PHYSICS EXPERIMENTS —131
8-1
Experiment 8
Centripetal Force
In this experiment you study the radial
acceleration of an object in uniform circular motion.
This acceleration aR is centripetal (toward the
center of the circle) and is given by
aR = v2/R
(eq. 1)
where v is the velocity and R is the radius of the
circular motion of the object's center of mass. You
verify this equation by using a centripetal force
apparatus (Figure 1) attached to a variable speed
rotator.
stamped onto its surface. The cylinder is attached
to a spring (indicated by Z on Figure 1). While
rotating, the cylinder stretches the spring and moves
within the metal frame of the apparatus. An
adjustable knurled tension screw (indicated by S on
Figure 1) adjusts the length of the spring, and
therefore the spring tension. It has an index and a
micrometer scale.
The tension, FT, exerted on the mass by the
stretched spring, keeps the mass in circular motion.
Newton’s Second Law (for the radial direction)
gives
∑FR = maR
leading to
FT = mv2/R.
The tension FT can be found directly by a
static measurement where the spring is stretched
vertically by a hanging mass.
This static
measurement is shown schematically in Figure 2.
R
m
M
Figure 1. Centripetal Force Apparatus
CAUTION: The rotating parts of this
apparatus can inflict painful and dangerous
wounds. Be alert to danger at all times when
this apparatus is operating. Do not run the
apparatus at excessive speeds, or with loose
hooks attached. Use the wood knuckle
guard.
Preliminaries.
The centripetal force apparatus contains a
mass m in the shape of a cylinder (indicated by M
on Figure 1). The value of the cylinder’s mass is
Figure 2. Static Determination of Spring Tension
The measured tension is to be compared with
the value computed from the centripetal force
equation above.
Procedure.
• Read and record the mass of the rotating cylinder.
• Place the centripetal force apparatus in the rotator
head so that the setscrew will engage the flat spot
8-2
PHYSICS EXPERIMENTS — 131
on the shaft. The rotator head must be in the vertical
position.
• Adjust the knurled tension screw to a position
such that the spring tension will not require rotation
of the apparatus at an excessive or vibratory speed.
Adjust the output speed of the rotator so that the
pointer (indicated by G on Figure 1) rises to the
level of the small disk. Depress the revolution
counter and find the number of revolutions in one
minute, keeping the apparatus adjusted to the
correct speed at all times. Be sure the revolution
counter does not coast after it is released. Record
the number of revolutions. Repeat this measurement
until you get reasonably consistent results.
• Remove the apparatus from the rotor and suspend
it from the support stand ring with the cylinder
downward in order to perform the static
measurement. Attach the mass holder and add
masses until the spring is stretched the same amount
as when the apparatus was rotating. Record the total
mass, adding in the mass of the mass holder and of
the rotating cylinder. Also, while the spring is
stretched the correct amount, measure and record
the radius of rotation R of the center of the cylinder.
Use a vernier caliper for this measurement.
Note. When you are done with the
experiment, lock the rotator driving plate out
of engagement with the driver plate. (if your
apparatus has this feature)
• Determine the weight necessary to stretch the
spring, which equals the tension FT exerted by the
spring on the rotating cylinder. Determine the
tension FT from the circular motion of the mass.
Determine the percent difference between the two
values.
Questions (Answer clearly and completely).
1. On what object is an outward force (away from
the center) exerted when the apparatus is spinning?
Explain the direction and magnitude of this outward
force in terms of Newton’s third law of motion.
2. Do you verify that the centripetal force in your
experiment is correctly computed using the
centripetal force equation eq. 1?
3. Suppose you had used a less stiff spring in this
experiment. How would it have affected your
results? Specifically explain which quantities would
have changed and how (increase, decrease, no
change). This includes hanging weights, rotation
speed, centripetal acceleration and centripetal force.