V-shaped ramp by grasping two meter sticks
side by side in one hand as shown in figure 7.12. Rest the bottom of
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A is correct; both ramp
sections have the same
incline. B is wrong; the
top half of the ramp is
steeper than the bottom
and the support box is
not at the joint.
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this V-ramp on the table, and hold the top of it only about 5 to 10 cm
above the tabletop. Release the tennis ball at the top, and let it roll
down the ramp. Ask the students how this motion is different. Is the
motion uniform? Apparently not, since the ball is not moving at the
very beginning and is moving later. What does happen after it starts
rolling? It’s hard to tell by just watching, and so let’s
study this in detail.
Distribute or show instructions to students for assembling the ramp
and ensuring that both of their ramp sections have the same incline.
DOI NG TH E ACTIVITY
Distribute materials and copies of Student Sheet 7, Rolling downhill, or
pose an open-inquiry alternative. As you move around the room observing and talking with individuals and groups while they work, ask them
to clarify what they are doing, what they see, and what they can conclude from it. Pose questions to help them solve any difficulties they
encounter, and to get them to probe the underlying concepts or discuss
how what they see connects with other things they have experienced.
Challenge them to think of other ideas that their investigations lead to.
Use the suggested responses below to guide student investigation and
discussion. Keep in mind that investigation, objective observation, and
ensuing scientific discussion are important to learning—as important as
the answers themselves.
This activity was designed for only a slight incline so that the timing
can be done with stopwatches.
What happens to the velocity when something is rolling down a
hill? You can investigate this question by timing a ball rolling
down the entire hill, and then timing it for shorter trips on only
part of the slope.
• Connect two track pieces together, and use them to make one
long ramp.
• Place the small ramp box under the joint between the two tracks.
Turn the box so that its taller side faces uphill. It should hold the
track prongs securely.
• Set the high end of the ramp at 6.5 cm.
• Make sure that the whole ramp has a uniform incline (no bend
in the middle).
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FIGURE 7.12
Making a V-ramp
using two meter sticks
SAFETY
Caution students to keep
control of the ball. If one
falls to the floor, immediately pick it up so that it
does not become a trip
hazard.
O P E N - I N Q U I RY
A LT E R N AT I V E
How does a ball’s velocity
change as it rolls down a
hill? Allow more time for
this option.
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Sketch figures 7.11 A and B in the “Getting Ready” section if you believe it
will help students set up the system correctly. Setting the top end of the
upper track at 6.5 cm and putting the ramp box at the joint between the
two ramp pieces ensures that the inclines are uniform.
Start ball and
timer here
Stop timing
here for table 1
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TEACH I NG TI P
Before students start their
data collection, make sure
that the ramps are set up
properly: ramp does not
extend over the edge of the
table, consistent incline (no
bend in the middle); no
jump or wobble of the ball
at the joint or on any part
of the ramp; and no movement or flexing of the track
while the ball is rolling.
A
FIGURE 7.13
1. Time how long it takes the ball to go the full length of the
ramp—from when you let it go at the top of the ramp to point A
at the bottom. Mark the starting point so you start the ball in the
same place each time. In table 1 record five good trials for the ball
rolling from start to point A. Measure and record the distance the
ball traveled. Enter the median time.
Table 1: Time and distance for ball to roll full length of slope
distance ball travels while
being timed (cm)
110 (the total length
of the ramp)
trial number
time (seconds)
1
2.57
2
2.47
3
2.43
4
2.54
5
2.50
median time:
2.50
The sticky arrows or masking tape are included in the materials list as
a way for students to mark their start and end points. Instructions for
doing this are minimal because students should already know from
Activity 5 how to do this and why.
Before collecting their data students should practice releasing the ball
and starting the stopwatch consistently. Their practice timing efforts
should not be recorded in the table. Data should not be entered in the
table until students can comfortably repeat their ball release and timing
so that the data is fairly consistent and not widely scattered.
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TEACH I NG TI P
Put a shallow box or lay a
book at the end of the track
just beyond measurement
range to stop the balls
before they fall off the table.
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2. Mark point B about three quarters of the way down the ramp.
Release the ball just as you did in Question 1, and time how long
it takes to go from start to B. Measure the distance from start to B.
Complete table 2.
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Make sure students always
use the same start point—
at the top of the ramp—
for Questions 1 through 4.
Always start the timer
when the ball is released.
Always do practice runs
before collecting data.
