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lab5-found-circularmotion

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Physics 211 Experiment #5 Uniform Circular Motion
OBJECTIVE: To study the motion of an object undergoing uniform circular
motion.
DISCUSSION: An object undergoing uniform circular motion (moving with
constant speed along the circumference of a circle) experiences a centripetal
force that is radially inward. This force causes the direction of motion of the
object to change, thus the object accelerates. The centripetal force, Fc, is
discussed and derived in the text, and depends on the mass of the object, m,
the speed of the object, v, and the radius, r, of the circular path along which
the object moves:

mv 2
ˆr .
Fc  
r
(1)
In the experiment, we will be able to measure m and r directly. To obtain the
speed, we will need to combine the angular speed, , with the radius of the
circular path, r, since the apparatus in the experiment will measure the angular
speed. The magnitude of the speed is simply related to the angular speed and
radius:
v  r
(2)
PRE-LAB EXERCISE:
1). Solve the following problem: A centripetal force apparatus is designed to
rotate a 50 g mass around a circle with a radius of 25 cm. A spring is used to
hold the mass at this radius. A force of 2.50 N is required to stretch the spring
to the correct radius. What is the speed of the 50 g mass? What is the angular
speed of the mass?
2). Create appropriate tables for the two sets of data you will to collect during
the lab.
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Overview
In this experiment, we will measure the force exerted on a spring in two
different ways: the force, F, due to gravity on a mass attached to the spring for
a non-rotating system, and the centripetal force due to a rotating mass. In the
experiment, we will arrange it so the force, F, exerted on the spring by the nonrotating mass, M, is the same as the force exerted on the spring by the rotating
mass, m. This is illustrated schematically on the following page, it is a threestep process. We will measure and compare the force exerted on the spring by
gravity, and by the centripetal force for systems with (1) constant force, and (2)
constant radius.
F = Mg
r
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EQUIPMENT:
Rotating Platform assembly with mounting rods
Aluminum rotating platform with 300 g square mass
Center post, spring and plastic indicator disk
Side post, 100 g mass with 3 hooks and two 50g attachable masses
Clamp-on pulley and thread
Small photogate
Pasco 5 g mass hanger and masses
Moveable
spring support
Colored index disk
Moveable
indicator
marker
Side
post
m
Center post
Figure 1. The centripetal force apparatus
Figure 2 Detail of the
photogate attached to the
rotating platform base.
PROCEDURE:
I. Leveling the apparatus base. It is very important that the apparatus be
leveled at the place it will be used, since the lab tables aren’t flat.
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Figure 3. Position of platform to adjust
right hand screw.
Figure 4. Position of platform to adjust left
hand screw.
1. Adjust the right leveling screw so that the 300 g mass and the
rotating platform are aligned along a line that passes over the left
leveling screw as shown in Fig. 3
2. Rotate the rotating platform 90o so it is parallel to the right leg as
shown in Fig. 4, and adjust the left leveling screw so the platform will
stay in that position.
3. Check whether the aluminum platform stays in any position to which
it is set. If the platform remains stationary, it is level. If the rotating
platform does not remain in any position it is placed, repeat steps 2
and 3 until the platform is level.
NOTE: In the following discussion m = rotating mass and M = mass and
weight hanger attached by string over a pulley to determine the force
exerted by the spring.
II Collecting Data (General Instructions) For each different radius or spring
tension the force the spring exerts must be determined by following the
procedure. Failure to determine this force will make your experiment
invalid.
1. With the side post set at r = 15 cm and the hooked mass at 200 g,
clamp the pulley to the end of the rotating platform. Set the spring
support on the center post so it is near the top of the post.
2. Attach a piece of thread to the hook on the mass toward the end of
the platform.
3. Place the thread over the pulley and place the weight hanger on the
end of the thread.
4. Add enough mass (30 to 75 grams) to the weight hanger until the
mass (m) with the hooks hangs vertically. (The threads supporting the
hooked mass must line up with the vertical index line on the side
post.)
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5. Determine the total weight of the hanging mass (M). This weight is
equal to the force exerted on the spring. NOTE: The value of M chosen
at this point will be constant throughout the experiment.
6. Adjust the horizontal indicator marker on the center post so it is
lined up with the orange radius indicator disk at this time.
7. Turn on the Science workshop interface first, then turn on the
computer.
8. Start Data Studio and select the Smart Pulley sensor.
9. Open the measurement menu, deselect Velocity, Ch 1, (m/s) and
select Angular Position, Ch1, (rad).
10. Open a graph window.
III. Dependence of Centripetal force and Velocity. (rotating mass is
constant (200 g), r is constant.)
1. Remove the weights and thread that are hanging over the pulley.
2. Start rotating the apparatus until the orange radius indicator disk is
centered in the indicator marker. While keeping the angular velocity
constant, record the data for several rotations by clicking on the
record button in the software window.
3. Expand the graph of angular position vs. time.
4. Select a straight portion of the graph indicating constant angular
velocity.
5. Select a linear fit.
6. Record the slope of the line (angular velocity), of the system.
7. Repeat the run 2 more times, and average the angular velocity for
these three trials.
8. Set up an Excel spreadsheet with appropriate columns, and record
the average the angular speed (or angular velocity) of the system.
Record any other information you will need to analyze the force on the
spring, such as the radius and the total force (determined while the
system was stationary). Make sure you have a column for the speed
of the rotating object, which can be obtained by combining the
angular speed with the radius.
9. Reattach the thread and weights removed in step 1. Change the
weight by at least 5 g (10 g is better). Do not change the radius.
10. Adjust the spring support bracket until the mass (m) hangs
vertically.
11. Adjust the indicator marker so it is centered on the orange disk.
12. Repeat steps 1 through 9.
13. Repeat steps 1 through 12 for an additional 3 masses which are
approx. 5g to 10 g apart. You will be done with this part when you
have run this for 5 different forces.
14. Calculate the average speed for each of the average angular speeds
you have determined in steps 1 through 13.
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IV. Centripetal force with constant radius (varying mass m and speed v,
with r constant, and M constant).
1. You will use the same value of M throughout this part. Your are
varying the rotating mass.
2. Keep the same radius used in Part III.
3. Take data as above for two additional runs: first by changing the
hooked mass by removing 50 g so that m is 150 g, and then by
changing the hooked mass m to 100g by removing the other 50 g.
The spring bracket position, the indicator marker, and the radius
should remain at the same location throughout this part of the
experiment.
4. Record the angular velocity required for each rotating mass, and any
other information you will need, into the excel spreadsheet. Calculate
the speeds (v) of each mass.
ANALYSIS OF DATA
1.
For the results you obtained while varying the centripetal force (in
step III), plot F (vertical axis) vs. v2 (horizontal axis) using Excel.
a.
Determine a linear trend line for the data.
b.
The slope is equal to m/r (see equation 1).
c.
Compare the slope to m/r from the constants of the
experiment by calculating the percent difference?
2.
For the results you obtained while keeping the radius constant (in
step IV), plot m (vertical axis) vs. v (horizontal axis) using Excel
a.
Determine the best-fitting power-law trend line for the data.
b.
The coefficient of x should be equal to Fr. (Remember to
calculate F by using Mg.) Compare the coefficient of x to Fr.
What is the percent error?
c.
The exponent of x should be equal to –2; compare the
exponent of x to –2, and determine the percent error?
3.
Your report should state the deviation (per cent difference)
between the expected values and values determined from your
graphs. In addition, you should comment on the nature of the
graphs and the reasons for your results.
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