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An object moving at a constant speed in a circular path is accelerating (i.e., the direction of
the velocity vector is constantly changing). This acceleration is caused by an unbalanced force
acting towards the centre of the circle (centripetal force). Any change in the unbalanced force will
produce a change in the orbital motion of the object.
Predict
How will the speed of an orbiting body change as the applied force
increases, if we keep the orbital radius constant?
Materials
rubber stopper
string
glass or plastic tube
paper clip
16 washers
stopwatch
electronic balance
unknown mass
Procedure
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1. |
Measure and record the mass of (i) the stopper and (ii) all of the
washers combined.
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2. |
Your teacher will show you how to construct the apparatus.
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3. |
Set the radius of revolution of the stopper between 40 and 80 cm
by keeping the paper clip just below the bottom
of the tube. Record
the distance from the top of the tube to the middle of the stopper.
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4. |
Attach eight washers to a second paper clip tied to the free end
of the string. Spin the stopper in the horizontal
plane, keeping the
paper clip suspended just below the bottom of the tube. Once you
have the stopper orbiting at
a constant rate, record the time taken
for 10 cycles.
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5. |
Increase the number of washers by two, keeping the radius
constant. Record the time for another 10 cycles. Repeat
until you
have results for at least five different masses.
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Application
You are given an object of unknown mass. Follow the procedure
described above and record the time taken for 10 cycles.
Analysis
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1.
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Use the geometry of a circular path to convert the period of motion
to linear speed for the stopper.
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2. |
Plot the speed v of the stopper against the mass mW of the washers.
What relationship between speed and mass
is suggested by the
shape of the plot?
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3. |
Replot the data using v2 againstmW. Calculate the slope of the line
(remembering to include the correct units).
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4. |
Draw free-body diagrams for the washers and the stopper.
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5. |
Use these free-body diagrams to derive an expression that relates v2 to mW. The angle between the string and
the horizontal should
be relatively small for all your results. Given this, let this angle equal
zero in your calculation.
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6. |
Use the expression derived in Step 5 to give a physical interpretation
for the slope of the plot of v2 against mW.
Compare the slope with
the value you would expect to get from the expression derived in
Step 5.
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7. |
Use the results to calculate the unknown mass. Compare your
answer to the value obtained using a balance.
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1. |
Two students are spinning identical stoppers at equal orbital radii.
One of the stoppers is moving noticeably faster
than the other.
What can you infer about the number of washers attached to the
faster stopper?
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2. |
Earth orbits the Sun because of gravitational attraction. How could
you use Earth's orbital data to measure the
mass of the Sun? Find
the relevant data and calculate the Sun's mass.
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3. |
The Sun orbits the centre of the Milky Way galaxy at a radius of
7.6 kpc (1 parsec = 3.26 light years) and at a
speed of 220 km/s.
Determine the mass of the Milky Way contained within the
Sun's orbit.
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4. |
Physicists estimate the mass of luminous matter in a galaxy by
measuring the galaxy's brightness. They have
observed that stars
within many galaxies orbit around their galactic centres at speeds
higher than expected. Using
ideas from this lab, give an explanation
for these observations.
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