HOLT PHYSICS
Pre-Chapter
Exploration
1
Discovery Lab
The Circumference-Diameter
Ratio of a Circle
MATERIALS
SAFETY
•
Review lab safety guidelines. Always follow correct
procedures in the lab.
✔ cord/string
✔ masking tape
✔ metric rulers
✔ pencil
✔ several cylindrical
OBJECTIVES
• Develop techniques for measuring the circumference and diameter of a
cylinder.
• Use data to construct a graph.
• Determine the slope of a graph.
• Analyze error in an experiment.
objects of varying
size
✔ white paper
Measurements of a cylinder
HRW material copyrighted under notice appearing earlier in this book.
Procedure
1. Select one of the cylinders. Examine the cylinder to determine how many different measurements would be necessary to give a complete description of the
cylinder. In this lab, you will use a cylinder’s measurements to identify one
cylinder from a group of cylinders, so make sure your measurements enable
you to distinguish the cylinder from similar cylinders.
2. In your group determine the best method of making the measurements you need
with the materials provided. Be sure you include ways to measure the
circumference of the cylinder in each method. Keep in mind that you must
measure each quantity directly; no values can be found through calculations.
3. Take all the measurements for the cylinder using the method you developed. Record all measurements in your notebook using the appropriate SI
units. Make sure to include all measured digits plus one estimated digit.
4. Place the cylinder into a container with a group of other cylinders. Trade measurements with another group. Use your method of measurement to find the
cylinder that matches the measurements you were given.
Analysis
A. What measurements did you make?
B. What was your method of measuring the circumference of the cylinder?
Describe your method in detail.
C. Did you find the cylinder that matched the measurements you were given?
If not, why not?
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D. Did the other group correctly identify the cylinder you measured? If not, why
not?
E. Compare your measurements with the other group’s measurements for the same
cylinder. Are the measurements the same? Explain any differences in your methods
or measurements.
Comparing methods of measurement
Procedure
5. Using the same method you used to measure the first cylinder, measure the
length, diameter, and circumference of several more cylinders. Label each cylinder with an identifying name written on masking tape. Record your measurements in your notebook using the appropriate SI units.
Data analysis
Procedure
HRW material copyrighted under notice appearing earlier in this book.
8. Use the data you selected in step 5. For each cylinder, find the value for the circumference of the cylinder divided by the diameter of the cylinder.
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HOLT PHYSICS Laborator y Experiments
Analysis
I.
Is the relationship between the circumference and the diameter the same
for all cylinders, or is it different for each one?
J. Based on your results, what measurements do you think are necessary to
give a complete description of a cylinder?
Graphing data
Procedure
9. Using the data you selected, make a graph of the circumference of the cylinders
versus the diameter of the cylinders. For each cylinder, plot a point on the graph
that represents the cylinder’s circumference and diameter.
10. Draw the best fit line to the points on the graph. Not all the points on the graph
will actually fall directly on the line, but the line should follow the shape made
by most of the points. The line should not connect each point directly to the
next one. Instead, it should be drawn as a smooth line connecting most of the
points.
11. Select two points on the line, one at the beginning and one at the end. Make
sure the points selected are points on the best fit line but are not data points.
Use the scales on the axes of the graph to determine the circumference and
diameter of the cylinders that would be represented by these points on the line.
HRW material copyrighted under notice appearing earlier in this book.
12. Label the points that you selected A and B. Find the difference between the values for the circumference at these points, and use this as the rise. In other
words, subtract the value for the circumference at A from the value for the circumference at B. Find the difference between the values for the diameter at
these points, and use this as the run. Subtract the value for the diameter at A
from the value for the diameter at B.
13. Find the slope of the line, using the equation slope = rise
run .
Analysis
K.
L.
M.
N.
On your graph, which quantity is the independent variable?
On your graph, which quantity is the dependent variable?
Describe the shape of the curve in your graph.
What is the value that you calculated for the slope of the curve in your
graph? Compare this to the relationship between the circumference and the
diameter that you calculated in step 8.