A
FIGURE 7.14
Table 2: Time and distance for ball to roll down three quarters of the slope
distance ball travels while
being timed (cm)
85
trial number
time
(seconds)
1
2.12
2
2.16
3
2.22
4
2.18
5
2.15
median time:
2.16
Choosing a different ending point (B in the figure) may confuse some
students. Help them understand that to study changes in velocity, we
need to time the ball for different parts of its trip down the ramp. In the
first table they timed it for the whole ramp. In this table they will time it
for a shorter distance, only about three quarters of the ramp. They get to
choose the point. It does not need to be exactly three quarters of the total
ramp; anything close to that is fine. However, it is important to measure
and record the distance they use.
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Stop timing
here for table 2
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3. Mark point C about halfway down the ramp, as shown in the figure. Time the ball’s trip from start to C. Complete table 3.
Stop timing
here for table 3
Start
C
B
A
FIGURE 7.15
Table 3: Time and distance for ball to roll down half of the slope
distance ball travels while
being timed (cm)
trial number
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time
(seconds)
1
1.75
2
1.75
3
1.71
4
1.87
5
1.72
median time:
1.75
4. Mark point D about one quarter of the way down the ramp from
the top. Time the ball’s trip from start to D. Complete table 4.
Start
Stop timing
here for table 4
D
C
B
A
FIGURE 7.16
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Table 4: Time and distance for ball to roll down the first quarter of the slope
distance ball travels while
being timed (cm)
15
trial number
time
(seconds)
1
1.35
2
1.38
3
1.22
4
1.34
5
1.28
median time:
1.34
5. Move your data for the distances and median times from tables 1
through 4 to the first two columns of table 5. Complete the last
column by calculating the velocity of the ball for each ramp
distance that you timed.
Table 5: Average velocity of ball rolling on a slope for different periods of time.
distance (cm)
median time (seconds)
average velocity (cm / sec)
110
2.50
44
85
2.16
39
54
1.75
31
30
1.34
22
0
0
0
Students will need to remember that dividing the distance traveled by
the time gives the average velocity over the run. The ball is speeding up
as it goes down the ramp, and so the final velocity is necessarily greater
than the average velocity. For the case of constant acceleration (velocity
increasing constantly with time, which it does in this case), the final
velocity is exactly twice the average velocity. If we were to calculate
acceleration, we would need the final velocity, rather than the average
velocity, but this is harder to determine experimentally. We’ve chosen
this simpler procedure (using average velocity) so that students can focus
on the concepts and not get mired in the process.
We added the (0,0) point because it is a legitimate data point; a part
of what happened. The ball is released and the watch started at the
same instant, and so at 0 seconds, it hasn’t gone anywhere and the
velocity is zero.
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6. Key question: Use table 5 to make a line graph of
average velocity vs. time. First you have to make the
scale for the vertical axis. Include the point (0,0) on
your graph, too. Make the line smooth, not jagged. It
does not have to touch each data point, but it should
go close to them.
Average velocity (cm/s)
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50
40
30
20
10
0
S U M M A RY
When the velocity of an object is changing, we say that it
is accelerating. If the velocity is increasing, the object is accelerating forward; if the velocity decreases, it is accelerating
backward, or decelerating.
7. Key question: From your graph what can you conclude about the
motion of a ball traveling on a slope?
The longer the ball is on the slope, the more its average velocity
increases. This means the ball is accelerating. The line is straight,
which means that the two variables—time on the slope and average
velocity—are clearly related.
If your students are ready, this is an excellent time to go into the proportional relationship implied by a linear graph. The average velocity is
increasing proportionally to how long the ball is rolling. This certainly
indicates that the actual velocity is increasing, too. In fact, the velocity at
any specific time is proportional to how long it has been rolling, which
means that the acceleration is constant.
CO N C L U D I N G T H E A C T I V I T Y
Question 7 includes the key concepts for this activity:
• Acceleration is a description of how velocity changes. In this activity,
there is acceleration because the speed changes.
• A ball on a slope accelerates: The longer the ball is on the slope the
faster it goes.
• This is different from a ball rolling on a level track, where it does not
speed up.
The fact that the average velocity is proportional to the time is
notable. It implies that acceleration is constant, and that the “instantaneous” velocity (the velocity at the particular time) is also proportional
to how long the ball has been accelerating.
It may be helpful to students if you draw sketches similar to figures 7.6
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1.0
2.0
Time (seconds)
3.0
FIGURE 7.17
Average velocity of a rolling
ball on a slope vs. time it
spends on the slope
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and 7.7, visualizations comparing uniform to non-uniform motion.
Transparencies 7.1 and 7.2 are graphs for students to interpret and discuss. They show a ball’s motion on ramps and level surfaces—accelerated
and uniform motion.
As you go through graphs A to F ask students to discuss how they
could set up the ball-and-track systems they have been working with to
produce each graph.
