PHY 122 Lab: UNIFORM CIRCULAR MOTION

PHY 122 Lab: UNIFORM CIRCULAR MOTION
Introduction: In this lab, you will calculate the force on an object moving in a circle
at approximately constant speed. To calculate the force you will use Newton’s Second Law
combined with the acceleration of an object moving in a circle at constant speed. You will
then compare that calculated force with a measured value.
You will measure the time t required for 30 revolutions of a hanging object; the object
will be held in a circular path of known radius r by a horizontal spring attached to the
axis of rotation. The time T for one revolution is then t/30 and the speed v of the moving
object is easily calculated from distance (the circumference of the circle 2r) divided by
time:
v =
2r
T
Since the object will have been moving in a circle at approximately constant speed v, the
amount of acceleration of the moving object is gotten by
a =
v2
r
Finally, multiplying by m, the measured mass of the object, will give the calculated total
amount of force on the moving object.
Procedure
Shown below is a photograph of the apparatus.
You will be asked to perform five trials of this experiment. For the first three trials, keep
the circle radius fixed and use three different values of the mass of the moving object. For the
last two trials, use two new values for the circle radius, but keep mass of the moving object
constant. For each trial, you will have to make three separate measurements of the time for
30 revolutions and take the average of those three. Here is the procedure for each of the five
trials.
1
1. Disconnect the spring from the bob and let the bob hang straight down. Add selected
masses to the top of the bob to produce the desired mass for the hanging object.
(Note: the additional mass can not be over 200g). With no added masses, the mass of the
bob is 349 g. Record the amount of the added masses in Data Table (zero added
masses is a possible choice).
2. Establish the radius of the circle in which the bob is to move by loosening the screw in
the horizontal arm and moving the arm until the bob hangs directly over the proper
centimeter mark on the base of the apparatus. Choose a radius between 15 and 21 cm.
Tighten the screw so that the arm will not slip when the shaft is spun. Record the
working radius in Data Table.
3. Attach the spring to the bob. Attach a horizontal string to the other side of the bob,
pass the string over the pulley, and suspend a mass hanger on this string. Put just
enough mass on the hanger so that the bob is pulled back over the selected centimeter
mark. The mass of the hanger is 50 g. Record the amount of mass added to the
hanger (not including the mass of the hanger) in Data Table.
4. Remove the added amsses from the hanger, then remove the amss hanger from the horizontal
string, and finally remove the horizontal string from the bob and get the string out of the
way.
5. Make sure the spring is attached to the bob, and that the paper strip is at the correct
radius, spin the shaft faster and faster until the bob is moving in a circle of correct
radius. When this is done correctly, the moving bob will pass precisely over the
selected centimeter mark once per revolution. Practice spinning the shaft, keeping
the bob in a circle of constant radius for at least 30 turns.
6. Use the stopwatch to measure the time for 30 revolutions. One student should get the
bob going at the right speed and do the counting out loud; a second student should
man the stopwatch. Count down to zero and then up to 30 (three,two,one, go, 1, 2,
3…30 etc.); the stopwatch should be started at the count of zero and stopped at the
count of 30. Record the total time for 30 revolutions; repeat three times and take the
average of the three values.
7. To find the error in monH use the same approach as you did in the lab Vectors and Statics.
Guide to Symbols in the Table
m = madd + bob mass of 349 g
mtot = monH + hanger mass of 50 g
t1 = time for 30 revs (1st count)
t3 = time for 30 revs (3rd count)
T = period-time for one rev. = tavg/30
a = v2/r with r in m
Fmeas = mtot(9.8 m/s2) with mtot in kg
madd = mass added to bob
monH = mass added to hanger
r = radius of circle
t2 = time for 30 revs (2nd count)
tavg = avg of t1, t2, and t3
v = bob speed = 2r/T with r in m
Fcalc = ma with m in kg
% discrepancy = 100% × |Fcalc –
Fmeas|/Fmeas 2
Data Table 4.1
Trial 1 Trial 2 Trial 3 Trial 4 Trial 5
madd (g)
m (g)
r (cm)
monH (g)
mtot (g)
t1 (s)
t2 (s)
t3 (s)
tavg (s)
T (s)
v (m/s)
a (m/s2)
Fcalc (N)
Fmeas (N)
3
Data Analysis
1. For one of the 5 trials:
a) Calculate spring force (Fcalc) and propagate the uncertainty in its value. (Note: the uncertainty in
Fcalc propagates through the error in the measurements of radius and period. The error in the radius
equals half width of pegs, which is about 2 mm. The error in period can be found using the stand.
deviation of the mean of the time for 30 rotations).
b) Calculate the value of the (Fmeas) and its uncertainty.
c) Do values of (Fcalc) and (Fmeas) agree with each other within the uncertainty ranges? In the
discussion explain, why or why not ?
4
2. In this experiment, a spring force was used to keep moving object traveling in a circular path.
The size of a spring force should be proportional to the amount of stretch in the spring. Does this
claim agree qualitatively with the data in your five trials? Why or why not?
3. You should have three trials which have a common mass m (trials 3-5); for those
three trials use Logger Pro to make table of Fmeas (in N) and the corresponding acceleration a (in
m/s2). Include proper labels with units in your table headings. Then make a graph a vs Fmeas of the
data. Apply Linear Fit and write down the value of the slope (number and units) and its uncertainty
for these data points.
4. What is the physical significance of the slope you have found in question 3? Calculate mexp
experimental mass of the rotating object and find uncertainty in its value. Do the values of
experimental mass and measured mass m of the rotating object agree within the error? If not,
explain what can be the reason for it in the Discussion section.
6
Going Further – is the part of the lab that can be completed for 6 extra credit points toward the lab
report.
1. For trials 1-3, in Logger Pro make table of the reciprocal of m (in 1/kg) and the amount
o f acceleration a (in m/s2). Include proper labels with units in your table headings. Then make a
graph a versus 1/m . Even there are only three data points but you should find that you still can
apply a liner fit. Write down the slope (number and units) of a best-fit line for your data points and
its uncertainty.
2. What is the physical significance of the slope you have found in question 1? Does its value agrees with
the value of the Fmeas within the uncertainty? Explain, the results you got in the Discussion part of the Lab
Report.
Summary
As a result of the lab students should have completed Data Table . Have tgraph(s) for TA to sign and show
sample calculations for Question #1 in Data Analysis section. In Lab Report students should explain the
concept of circular motion and how Newton’s Second Law applies to the object in circular motion. Follow
previous templates structure to complete this lab report.