O. Based on your data and your graph, do you think it is better to find the
relationship between the circumference and the diameter by using the
slope of the graph or by calculating individual values? Explain your answer.
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HOLT PHYSICS Laboratory Experiments Teacher’s
Edition
Discovery Lab
Pre-Chapter
Exploration
1
The Circumference-Diameter Ratio of a Circle
OBJECTIVES
Classroom Organization
Students will
•
• use data to construct a graph.
• determine the slope of a graph.
• analyze error in an experiment.
Planning
Recommended Time
1 lab period
Materials
[for each lab group]
✔ cord
✔ masking tape
✔ meterstick
✔ metric ruler, 15 cm
✔ pencil
✔ several cylindrical objects of varying size:
pencils, soup cans, juice cans, stand rods, wooden
cylin- ders, dowels, etc.
✔ 2 sheets white paper
Materials Preparation
Each group will need to have access to several
cylin- ders. Cylinders should be in a wide range of
sizes. Make sure cylinders are clean and free of
sharp or jagged edges. If possible, label all cylinders
before
the lab. Use masking tape, and identify each cylinder
with a unique label. This will allow students to identify their cylinders in the first part of the lab.
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• The cylinders may be placed in groups of eight or
more for every two groups of students, or they
may be placed together in a central location. The
cylinders should be placed in a box or other container to keep them from rolling onto the floor.
Instruct students to return cylinders to containers
when not in use.
Techniques to Demonstrate
If you are using graphing calculators or other
graphing software, show students how to use the
equipment to graph their data.
Checkpoints
Step 1: Some students will have trouble approaching the question and will wait for you to tell them
what to do. It may help to present them with two
different cylinders. Ask what information they
would need to identify one of the cylinders from a
written description.
Step 4: Students should “hide” their cylinder among
the others and should trade measurements with a
group on the other side of the room. If cylinders are
placed in groups around the room, groups should
trade stations when they trade measurements.
Step 5: If cylinders are already labeled, students
can record the label instead of relabeling the
cylinders.
HOLT PHYSICS Laborator y Experiments Teacher’s Edition
HRW material copyrighted under notice appearing earlier in this book.
• develop techniques for measuring the circumference and diameter of a cylinder.
This lab may be performed by students working
alone or in pairs. Because groups trade measurements in the first part of the lab, there should be
an even number of groups.
HOLT PHYSICS Laboratory Experiments Teacher’s Edition
continued
Step 6: Some students may need help finding a second method to measure the cylinder. Check any
groups that seem to be stuck, and offer hints.
Students may wrap string around the cylinder and
mark and measure the string, or they may roll the
cylinder along a piece of paper and measure the distance from the initial position to the final position.
E. Answers will vary. Students should explain how
differences in methods could cause different
measurements.
Step 10: Students may need help finding the best fit
line on the graph. Ask students to explain why the
line need not include all data points.
G. Answers will vary but should describe the
strengths and weaknesses of the different
methods.
Step 11: Some students may need help finding the
coordinates of the chosen points. If using graphing
calculators or software, make sure students know
how to find the values of the points.
H. Answers will vary but may include taking many
measurements, having other people confirm
the measurements, and using more precise
instruments.
F. Answers will vary. Students should realize that
different methods may give slightly different
results.
I. It is the same.
Answers To
HRW material copyrighted under notice appearing earlier in this book.
Analysis
J. the diameter (or the circumference) and the
length
K. the diameter
A. Answers will vary, but many students will measure
the length, circumference, and diameter or radius.
Some students will realize that they only need to
measure the length and the circumference.
M. The graph should be a straight line pointing up
and to the right.
B. Answers will vary. Answers should be specific
and should demonstrate a concern for accuracy
and precision.
N. Answers will vary but should be close to 3.14.
Make sure students use the appropriate number of
significant figures based on their measurements.
C. The answer should be “yes.” If not, answers
should identify possible causes of the discrepancy,
such as incomplete or inaccurate measurements.
O. Students should realize that using the graph prevents bad data from affecting the results.
L. the circumference
D. same as C
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