Then go through the graphs again and ask students to describe an
everyday situation that would produce each one.
Graph D: Distance vs. time for the
situation in Graph C.
As the ball moves faster and
faster, it can cover distances more
quickly, so this graph is not linear.
Graph E: Zero velocity for a period
of time means it’s not moving.
Then it starts speeding up linearly.
This could be a graph of a ball held
still on a ramp after the timer starts,
and then the ball is released and
accelerates.
Velocity
Time
0
Time
Distance
Graph C: The velocity is increasing
with time. The ball is accelerating.
This is what we just found for the
motion of a ball rolling down a ramp
in Activity 7, increasing in speed as
it goes.
0
0
Time
Velocity
Graph B: If you used the same data
from graph A but plotted distance
vs. time instead of velocity vs. time,
this is what it would look like. This
is the same data that made graph A.
As time increases, distance does too
at the same rate.
Distance
Velocity
Graph A: The velocity is not changing
with time—it’s constant; the ball is not
accelerating. This is what happens on
a level horizontal track.
Ask students what this same motion
0
Time
plotted as distance vs. time would look
like. Remind them that they made such a graph at the end of Activity 5.
That’s the next graph, B.
0
Time
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Question Board
The following are actual questions posed by students during this
activity. They are not for display but rather are examples of the
kinds of open-inquiry questions that students can generate and
then pursue through hands-on investigations.
• What if the ramp was not straight, and instead curved up?
• What if we put a piece of tape right down the middle of the ramp?
• What if we cover the ramp with a layer of tissue paper?
• Is there a maximum speed where acceleration stops?
Open-Inquiry Alternatives
Instead of using the printed student activity, provide the same investigative materials and allow students to experiment with these. As they
explore, ask them to develop and then pursue their own questions around
the topic, “How does a ball’s velocity change as it rolls down a hill?”
Other more specific questions offer a bit more guidance: What happens to the velocity of a ball while it is rolling down a hill? Does it
change? How do you measure and show the change? Is the amount that
it changes predictable?
To provide even more guidance, prompt students to “measure how
long it takes the ball to cover different lengths of a sloped track, and from
that calculate its velocity along different parts of the slope.”
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Time
D
Graph F: The ball accelerates for a period of time, and then the graph
shows acceleration stops because velocity is constant. This could be the
ball rolling down a ramp and then out onto a horizontal track.
An everyday version of this graph would be the motion of a car on a
city street. It starts from rest and speeds up until it is going at normal
traveling speed.
Imagine that it stays at constant speed until it gets to a stoplight. What
would the graph look like if it were extended to show the car slowing
down and stopping?
More graphs are on the CD.
Velocity
An everyday version of this would be the motion of a car at a stoplight:
It waits for the light to turn green, and then smoothly accelerates. It could
also describe an apple that hangs in the orchard until one day it drops
(now the direction of the velocity is down but we can still show the graph
going up because the velocity is increasing).
What would the distance vs. time graph look like for this motion? (It
would be much like Graph D but would start with a horizontal line for
the initial time period when it’s not moving.)
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EXTENSIONS
1. Describe your velocity, and its changes, when riding your bike
(or skateboard) on a level road, down a hill, and up a hill.
2. If we assume that the final velocity is twice the average velocity,
we can calculate the acceleration of the rolling ball from
acceleration = (final velocity — initial velocity) / time elapsed
4. Measure how long it takes for a car to get from a stop to 22 mph:
1 second, 5 seconds, or 20 seconds (assuming normal driving)?
Measure how much longer it takes to change speed to 45 mph.
And measure how much longer again it takes to get to 67 mph.
And then measure how long it takes to slow the car back down
from 67 mph to 45 mph, to 22 mph, and to a stop. Use the results
to calculate the acceleration of the car for these six cases (note: 22
mph is 10 meters per second; 45 mph is 20 meters per second;
and 67 mph is 30 meters per second). Finally, compare all of these
to the acceleration for a falling object 9.8 (meters per second) per
second.
5. Military aircraft and spacecraft can accelerate very fast. It
becomes important to know whether the pilot can stand accelerations of 1 g, 2 g, or 5 g (meaning, 1, 2, or 5 times the acceleration of a freely falling object). How do these numbers compare
with the accelerations we meet everyday, in elevators and cars?
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3. (For students ready to grasp the mathematical representations of
acceleration)
When an elevator starts to move up or down, it has to accelerate:
The velocity was zero, and now we want to go somewhere! But
the passengers will get upset if the acceleration is more than a
few meters per second per second. This limits how fast the elevator can be going after 10 seconds, and this in turn limits how far
the elevator can go in this time. Halfway to its destination, the
elevator must start slowing down again, too! So, about how far can
an elevator go in 20 seconds?
