Name ______________________ Date_____________ Block______
Lab: Introductory Lab Techniques
Procedure I: Examining the circumference of a circle as a function of its diameter:
1.a. Measure the diameter and circumference of the cylinders provided. (Measure the
circumference without wrapping anything around the cylinder.)
diameter (cm)
circumference (cm)
1.b. Plot a graph of circumference as a function of diameter. Calculate the slope of the graph.
Procedure II: Determining the period of a pendulum:
2.a. Measure the time it takes a pendulum to complete 10 complete cycles. Change the length
of the string and repeat the measurement.
**Use four lengths with as much variation as possible given the equipment.
**Your shortest measurement for 10 cycles must be less than 10 seconds.**
2.b. Calculate the period (time for one cycle) and the frequency (number of cycles in one
second) of the pendulum.
time for 10 cycles (s)
period (s/cycle)
frequency (cycles/s)
(note: The unit for frequency, cycles/second, is also given the name Hertz (Hz).)
1
Questions and Analysis:
Read section V: Graphing Data in the Physics Reference Material package.
1) From procedure I, plot a graph of circumference as a function of diameter. Directly on the
graph, calculate the slope of the graph and calculate the % error between this slope and the
theoretical value for the slope. The theoretical value for the ratio of circumference to
diameter is . (The formula for % error is on the front page of the Physics Reference package.)
Read section III: The Precision of Measurements in the Physics Reference Material package.
2) Practice with the precision of measurements: For each scale, state the smallest division, the
precision, and the measurement at each arrow.
0.5
a) |
0.6
|
0.7
|
2.a.i
0.8
|
0.9 cm
|
2.a.ii
2.a. smallest division
2.a. precision
2.a.i
2.a.ii
0
b)
|
| | | |
|
0.1
| | | | | | | | |
2.b.i
|
0.2 cm
| | | | |
2.b.ii
2.b. smallest division
2.b. precision
2.b.i
2.b.ii
3) a. State the rule that required us to measure the lengths in this lab to the nearest
one-hundredth of a centimeter.
b. From procedure 1, convert your diameter measurements into meters. Keep in mind that
you cannot lose precision or significant figures by converting. (Note: What is one-tenth
of the smallest division on the meter stick in meters?)
diameter (cm)
diameter (m)
2
Read section IV: Calculations & Significant Figures in the Physics Reference Material package.
4) Practice calculations with significant figures: Write the answers with the correct sig figs both
in normal style and in scientific notation.
answers
scientific notation
(to the correct # of sf’s)
(all sf’s shown in coefficient)
a) 601 x 40. =
b) 3000.0 x 1.7235 =
c) 420 x 75.0 =
d) 11.0 32.3 =
e) 0.007270 .01 =
f) 0.0000032 0.17 =
Read section VI: Proportionality in the Physics Reference Material package.
5) a. From procedure 1, what is the theoretical mathematical relationship (these words mean
“state the proportion that describes the relationship”) between the circumference of a circle
and its diameter? Explain. (Your answer should compare the equation for the circumference of a circle to
the equation for the proportion that matches it.)
b. How does the shape of your graph supply you with the same answer to the previous
question?
6) State the equation for the area of a circle. Which of the proportions in your reference
package has the same form of an equation as the area equation? Sketch a graph of area as a
function of radius and state the proportion that the sketch represents.
(note: “sketch” is NOT the same as “plot”. A sketch is placed with your other lab answers –
not on graph paper. A small pair of axes is drawn and labeled. The appropriately shaped curve
or line is drawn free hand – indicating the correct relationship (proportion) between the
variables.)
7) Frequency is the number of cycles per unit of time (cycles/second); while period is the time
required for one cycle (seconds/cycle). Therefore, the two quantities are reciprocals of each
other, i.e. frequency = 1/ period.
Which of the proportions has the same form of an equation as this equation? Sketch a graph
of the frequency of a pendulum as a function of its period and state the proportionality that
the sketch represents.
3
Name: __________________________________
Lab Period/Day _______
Lab 1: Introductory Lab Techniques
Answer Sheet
(In data tables where the units are given in the heading, do NOT repeat them in the table. Just write the numbers.)
Procedure I:
diameter (cm)
circumference (cm)
Procedure II:
time for 10 cycles (s)
period (s/cycle)
Questions and Analysis:
1.graph paper attached
2.a. smallest division
2.a. precision
2.a.i
2.a.ii
frequency (Hz)
2.b. smallest division
2.b. precision
2.b.i
2.b.ii
3.a.
3.b.
diameter (cm)
diameter (m)
4
4)
answers
scientific notation
(to the correct # of sf’s)
(all sf’s shown in coefficient)
a) 601 x 40. =
b) 3000.0 x 1.7235 =
c) 420 x 75.0 =
d) 11.0 32.3 =
e) 0.007270 .01 =
f) 0.0000032 0.17 =
5.a.
5.b.
6. area of a circle =
State the proportion ________________
Sketch the proportion below…
7.
frequency = 1/period
State the proportion ________________
Sketch the proportion below…
5
6