CENTRIPETAL FORCE
(90 minutes)
Exp. # 11
(Alward/Harlow web File: "centrip.doc" 1-29-04)
Name: _____________________ Partners: _______________________Section No. _______
EQUIPMENT: force sensor cylindrical weight (50-300 grams: 1" diameter minimum) 130-cm
string photogate + stand vernier calipers 2-meter pole table clamp utility clamp 45-cm rod pan
balances
PURPOSE AND THEORY
The purpose of this laboratory activity is to measure the centripetal force exerted on a mass swinging in
a circle at the end of a string and to compare the measured force to the calculated force based on the
speed of the mass. A particle moving with speed v in circular path of radius r experiences an inwarddirected (centripetal) acceleration given by Equation (1). If the particle is moving in a vertical plane,
then the Earth’s pull on the mass at the bottom of its swing is opposite in direction to the string’s upward
pull, T. Equation 2 is Newton’s Second Law applied to the mass at that instant.
a = v2/r
(1)
T - mg = mv2/r
(2)
T = mg + mv2/r
(3)
a = v2/r
The predicted value of the tension in the string is given by Equation 3.
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SETUP
These steps may be skipped if a graph display of
force versus velocity or the interface screen is
already on the screen.
1. Turn on the signal interface, then turn on the
computer.
2. Connect the force sensor’s plug into Analog
Channel A on the interface.
3. Connect the photogate’s plug into Digital
Channel 1 on the interface.
4. From the File pull-down menu, Open the file
named "centrip.sws".
PROCEDURE
The swinging mass will be suspended from the hook at the bottom of the Pasco force sensor which will
measure the tension in the string, and these values will be automatically recorded and plotted.
1. Place the photogate assembly on the floor (not on table). Attach 2-meter pole to side of table as close
as possible to the black interface box, and connect 45-cm rod to utility clamp. Hang force sensor from
the rod and tighten the lock nut so that the sensor will not wobble.
2. Attach a string of length 1.0 to 1.5 meters long to the hook at the bottom of the force sensor. At the
end of the string hang an cylindrical object of mass m not less than 50 grams and not greater than 500
grams. Make sure that the cylinder is capable of fully blocking the photogate’s infra-red beam It is not
necessary to adjust the length of the string; just raise or lower the photogate. Important: Adjust the
position of the photogate so that the object is about one centimeter from the detector (located on the
same side as the red indicator lamp).
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3. Measure the distance r between the string’s knot on the hook and the center of the hanging mass (you
will have to estimate the location of the center of the mass). This distance will be the radius of the
circular path along which the mass will be swinging. Record this radius in Table II.
4. Use the vernier calipers to measure the actual diameter d' of the cylinder, and the pan balance to
obtain its mass. Record both values in the table below. Since the first one millimeter of the object is
needed to completely block the infrared beam, the effective length of the object will be assumed to be 1
mm less than the actual diameter; subtract 0.001 from the actual diameter, and record the effective
diameter, d.
TABLE 1: CYLINDRICAL WEIGHT
Mass:
m = _______________ kg
Note: some of the cylindrical masses are
marked 0.500 kg for use on the pan
scales, but the actual mass is some other
value. Make sure you record the actual
value.
Actual diameter: d' = ____________ m
Effective diameter: d = d' - 0.001 =
______________________________ m
5. Calibrate the photogate. The speed of the swinging mass as it passes through the photogate beam
is calculated by dividing the diameter of the cylinder by the travel time through the beam. This
calculation is done by the computer software, but first it must be told the diameter of the cylinder. To
enter the diameter, first click on Experiment, then select Setup; make the setup window big and delete
any existing data sets. Click on the photogate icon (see Page 2). This will open up the Photogate Setup
window. In the Object Length box, enter the diameter of the cylinder, then click OK.
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6. When the the hook at the bottom of the force sensor is pulled, a special metal strip inside the sensor
is stretched, causing a small electrical current to flow from the cable into the interface box. The amount
of this current is measured in volts; the larger the pull, the greater the voltage reading. Thus, the voltage
is proportional to the force. Even when there is no pull on the sensor, it still may generate a small
voltage. We need to "zero" the sensor to cancel out this voltage. To zero the sensor, lift the string and
hanging weight and place it temporarily on the table. Next, press the "tare" button on the side of the
force sensor. This will zero the sensor.
7. Release the string and mass from a point approximately 45 degrees from vertical, and then press
ALT-R. Make sure the mass does not hit the photogate, and also make sure that the mass passes
through the gate at an angle which is perpendicular to the plane of the gate. After about six or seven
swings, data collection will end. Force and velocity curves should appear on the screen. Note that there
are many more force data points than velocity data points. This is because the force sensor collects data
several times per second, while the photogate calculates velocity only when the mass crosses the gate.
Note also that the force varies as time passes. This is because the angle changes. The force is maximum
when the string is straight up and down, and is minimum when the mass is momentarily at rest at its two
extreme positions to the left and right. We are only interested in the maximum values of the force; these
maxima are at the peaks of the oscillating force curve.
8. Use the cross-hairs cursor to read the values of the force and velocity for five different points and
record these values in Table II. Use pencil; in case your data is incorrect, you can erase it and start
over.
9. For each velocity, calculate the predicted value of the force (the tension in the string) according to
Equation 3, and record the result in Table II.
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10. For each of the five sets of numbers, calculate the percentage difference between the actual
measured tension and the predicted tension. The percentage difference is the absolute value of the
difference between measured and predicted values, divided by the predicted value, times 100.
TABLE II
Length of pendulum: r =
Number
cm =
Speed
Measured
Tension T
(Newtons)
v
(m/s)
m
Predicted Tension
Percent
T = mg +mv2/r
Difference
(Newtons)
%
1
2
3
4
5
Average:
5
%