PHYSICS 221
CIRCULAR MOTION
Work in a group of 4.
Part 1: Measuring a coefficient of friction (again!)
A. Given the rotating apparatus, come up with a procedure to measure the coefficient of
friction between a penny and the ruler. Ask me for anything than you think you will
need (Hint: e.g. a stopwatch). Of course, your procedure must somehow include the
rotation of the ruler. Will you measure static or kinetic friction?
B. Do the experiment and take measurements.
C. Find the coefficient of friction from your measurements.
D. There are other ways to find the coefficient of friction between a penny and the ruler.
Find another such way (Hint: you could use the ruler as an incline). Do you get the
same answer?
Part 2: Why does the water stay in the bucket?
A. Imagine swinging a bucket of water over your head. How fast should you swing the
bucket to keep the water in the bucket? Make a prediction.
B. Do the experiment. Instead of water, put a tennis ball in the bucket (…unless you
really trust your prediction). Take measurements.
C. Conclusion: how well did the experiment match your prediction?
Part 3: acceleration of a swing
A. Measure with the accelerometer the radial and tangential accelerations of one member
of your group swinging on a swing. 2 or 3 oscillations are enough. When you take
the measurements, make sure that the person on the swing is not moving (i.e. he/she
is not pumping energy in the motion). Align one axis of the accelerometer with the
radial direction, and another axis with the tangential direction.
In DataMate, don't collect too many datapoints. You might run out of memory.
Choose a time interval of 0.05 s, and collect 200 points for a total of 10 s.
Measure also the length of the swing, the maximum angle that the swing makes with
the vertical (it can be done by taking height measurements), and the weight of the
person (A scale and a measuring tape are available).

B. The accelerometer doesn’t directly measure the acceleration a . It gives the
 
 
components of the vector a  g . Use your data to plot the magnitude of a  g as a
function of the time t (include at least one complete oscillation). Use Excel or Logger
Pro to plot your data.
C. Draw a free body diagram for the system seat + person. Find the components (along
 
the radial, tangential and z directions) of the acceleration minus gravity ( a  g ) as a
 
function of the angle  of the swing. Compute the magnitude of a  g . For what
 
angle  is the magnitude of the acceleration a  g a maximum? A minimum?
D. Use your answer from C to mark the position of the swing at the maxima and minima
of your graph in B (is it a high point or a low point?). Compare the theoretical
maximum and minimum values with the experimental maximum and minimum
values.
E. Use your data to compute the magnitude of the force on the person + seat by the
swing. Plot the magnitude of the force versus the time t.
F. Use your equations in C to find the magnitude of the force on the person + seat by the
swing as a function of the angle . For what angle  is the force on the person by the
swing a maximum and a minimum? How do the theoretical values of the maximum
and minimum force compare with your data?
Report:
This is a group write up. It must be word-processed. All graphs must be integrated into
the text.
1. For each part, describe the procedure. This acts as an introduction to what you
measured, and how you took your measurements. For part 3, include how you held
the accelerometer, your sampling rate and your experiment time.
2. Present your data in a table (parts 1 and 2) or in a graph (part 3).
3. Write an explanation of the motion that your table or graph describes.
4.
For all parts include a free body diagram of the object/person in motion.
5. Include a clear theoretical calculation of what you have measured. For part 1, show
how the coefficient of friction can be derived from your measurements. For part 2,
compute the minimum angular velocity needed to keep the ball in the bucket. For
part 3, compute the net acceleration and force acting on the person by the swing,
given the maximum angle of the swing, his/her mass, and the length of the swing.
6. For each part, analyze how well your measurements agree with your computations.
Include relative error computations, e.g. for part 2
 measured  computed
100%
 computed
Give possible explanations for discrepancies.