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The units for acceleration are “(meters per second) per second,” or
m/sec2. You can calculate the acceleration of a falling object the
same way, starting from the data gathered in Activity 1. The accelerations for the rolling ball and for the falling ball are very different.
Both are constant but the falling object accelerates more quickly.
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While the module does not address the idea of “g,” it is a logical extension
from the basics of acceleration we have just covered. One g is the acceleration on Earth of a freely falling object—about 10 (m/sec)/sec. An accelerating car cannot get from 0 to 10 m/sec (22 mph) in one second, so its
acceleration is much less than 10 (m/sec)/sec. One g is a panic stop
made by slamming on the brakes in a car. Half a g is running a car going
20 mph into a bush that brings it to a stop in 1 meter—not quite the
equivalent of running into a tree but close to it.
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STUDENT SHEET 7
Rolling downhill
What happens to the velocity of a ball while it is rolling down a hill instead of
along a level track? Does its velocity change? Can you predict how it changes?
M AT E R I A L S
1 long ramp system
1 tripod base (A)
1 half-meter stick
1 height marker (B)
1 support bar (C)
1 ramp box (E)
2 tracks
1 metal ball
1 measuring tape or meter stick
1 stopwatch
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2 sticky arrows or masking tape
What happens to the velocity when something is rolling down a hill? You
can investigate this question by timing a ball rolling down the entire hill,
and then timing it for shorter trips on only part of the slope.
• Connect two track pieces together, and use them to make one
long ramp.
• Place the ramp box under the joint between the two tracks. Turn
the box so that its taller side faces uphill. It should hold the track
prongs securely.
• Set the high end of the ramp at 6.5 cm.
• Make sure that the whole ramp has a uniform incline (no bend in
the middle).
Start ball and
timer here
Stop timing
here for table 1
A
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1. Time how long it takes the ball to go the full length of the ramp—
from when you let it go at the top of the ramp to point A at the bottom. Mark the starting point so that you start the ball in the same
place each time. In table 1 record five good trials for the ball rolling
from start to point A. Measure and record the distance the ball traveled. Enter the median time.
Table 1: Time and distance for ball to roll full length of slope
distance ball travels while
being timed (cm)
trial number
time
(seconds)
1
2
3
4
5
median time:
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2. Mark point B about three quarters of the way down the ramp.
Release the ball just as you did in Question 1, and time how long it
takes to go from start to B. Measure the distance from start to B.
Complete table 2.
Stop timing
here for table 2
Start
B
Table 2: Time and distance for ball to roll down three quarters of the slope
distance ball travels while
being timed (cm)
trial number
time
1
2
3
4
5
median time:
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(seconds)
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3. Mark point C about halfway down the ramp, as shown in the figure
above. Time the ball’s trip from start to C. Complete table 3.
Stop timing
here for table 3
Start
C
B
A
B
A
Table 3: Time and distance for ball to roll down half of the slope
distance ball travels while
being timed (cm)
trial number
time
(seconds)
1
2
3
4
5
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median time:
4. Mark point D about one quarter of the way down the ramp from the
top. Time the ball’s trip from start to D. Complete table 4.
Start
Stop timing
here for table 4
D
C
Table 4: Time and distance for ball to roll down the first quarter of the slope
distance ball travels while
being timed (cm)
trial number
time
1
2
3
4
5
median time:
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5. Move your data for the distances and median times from tables 1 to
4 to the first two columns of table 5. Complete the last column by
calculating the velocity of the ball for each of the four sloped ramp
distances that you timed.
Table 5: Average velocity of a ball rolling on a slope for different periods of time.
distance (cm)
median time (seconds)
average velocity (cm / sec)
0
0
0
6. Key question: Use table 5 to make a line graph of average velocity vs.
time. First you have to make the scale for the vertical axis. Include the
point (0,0) on your graph, too. Make the line smooth, not jagged. It
does not have to touch each data point, but it should go close to them.
Average velocity (cm/s)
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Average velocity of a rolling
ball on a slope vs. time it
spends on the slope
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30
20
10
0
1.0
2.0
Time (seconds)
3.0
S U M M A RY
When the velocity of an object is changing, we say that it is accelerating.
If the velocity is increasing, the object is accelerating forward; if the
speed decreases, it is accelerating backward, or decelerating.
7. Key question: From your graph what can you conclude about the
motion of a ball traveling on a slope?
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Distance
Velocity
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Velocity
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A.
Time
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C.
Time
0
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B.
Time
D.
Time
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Velocity
Velocity
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E.
Time
0
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F.
Time
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END OF SECTION
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