Centripetal Acceleration Lab
January 31, 2013
Introduction
The purpose of this lab was to prove the concepts and
equations of centripetal acceleration by designing an
experiment using a tube, string, and stopper apparatus.
How does increasing the radius of a constant, horizontally
rotating mass connected to a hanging mass affect the time
it takes to complete a set number of revolutions? I
hypothesized that as the radius of the constant,
horizontally rotating mass is increased, the time it takes to
complete a number of revolutions will increase where
𝑡∝ 𝑟
Procedure and Materials
An 8.4 gram stopper is tied to one end of a string, and
a constant mass of 69.5 grams is applied to the other end.
A pen casing is used as a pulley to change the direction of
the string. Rachael places the top of the pen casing at
some radius r from the bottom of the stopper, and begins
to swing the stopper in a horizontal circle above her head
at radius r so that the radius remains constant. Andrew
starts a timer and Liv begins to count 20 rotations of the
stopper. At the 20-rotation mark, Liv says, “Stop.”
Andrew stops the timer and the time is recorded.
Diagram
Lab Partners: Liv and Rachael
Graph
12 11 Time of Rotation, t (s) Andrew McAfee, Section A
t[r] = 1.3955r0.5 R² = 1 10 9 t[r] = 2.4332r0.3426 R² = 0.72933 Measured 8 Theoretical 7 6 5 10 20 30 40 50 60 Radius of m1, r (cm) Analysis
With an R2 value of 0.729, it is clear that this model is a
weak fit for the data. The average %Error of the
measured values is 7.2%, indicating that the data is
moderately accurate. Finally, %RSD of 4.24 shows that
the data was moderately precise. The equation for the
theoretical model comes from the derived equation for
t. The constants in the theoretical and measured
equations were 1.3955 and 2.4332, respectively. These
numbers represent the scale of the lines, and represent
!"#$%&!
. Both equations have no max value, but the x
!"#"$%
and y-intercepts both occur at the origin, because the
radius must be greater than zero to rotate the string.
Constants and Equations
m1=8.4g=0.0084 kg
m2=69.5g=0.0695 kg
2
g=9.8 m/s
𝜃 = 20 𝑟𝑜𝑡 = 125.66 𝑟𝑎𝑑
∑𝐹! : 𝐹!! = 𝑚! 𝑎!
Summarized Data
𝐹!! = 𝑚! 𝑔
𝜃 𝑚1𝑟𝑚2𝑔
𝑡!"#$ =
𝑔𝑚2
(See appendix)
Conclusions
At the completion of this lab, it is clear that my
hypothesis was correct. As the radius of m1 was
increased, the time it took to complete 20 rotations
increased proportionately. A main source of error in the
lab could have been the sag effect due to the force of
gravity on m1. Failure to account for the sag effect
would cause the time to be greater because it would
cause the ω of m1 to decrease, and thus the time would
increase. Friction is another error that was not
accounted for in this lab. The presence of friction
causes the measured times to be smaller, because ω
would increase as a result of needing more energy to go
to friction. As an extension of this lab, m1 could be
changed to use different independent variables, or tests
could be used to more accurately measure the times
with friction and the sag effect.