Honors Physics Lab 2:
Acceleration from Tape Timer Measurements
Purpose: To graph the position and velocity of an object that falls freely due to the force of
gravity.
Theory: The tape timer is designed to create a Motion Diagram in the form of carbon
impressions on a long piece pf paper (the "tape"). The tape will fall through the timer
under the influence of a hanging mass falling freely due to gravity. The timer makes
impressions at the rate of 40 per second. The displacements can then be plotted as a
function of time - it should look like an upward parabola as we have discussed. The
average speed can be determined for each time interval. The speed vs. time graph
should approximate a straight line.
The acceleration (rate of change of velocity) is the slope of that average speed line.
Apparatus & Set up:
Tape timer (40 Hz setting)
1 meter length of tape (approx.)
with a reinforced hole in one
end
Carbon discs
Mass (variable—200+ gram
suggested)
Meter stick
Ring stand, clamps etc.
Tape
Time r
Stand
M ass
Procedure: The tape timer is attached to the ring stand. Paper tape will be attached to the
mass so that it may drop freely through the tape timer. The tape timer will be set at a
fixed 40 Hz setting and will make carbon impressions on the tape as it passes through.
The timer should be started and the mass and tape released. On the tape, mark the value
of the mass used. Mark also the location of the tape timer just before the mass hits the
floor. Do not use any dots after this.
Analysis: Locate in the central portion of your tape a section of approximately 12 carbon
impressions. Do not use the first dot or dots made after the mass hits the floor. Number your
chosen dots on the tape, beginning with the number zero. (Note that Dot 0 is not the first dot on
the tape.)
t0t1
t2
t3
t4
t5
t6
t7
Measuring: Tape the paper to a meter stick so that you can read the postion of each dot in
cm. Carefully measure the position of each dot (the distance from it to your dot number
0) and create a table (see below). Have your lab partners do a cross-check on your
measurements. Record the position using decimal numbers in your data table (see
below). Consider your first dot at time zero (0) and each successive dot 1/40 of a second
later (0.025 seconds). Don’t forget to note what units of distance you are measuring.
After your group has established a table of displacements, every student is responsible for
preparing her/his own data tables, graphs and conclusions. You may (and you should)
check your calculaitons with each other. One person from your group will hand in the
tape attached to his or her report. Note your group members on your report, and state
which person is handing in the tape. Every student in the group loses a point of the tape
is not handed in with the report.
Graph 1—position versus time. In your Lab Report, make a full-page graph of position as
a function of time. It might not go through the origin.
Calculations & Graph 2's (average velocities versus time): Determine the average speed
in the middle of each trio of position values. For example, to find the speed at time t4 you
Do this part
should find the average velocity for the interval from t3 to t5 (remember the definition of
carefully or
your graph will
average velocity is displacement divided by elapsed time). Once it has made a dot, how
be wrong and
much time does it take the timer to travel to make two more dots? The answer is not 3/40
you'll have to
sec.
re-do it.
We will refer to the average speed from t3 to t5 as v4, and the average speed from t4 to t6
as v5, etc. Note that there will not be a v0 or v12. Do not calculate velocities for the first
and last dots or graph them, as any numbers are meaningless. The average speed for each
interval is (the position at the end of the interval minus the position at the start of the
interval) divided by the amount of time it takes to travel three dots, or 0.05 s).
The average velocity for each trio of dots changes as the mass falls. Produce a full-page
graph of velocity as a function of elapsed1 time. Do not force it to go through the origin.
This graph may be done in EXCEL, but you must do the slope triangle and find equation
by hand. Find the slope of the average velocity line and write the equation of that line.
Start with y = m x + b and (as we did on Lab #1) replace the slope and variables x, y, m,
to those that indicate the meanings for this Lab. Ignore the y-intercept.
Bring these graphs to the next class period.
Data Tables. In this Lab Report, here's how to set up your Data Tables. (For future Lab
reports, you will have to decide on the best format for the Data Table).
interval
number
1
Table 1 - (Give your table a unique Title): m = 200g
elapsed time1
position (displacement displacement traveled in
(time taken from
from your Dot 0)
a trio of dots
your Dot 0)
average speed (speed during
an interval over three dots)
"Elapsed time" means the time from when your Dot 0 was made. For example, for the fourth interval, there were
four intervals of .025s from the time Dot 0 was made, so the time value on your x-axis is 4 * .025 = 0.1
0
1
0
0
N/A
N/A
1/40 sec * 1
These values are measured
from dot "zero" (which is
not the first dot on the
tape).
Displacement traveled from
your Dot 0 to your Dot 2
Distance in interval #1 divided by
0.05 (the amount of time it takes
to travel two intervals)
2
1/40 sec * 2
Distance in interval #2 / elapsed
time in second column
3
etc.
Displacement traveled
from your Dot 1 to your
Dot 3
Displacement traveled
from your Dot 2 to Dot 4
etc.
4
etc.
etc.
Due for your report, due Monday:
a. A header consisting of the experiment title, your name, and the name of your lab
partner(s) and which of you is handing in your two tapes. Include the following
Sections of the Lab Guidelines:
 Section I - Objective
 Section IIb - Drawing of the tape and your measurements on it. Show in the
drawing SPECIFICALLY WHAT YOU MEASURED ON THE TAPE and how
the variables elapsed time, instantaneous position, displacement over a trio of
dots, time for a trio of dots, are represented on the tape. You do not need to draw
the setup (lab bench, coil of tape, your hand, etc.)
 Section IV Data and Graphs
 Section VI Answers to Questions (see Questions below)
 Overall Conclusion - after doing all this work and writing the report, what does it
all mean?
b. NOTE: One Graph 1's and one Graph 2's (one for each student). Graph 2's with
slope triangle, slope calculation, and equation (show the slope triangle and slope
calculation by hand if you use EXCEL). Each graph must be a full page and follow
the Lab Guidelines, and no extra text on the graphs. Be careful - thoughtful - about
the units of the axis of each graph and what the units of the slope must be. Choose
appropriate titles for each graph as explained in the Lab Guidelines (not just a
repetition of the axes).
c. QUESTIONS: Answer the following questions in complete sentences that incorporate
the question and using the physics terminology that we have used in class.
1. When we graph position versus time, briefly explain the shape of the trendline
that would fit this graph. State the name of this type of curve. Explain in
words why is it shaped the way it is. Your explanation should refer to the way
position is changing in succeeding time intervals.
2. For Graph 2's, make the slope triangle as described above and find the
equation of the line. Each of the numbers in the equation corresponds to some
physical reality or physics concept. What does each of the terms (the
numbers) in the equation of the best-fit line represent in the physical situation?
3. Would you expect Graph 1 and Graph 2 to go through the origin? Why or
why not?
Don’t forget - you also have some regular HOMEWORK due Monday.