PHYS 1405 –
Conceptual Physics I
Motion Diagrams
Materials
Bowling Ball
Paper Towels
Stop Watch
Tape
Meter stick
Introduction
This activity will introduce the basic
concepts of kinematics, the description of motion. You will construct a motion
diagram which shows the position of an object after equal time intervals.
Procedure
Tape a piece of paper about 8 feet long on
along the floor. Roll a bowling ball
along the paper and mark the location of the ball at 1 s intervals. You want to have at least six marks, so
adjust the speed of the ball accordingly.
If you record several different runs, make sure that you can distinguish
the marks from each run.
Data Analysis
In
the following there are numbered paragraphs and numbered questions. Answer the questions in the provided
space. The numbered paragraphs direct
you to put in information into the data table or else draw diagrams or graphs.
1. The position, x, records how far the ball
is from the origin of some coordinate system that we choose. In this case, we will choose the origin of
the coordinate system to be the first mark on the paper. In the data table this mark is already recorded
as x = 0 m and
t = 0
s. Use a meter stick to measure the distance
of the other marks from the first mark and fill in the positions for each and
their corresponding times in the data table on the next page.
Q1) How much time passed
between each mark?
2. We call the length of time between each mark
the time interval Δt. Fill in Δt
for each interval.
3. The position is the distance from each
mark. We can also, of course, measure
the distance between the marks. We call the
distance between marks the displacement,
Δx. We
can measure the distance between marks directly, but since we have already
measured position, we can use the position data to find the displacement.
Q2) How can you find the
displacement from the position data?
Record
the displacement in the data table. Note
that we have to have two positions to find a displacement so there is dash in
the first space where we will leave the displacement blank.
4. The displacement tells us how far we moved
between successive marks, but we might like to know how fast we covered the
distance. Did we travel 1.0 m in a
second or in a week? The average
velocity is defined as vave = Δx/Δt. It is
how much the position changes per time.
We describe it by saying the velocity is the rate at which position
changes. Find the average velocity of
the ball between each mark and record it in the data table.
Q3) You probably noticed
that vave and Δx
are numerically equal. This is not true, generally, but is an artifact
of how this experiment is designed. Explain
what feature of this experiment makes the two the same, and how you could
change the experiment to make that coincidence go away.
Q4) Examine your data. Is the velocity constant for every time
interval?
5. You probably noticed that the velocity changed
a little on each interval. Factors like
friction, bumps in the floor, and a slight slope to the floor will all cause
the velocity to change. We can calculate
the change in velocity on each interval as Δv = vf – vi. In
the data table under Δv, we skip the first two
spaces. When calculating a change,
always use the final value minus the initial value.
Q5) Examine your data. You may have noticed that some of the changes
in velocity are negative. What does this
mean about the motion?
6. Does the velocity change slowly or
rapidly? To answer that question, we use
the average acceleration. The average acceleration is defined as
aave = Δv/Δt. It is the rate at which velocity
changes. Notice that velocity is
m/s. Acceleration will
velocity per time. It will have units of
m/s/s. Find the average acceleration of
the ball between each mark and record it in the table.
Q4) You probably noticed
that aave and Δv
are numerically equal. This is not true, generally, but is an artifact
of how this experiment is designed.
Explain what feature of this experiment makes the two the same, and how
you could change the experiment to make that coincidence go away.
7. Use LoggerPro v.3.1
to construct a graph of position vs. time for the motion. Attach the graph to the report.
8. On a sheet of white paper (the back of this
handout is fine), construct a scale motion diagram for the ball’s motion. Use a circle to locate the position of the
ball at each time and use a scale of 2 cm :: 0.5 m
The
following three questions are about application of the ideas in this lab and do
not relate to the data. Label each
diagram with the type of motion it represents.
9. Sketch a motion diagram showing motion at a constant velocity on the same sheet of white paper as your first motion diagram.
10. Sketch a motion diagram showing motion with a
positive acceleration on the same sheet of white paper.
11. Sketch a motion diagram showing motion with a
negative acceleration on the same sheet of white paper.
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t
(s) |
Δt
(s) |
x
(m) |
Δx
(m) |
vave (m/s) |
Dv (m/s) |
aave (m/s/s) |
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0 |
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0 |
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Answer
the following in your own words.
Q6) What is position?
Q7) What is
displacement?
Q8) What is average
velocity and how is it related to position?
Q9) What is acceleration
and how is it related to velocity?