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.
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.)
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 should find the average velocity for the interval from t3 to t5 (remember the definition of average velocity is displacement divided by elapsed time). Once it has made a dot, how much time does it take the timer to travel to make two more dots? The answer is not 3/40 sec.
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 elapsed[1] 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).
Table 1 - (Give your table a unique Title): m = 200g
interval number / elapsed time[1](time taken from your Dot 0) / position (displacement from your Dot 0) / displacement traveled in a trio of dots / average speed (speed during an interval over three dots)
0 / 0 / 0 / N/A / N/A
1 / 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 / Displacement traveled from your Dot 1 to your Dot 3 / Distance in interval #2 / elapsed time in second column
3 / etc. / Displacement traveled from your Dot 2 to Dot 4 / etc.
4 / etc. / etc.
Due for your report, due Monday:
- 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?
- 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).
- 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.
[1] "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
[1]