Download lab: uniform circular motion

LAB: UNIFORM CIRCULAR MOTION
APPARATUS:
Centripetal Force Apparatus
Slotted Mass Set with Weight Hanger
Metric Ruler
Stop Watch
Triple Beam Balance
BACKGROUND:
In this experiment, you will observe a rotating object and use circular motion equations to calculate the
centripetal force acting on the object. Then you will measure the force by stretching the spring to the
same length it had while spinning the object.
First, you will rotate the apparatus so that the object travels in a circle passing over the indicator rod (as
shown above). Using the mass of the object, the period of revolution, and the radius of the circular path,
you will calculate the centripetal force that should be required to keep the object in motion.
To check this value, you will try to measure the amount of force the spring exerts on the hanging bob
while it is rotating. Since there is no gauge or meter showing the force exerted by the spring, you will
measure the spring force by hanging weights over a pulley until the bob hangs at rest over the indicator
rod (as shown below). When the bob is in equilibrium, the weight hanging over the pulley will be equal
to the spring force pulling back on the object.
PROCEDURE:
Part 1.
1. Measure and record the mass of the rotating object. The triple-beam balance measures in grams, to
the nearest tenth of a gram. You will need to convert the mass to kilograms before performing your
calculations later in the lab.
2. Hang the object from the end of the support arm without attaching the spring; it should hang
vertically above the indicator rod. Then, attach the spring so that the object hangs inward, toward the
central shaft. It is possible to level the apparatus or adjust the counterweight so that the apparatus is
balanced; consult your instructor if you feel that is necessary.
3. Measure and record the radius of rotation from the center of the rotating shaft to the indicator rod.
Your ruler measures in centimeters, but you will need to convert the radius to meters before
performing the calculations below.
4. Rotate the shaft so that the hanging bob is rotating directly above the indicator rod. Record the time
to make 50 revolutions, keeping the object above the indicator rod each time it passes. Repeat twice
more for a total of three measurements, recording the time to make 50 revolutions for each trial and
then averaging your three times together.
Part 2.
Now, we will attempt to measure the actual force the
spring exerts on the hanging bob while it rotates. Since
we don’t have a gauge that shows the force being
exerted by the spring, we have to do it by stretching
the spring to the same length it had while the bob was
rotating. We’ll keep the spring stretched by hanging
weights over a pulley so that the bob hangs in
equilibrium over the indicator rod.
It is important for the string connecting the bob to the pulley to be horizontal so that the tension
corresponds to the horizontal force that kept the bob in motion in Part 1.
5. Tie a line to the outer edge of the bob and tie the other end around a weight hanger. Drape the line
over the pulley and add weights from the slotted mass set to the weight hanger until the spring
stretches to the position shown (with the bob directly above the indicator rod).
6. Make sure the string is horizontal, or as close to horizontal as possible, before it passes over the
pulley. If necessary, adjust the height of the pulley so that the string pulling outward on the mass is
completely horizontal.
7. Record the total mass hanging over the pulley, including the mass of the weight hanger itself, and
convert this value to kilograms.
CALCULATIONS:
First, use circular motion equations to calculate the predicted centripetal force value. Then, calculate the
measured centripetal force using your data from Part 2.






Using the data from step 4, calculate the period (in seconds) and frequency (in hertz) of the rotating
object.
Calculate the linear speed of the object as it rotates (in meters per second).
Calculate the centripetal acceleration of the rotating object.
Calculate the centripetal force required to keep the object moving in a circular path. This represents
the calculated centripetal force acting on the bob.
Now, calculate the weight of the assembly hanging over the pulley in Part 2 of the lab. Since the
weight hanger is in equilibrium, the total weight should be equal to the tension in the string. It will
therefore match the spring force pulling inward on the bob. This force represents the measured
centripetal force acting on the bob.
Now that you have two measures of the centripetal force acting on the bob—one measured directly
by stretching the spring, and one calculated by observing the circular motion of the bob—calculate
the percent difference between your two values. How well do your results support the theoretical
relationship between centripetal force and circular motion?
Additional Questions. Answer in your lab notebook, using complete sentences!
1. Copy the “top view” diagram at right into your lab notebook.
Then, draw three separate vectors to represent the centripetal
force, centripetal acceleration, and linear velocity of the
rotating object at the instant shown.
2. What is a centripetal force? During the lab, what provided
the centripetal force acting on the rotating object? How do
you know?
3. Does the centripetal force acting on the mass cause it to
change speeds? Explain.
4. Sketch a “side view” free-body diagram showing all forces
acting on the rotating object as it passes over the indicator
rod in Part 1 of the experiment. Are the forces on the object balanced or unbalanced during this
part of the experiment? How do you know?
5. Sketch a “side view” free-body diagram showing all forces acting on the object as it hangs over
the indicator rod in Part 2 of the experiment. Are the forces on the object balanced or unbalanced
during this part of the experiment? How do you know?
6. Explain the relationship between the measured and calculated values of centripetal force you
obtained in this experiment. Should they be equal in magnitude? Why or why not?
7. For an object moving in a circular path:
(a) How does radius affect the required centripetal force? Explain.
(b) How does velocity affect the required centripetal force?
(c) How does mass affect the required centripetal force?
(d) If the mass and the radius are held constant and the period (T) is reduced to 1/2 of its
original value, how much does the centripetal force change from its original value?
Explain your answer.