PHYS 1401 – General Physics I
Motion Diagrams and Uniform Motion
Leader:
___________________ Recorder:
__________________________
Skeptic:
___________________ Encourager:
________________________
Materials
Toy Tractor
Paper towel rolls
Stop Watch
Masking Tape
1 x Graph paper
Ruler
Introduction
This activity will introduce the basic
concepts of kinematics, the description of motion. You will construct motion
diagrams which show the position of an object after equal time intervals.
Note on Equipment Use:
The toy tractors will break if they are handled
roughly. Start and stop the tractor by
using the on/off switch only. In
particular do not force the tractor to remain stationary by holding it in place
as this can strip the gears or burn out the motor. Also do not let the tractor run off the
table. To preserve battery life, turn
off the tractor when not in use.
Uniform Motion
Procedure
Tape a piece of paper about 5 feet across
the top of your lab table. Turn on the
toy tractor and practice aiming it so that it runs along the piece of
paper. If necessary, you can place a
meter stick on the paper and have the tractor run next to it to keep it
straight. Once you’ve got the tractor
running along the track, make one run along the piece of paper while marking
the location of the tractor at 1 s intervals.
Turn off the tractor.
Q1) If you ran the
tractor completely across the table you should have made about 5 – 7 marks on
the paper. Describe the appearance of
the marks in terms of the spacing between them.
Q2) What does the
spacing between the marks tell you about the motion of the tractor?
D3) On the paper, place
an O next to the first mark that you made.
This will denote the origin of our coordinate system.
The position, x, records the location of the
tractor measured from the origin of
our coordinate system. We will take the first mark that we labeled as the
origin to be x = 0 m and t = 0 s. Use a
meter stick to determine the position in m at each corresponding time and
record the position and the time in the table on the report page.
D4) Fill in the
following table with the position and time for each mark made on the paper.
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Time
(s) |
Position
(m) |
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0 |
0 |
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The
piece of paper you have marked with the position of the object at equal time
intervals is called a motion diagram. We can use motion diagrams to indicate
different types of motion, although typically we will scale it to fit on a
page. In a motion diagram, the position
at each time interval is typically shown with a small circle.
Q5) Using a scale of 20 cm to 1 cm, make a scale
motion diagram of the motion of the toy tractor on the line below.
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The displacement is the change in position
in each time interval. The time interval is the amount of time
between each mark.
D6) Record the time interval, Δt = t2 – t1, between each
mark, and the displacement between each mark in the table below. Note that there is one row less in the table
since you need two successive points to determine a time interval and a
displacement. Also note, you do not have to measure
the distance between each mark to find the displacement. You can use the position data and simply
subtract the successive positions, Δx = x2
– x1.
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Time
Interval = Δt (s) |
Displacement (m) |
Average
Velocity = Δx /Δt (m/s) |
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Once
we have displacement and time interval data, we can find the average velocity of the tractor on each
time interval. The average velocity is
defined as vave = Δx/Δt.
D7) Fill in the
average velocity column in the data table above.
Q8) Based on your data,
would you say that speed of the tractor remained approximately constant during
the motion?
Q9) You should have
noticed that for this case the displacement and the average velocity columns
are identical numerically. What feature
of the design of the experiment makes this so?
Q10) Are Δx and vave the same physically? Explain.
Q11) How could you change
the experiment so that the coincidence of Δx and
vave being the same numerically would go
away?
Q12) If you made the
change to the experiment you answered in Q11) would you expect the value of Δx or vave to
change. Explain.
Q13) How would the
motion diagram you drew in Q5) change if the tractor traveled twice as fast?
Q14) How would the
motion diagram you drew in Q5) change if the tractor traveled half as fast?
The
change in velocity , Δv
= v2 – v1 represents how much the velocity changes in
each interval.
D15) Copy the time interval and Vave into the table below. Find the change in velocity for each time
interval and record in the table. Note
that the first row is left blank in this case since we must subtract two
successive velocities to obtain a change in velocity.
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Time
Interval = Δt (s) |
Average
Velocity = Δx /Δt (m/s) |
Change
in Velocity = Δv (m/s) |
Average
Acceleration = Δv
/Δt
(m/s/s) |
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The average acceleration is defined as aave = Δv/Δt. It is the rate at which velocity changes, in
other words it is how much the velocity changes per time
D16) Fill in
the last column in the table above with the average acceleration.
Q17) Is the average
acceleration approximately 0 in this case?
What does that say about the motion of the tractor?
D18) On the provided
graph paper construct a graph of Position vs. Time for the motion. Use the following guidelines for good graphs.
Please
note that graphs are always described by saying the y coordinate vs. the x
coordinate. So in this case position will be on the
y-axis and time will be on the x-axis. A
good graph should have the following features
i.
A descriptive title
ii. Each axis labeled
with the quantity it represents. The
units of measure should be included in parentheses following the label.
iii. Each axis should
have tick marks with values labeled
iv. The data should
fill the graph appropriately
Q19) Once guided the tractors
traveled in a straight line at constant speed, which is known as uniform motion. How would the motion diagram you drew in Q5)
change if the tractor was speeding up?
D20) Draw a motion diagram for an object which is
speeding up on the line below.
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Q21) How would the motion diagram that you
drew in Q5) change for an object that was slowing down?
D20) Draw a motion diagram for an object which is
slowing down on the line below.
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