Lab
Mass of a Paper Clip
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The
purpose
of this lab is to use the principles of rotational equilibrium to determine the mass of a single paperclip.
Part I Procedure:
I. Use a triple beam balance to mass a meter stick. Be certain that its center of gravity is in the center of the pan and that the length of the stick is oriented perpendicular to the beams. Record its mass in grams.
II. Measure the mass of your 5 washers. Record their mass in grams.
III. Balance the meter stick on the bridge. Record the position of knife edge in centimeters.
IV. Bend two paper clips to hold the five washers and the balancing clips.
V. Place the clip that is to hold all 5 washers
exactly 10 cm
from the knife-edge--
NEVER move it!
Record its position in centimeters.
In this experiment, the 5 washers are providing a counterclockwise (ccw) torque which has a magnitude that remains constant. By changing both the number of balancing clips and their position relative to the knife-edge, you will be generating 10 data points that have equivalent clockwise (cw) torques.
VI. Through a combination of moving the balancing clip hanger and varying the number of clips, find ten (10) different locations that balance the five washers. Fill in the following chart as you proceed through the lab.
Note that you are NOT to include the hanging clips in your totals since they cancel each other out.
Both the 5-washers and each collection of paper clips are suspended by a paper clip-hanger.
# of clips
Position
of clips
Moment arm
of clips
Reciprocal
of moment arm
TRIAL
N
L
1 / L
(cm)
(m)
(1/m)
1
2
3
4
5
6
7
8
9
10
Using EXCEL, plot a graph of
# clips vs 1/moment arm
. Save your file as
lastnamelastnametorque
to the computer's thaw space. Before printing your graph, be sure that the print area includes all of the data table and the graph.
Use the following format for your EXCEL spreadsheet.
Part II Procedure:
Remove the washers and offset the knife-edge 6-cm from its location in Step I. Then use paper clips to bring your beam back into equilibrium. Record the new knife-edge position, number of paper clips (counting the hanger) and the position of the clips in the blanks below. Then calculate the moment arms for the meter stick and clips.
Refer to the following information for the next five questions.
number of clips, N, to bring the meter stick back into equilibrium
position of clips (cm)
new knife-edge position (cm)
moment arm of paper clips (cm)
moment arm of meter stick's center of gravity (cm)
Refer to the following information for the next two questions.
Conclusion #1:
We will now use linear regression techniques to determine the mass of a single paper clip. To begin, we need to write the theoretical equation that models the data you graphed.
Recall from Part I of your lab that the paper clips provided the clockwise (cw) torque and the washers provided the balancing counter-clockwise (ccw) torque to produce rotational equilibrium. Mathematically we can write this relationship as
Since your EXCEL graph is titled
N vs (1/L)
you need to solve the equation given above for the number of clips, N, so that this equations parallels the form of the generic equation of a line: y = mx + b.
What was the numerical slope of your trend line in EXCEL?
Now solve for the mass of a single clip, m
_{clip}
by setting the coefficient of (1/L) equal to your trend line's numerical slope. Express your answer in kilograms.
Refer to the following information for the next four questions.
Conclusion #2:
We will now use your data from Part II to obtain a second value for the mass of a single paper clip.
In this part of your lab the weight of the meter stick provided the clockwise (cw) torque and the paper clips provided the balancing counter-clockwise (ccw) torque, so our initial equation would be
Note that
N
must include the hanging clip since the meter stick's center of gravity does not have a corresponding clip to cancel out its weight.
How many papers clips were required to bring the meter stick back into balance?
What was the position of the papers clips?
What was the position of the knife edge?
By substituting in your known values (the mass of the meter stick in kg, the number of paper clips, the moment arm of the paper clips in meters), solve for the mass of a single paper clip in kilograms.
Error Analysis
Compare the two values for the mass of a single paper clip by calculating a percentage difference between the values found in your two conclusions.
After submitting your lab results online, turn in one copy of your EXCEL data sheet and graph (displaying the trend line's equation and R
^{2}
value). Make sure that the names of your group members have been filled in.
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