Centripetal Motion Lab: Determination of an unknown mass
Purpose:
To determine the mass of an object suspended from a centripetal motion apparatus using the centripetal
force of a horizontally rotating stopper.
To compare the experimental mass of the object to the actual mass of the object.
Theory:
All rotating objects require a force to pull them back toward the centre of rotation as they rotate. This
centripetal force can take many forms, including frictional, natural (normal), and gravitational forces. In
this experiment, tension of a string will provide the centripetal force keeping the rotating stopper at a
constant radius about the glass rod.
In this experiment, his centripetal force can be calculated once the radius r, mass m of the stopper, and
period T have been measured, by using the formula
⎛ r ⎞
Fc = m ⋅ 4 π 2 ⎜ 2 ⎟
⎝ T ⎠
This tension on the string acting horizontally inward is the same tension acting upward on the same string
attached to the suspended object. Therefore, the centripetal force should be equal to the weight of the
suspended object, according to
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Fc = T = Fg
⎛ r ⎞
m ⋅ 4 π 2 ⎜ 2 ⎟ = M ⋅ g
⎝ T ⎠
, where M is the mass of the suspended object.
In this investigation, the radius is the independent variable and resulting period is measured (dependent
variable). The plotted graph of the radius r against the square of the period T2 should produce a linear
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line of best fit whose gradient (slope) is
Δr
F
gradient =
= 2c
2
ΔT
4π m
Therefore, the mass M of the suspended object can be determined from this gradient ∆r/∆T2 and the mass
m of the stoppers.
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Materials:
stopwatch(es)
Procedure:
The object was attached securely to the loose end of the string.
A long radius (r>1m) was selected for the first set of trials.
The stoppers were rotated at a steady frequency at the selected radius to suspend the object
As a group, the number of rotations to be measured was chosen and the time interval for that number of
rotations was measured using one or more stopwatches.
Three similar times were measured for this radius.
glass tube
string
stoppers
ruler/metrestick
This procedure was repeated for the same apparatus using 4 other radii.
Data Analysis A graph of Radius, r (y-axis) versus Period Squared, T2 (x-axis) was made.
From the gradient (slope) of this graph, the centripetal force was calculated.
The mass M of the suspended object was calculated.
Error AnalysisAfter the experimental mass was stated to the instructor, the true mass of the object was found.
The absolute and relative errors were calculated.
Conclusion: State the experimental and accepted values of the mass of the suspended object.
State and evaluate the absolute and relative errors.
Identify significant sources of experimental error.
Suggest methods to reduce these errors and to improve the investigation.
object
Results
SHOW SAMPLE CALCULATIONS
Table 1.
Determination of period T and the square of the period T2.
Radius,
Number of Rotations
Time Interval,
r/m
t/s
Figure 1.
Graph of radius, r, against the square of the period, T2
Period,
T/s
Square of the Period,
T 2 / s2