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Grade 12U Physics
The Conical Pendulum Lab: Measuring the gravitational field strength of the earth
Instructions: At home or in class, attach one end of a long string to a pivot point fixed to the ceiling or
some elevated support as shown in the diagram. Attach the other end to a compact object which is
much heavier than the string used. Allow the object to hang at rest so the string defines a vertical or
plumb line. Using a metre stick or metric measuring tape, measure the distance from the pivot point to
the centre of the suspended object, called the pendulum length L . Being mindful that only one
“rightmost” digit is allowed to have some uncertainty, record the pendulum length measurement to the
correct number of significant digits on the space provided below. Now pull back the mass roughly 30°
to 40°. Using a metre stick or metric measuring tape, measure the perpendicular distance from the
vertical or plumb line to the centre of the object, called the pendulum radius R . Being mindful that
only one “rightmost” digit is allowed to have some uncertainty, record the pendulum radius
measurement to the correct number of significant digits on the space provided below. Note that the
string now makes an angle Θ to the vertical or plumb line. With practice, the object can now be given
a push perpendicular to the radius and on the horizontal plane so the object traces out a approximate
UCM (uniform circular motion) on that horizontal plane. Using a timing device such as a smart phone,
stopwatch or watch, measure the time it takes the object to make ten revolutions or cycles. Being
mindful that only one “rightmost” digit is allowed to have some uncertainty, record “the time to make
ten revolutions” measurement to the correct number of significant digits on the space provided below.
Record measurements to
correct number of significant
digits here:
Ceiling
a) L = ______________________ m
State measuring device:
(ex. mm or cm ruler etc. )
_____________________________
_____________________________
Pivot
String
L
L
R
b) R = ______________________ m
object
State measuring device:
(ex. mm or cm ruler etc. )
_____________________________
_____________________________
c) time to undergo ten revolutions in UCM on horizontal plane:
__________________________ seconds
State measuring device:
(ex. Stopwatch, clock etc. )
_____________________________
_____________________________
Θ
Plumb
line
page #2
Questions and Calculations:
A formal report is not required. Hand-in a cover page with your name, due date and your instructor's
name. Other than the cover page, your report must be in your own handwriting, not computer
generated. Plagiarism will result in a zero for all parties concerned. For calculations, all steps must be
show in a neat and logical manner. Explanations must be concise and in complete sentences. Marks
will be deducted for missing steps, missing units and incorrect # of significant digits. Hand-in this
question booklet with your report. Use the marking scheme on the next page as a checklist.
1. Assuming R stays constant during the ten revolutions of the conical pendulum, calculate Θ to
the correct number of significant digits. Be sure to show formula and substitutions.
2. Read about “reporting data involving measurements” in the new textbook p 694 or “error
analysis in experimentation” in the old textbook p755. Using your reading as a guide, state the
uncertainty in L and R, then convert these uncertainties to percentage uncertainties. Be sure to
show the steps in the conversions. Noting that a division is required to obtain Θ, find the
percentage uncertainty in Θ. Be sure to show steps.
3. Find the period of revolution for the conical pendulum. Assuming the “ten cycles” are exact,
state the uncertainty and percentage uncertainty in the period.
4. Why is it better to measure the time to complete ten cycles as opposed to measuring the time to
complete one cycle?
5. Review the derivation for the formula of a car rounding a circular banked curve with negligible
friction. Using this derivation as a guide, derive or create a fully-simplified formula for the
period (T) of the conical pendulum in terms of Θ , L and g. Ignore any friction effects in this
derivation. Set up the positive x-axis so it is aligned with the centripetal acceleration of the
object. This derivation must include a properly labelled FBD, equation of motion, vector and
scalar statements, and all steps in logical order. Use the marking scheme that follows as a
checklist to complete your derivation correctly. Note “g” is the magnitude of the gravitational
field strength of the earth in N/kg. Now solve for “g” in terms of Θ, T and L.
6. Showing all steps, use the derived formula for “g” to find the experimental measured magnitude
of the earth's gravitational field strength to the correct number of significant digits.
7. Using the reading in question #2 as a guide, and showing all steps, find the percentage
uncertainty in the measured value calculated. Would there be any reason why the percentage
uncertainty would be higher? Explain.
8. The accepted value for the magnitude of the earth's gravitational field strength is 9.81 N/kg.
Using the reading in question #2 as a guide, and showing the formula and substitutions, find the
% error in the measured value of the magnitude of the gravitational field strength as determined
by this experiment.
9. Use proportionality to explain how a decrease in Θ during the experiment might affect the value
“g” ? (too high or too low)
10. Is the % error in the measured value within the percentage uncertainty calculated? Other than
the factor examined in question #7, list at least two other significant factors as to why the
experimental or measured value of “g” might not be equal to the accepted value. For each
reason or factor listed, explain how this affects the measured value of “g” (too high or too low)
For your experiment, how do these factors relate to the discrepancy between the % uncertainty
and % error?
11. Why is the mass of the object not a factor in this experiment? How would the calculation of the
measured value of g change if the string and object had similar masses?
Page #3
Marking Scheme: 80 marks
A. Cover page with name, due date and instructor's name:
/2
B. Lab handout included with recorded measurements on p1:
 recorded measurement of L, R, and time/10 rev
 measuring instruments stated
 proper # significant digits
/3
/3
/3
Questions and Calculations:
1.
Calculate Θ... formula, sub, ans
/3
2.


Uncertainty in L, R
% uncertainty in L, R with steps shown
% uncertainty in Θ with steps shown
/2
/4
/2
3.


Period and calculation (correct sigs)
Period uncertainty
% period uncertainty and step shown
/2
/1
/2
4.
Explanation about time measurement
in complete sentences.
5.
FBD...
|-----------|----------|
0
1
2
poor
excellent



real forces on diagram with arrows.
acceleration direction and expressed as scalar
XY plane, components drawn
steps to find components expressed in terms of Θ
Y-forces
equation of motion, vector statement, scalar statement
X-forces
equation of motion, vector statement, scalar statement
combining x and y equations to simplify for T
simplified equation for g
/3
/4
/1
6.
Measured value of g (correct sigs)...formula, sub, ans
/3
7.

% uncertainty in g with steps shown
Explanation about higher % uncertainty
in complete sentences.
8.
% error calculation with formula, sub, ans
9.
proportionality determined, arrow notation steps, conclusion


/7
/4
/3
/2
|-----------|----------|
0
1
2
poor
excellent
/3
/6
10. % error statement
 two factors for ex error plus explanation in complete sentences

how factors are relevant to difference in %error and %uncertainty
in complete sentences
11. explanation for mass irrelevance in complete sentences

explanation in complete sentences
if mass of string ≈ mass of object
/1
|----------|-----------|
0
2
4
poor
excellent
|-----------|-----------|
0
2
4
|------------|-----------|
0
1
2
|------------|-----------|
0
1
2