PHYS 220
LAB 2 - GRAPHING
In this lab you will examine the functional relationship between two measured
quantities. You will do this examination for:
(a) The circumference and diameter of a circular object.
(b) The height and volume of a cylinder.
Procedure I. Circumference and diameter
Materials and equipment: round objects, ruler, string
Step 1 - Measure the circumference and diameter for six round objects. Enter
these data into a table that you create using EXCEL. Your table should have
columns for: object name, circumference, and diameter. Be sure to include units
for your measurements.
Step 2 - Create a graph for circumference versus diameter. Use EXCEL to
determine the slope and y-intercept.
Step 3 - Compare, using the percent error (see Appendix), your slope to a well
known constant. Be sure to include all calculations in your laboratory report.
Theoretically, what should the y-intercept of your line be? Compare, in words, your
y-intercept to the experimental one.
Step 4 - Select one of your data points and use this point to find the constant
mentioned in Step 3. Compare this result to your slope using the percent
difference. Using a single data point is usually not good experimental procedure.
Why not? What is the advantage in using the slope method?
Step 5 - Write down the equation that represents the relationship between
circumference and diameter, using your value of the slope.
II. Volume versus height for a cylinder
Materials and equipment: graduated cylinder, ruler, water
Step 1 - Measure the height of six different volumes of water in a graduated
cylinder (1 ml = 1 cm3). Create a table in EXCEL that shows your data.
Step 2 - Create a graph in EXCEL for volume versus height. Determine the slope
and y-intercept for your graph.
Step 3 - Write out the equation for the volume of a cylinder. What does the slope
of your graph correspond to in this equation? What should your y-intercept be?
Step 4 - Do the necessary measurements to determine the cross-sectional area
of the graduated cylinder. Compare your result to the slope you found in Step 2
using the percent difference.
III. Questions
(1) How satisfied are you with your results from parts I and II? List specific
changes to your experimental procedures that might have improved your
results.
(2) When considering the graphs that we’ve been using in class and lab (position
vs. time, velocity vs. time, acceleration vs. time) do we say the variable on
the y axis or on the x axis first? Is it y vs. x or x vs. y?
(3) Consider the following graph.
a. Draw your prediction for this graph if it had a y intercept of 2.
b. Draw your prediction for the given graph if only the slope is changed
to -1.
c. Open the PhET simulation “Equation Grapher” and test your
predictions. Describe how your answer changed and anything that
surprised you about what the simulation shows.
(4) What are the slope and y-intercept for the following equations?
(a) y = 3.67x + 1.09
(b) y = (6ab3x - 16.03bc)/12
(c) 3ab2y = 5cx -2g
(5) In an experiment you take data to determine the value of g, the acceleration
due to gravity. You drop an object from rest and measure the distance it has
fallen and the time it took to reach that distance. The equation relating the
distance y to the time t is y = 1/2gt2. How would you plot your data and then
analyze your graph to determine g?
(6) In a similar experiment, you again attempt to determine g. This time by
measuring the distance and speed of the object at several points in its fall.
The equation relating the distance y to the speed v is v =
. Again, how
would you plot your data and then analyze your graph to determine g?
IV. Analyzing a Vertical Jump
Materials and equipment: motion detector mounted or held at ceiling
You will use the motion detector to record the motion of a jumper. The jumper
must stand directly below the sonic ranger and jump vertically upward with their
hands at their sides. When the jumper lands, they should return to their original
stance before the jump and stand there until the detector has stopped “ticking”.
The jumper should practice the jump until they can generate smooth graphs.
Step 1 - Collect the graphs and save (at least don’t erase them) and print them.
Then use the position versus time graph to do the following:
(a) Mark on the graph when the motion started and stopped and indicate which
part was the upward motion and which was the downward motion.
(b) How much time did the jump take?
(c) How high did the jumper jump? Clearly explain how you determined this.
Step 2 - Describe how you would use the velocity versus time graph to determine
the accelerations of the jumper on the way up and on the way down. Then use your
procedure to find the accelerations. Compare the accelerations to each other. Use
the percent error to compare the acceleration to the accepted value (in Greeley,
9.79 m/s2).
Appendix: Percent Error and Percent Difference
When reporting your experimental result, you will compare it to either an accepted value or an
experimental value measured using a different procedure to check for consistency.
A. Comparing an experimental value to a theoretical value
Percent error is used when comparing an experimental result E with a theoretical value T that is
accepted as the "correct" value.
percent error =
For example, if you are comparing your measured value of 10.2 m/s2 with the accepted value of
9.8 m/s2 for the acceleration due to gravity g, the percent error would be
percent error =
= 4%
Often, fractional or relative uncertainty is used to quantitatively express the precision of a
measurement.
B. Comparing two experimental values
Percent difference is used when comparing two experimental results E1 and E2 that were
obtained using two different methods.
percent difference =
Suppose you obtained a value of 9.95 m/s2 for g from a second experiment. To compare this with
the result of 10.2 m/s2 from the first experiment, you would calculate the percent difference to be
percent difference =
= 2.5%