PHYS221
Experiment 7 - Centripetal Force
Spring Tension Setting
Bob Apparatus
Variable Speed Control
Automatic Counter
Fig. 7-1 Centripetal Force Apparatus. Note: NO HANGER when upright!
Fig. 7-2 Centripetal Force Apparatus. Note: UNPLUGGED when horizontal!
Equipment
Centripetal Force Apparatus
Hanger & masses
Stopwatch
Vernier Caliper
Goggles
PHYS221
Experiment 7-Centripetal Force
Advanced Reading
is continually changing.
Thus, the
Halliday, Resnick and Walker
mass does not have a constant
Chapter 6, Section 6-5
velocity; it is being accelerated as it
rotates.
Objective:
According to Newton's Second Law,
The objective of this experiment is to
F = ma, in order to accelerate an object
measure the centripetal acceleration of
with mass m a non-zero net force must
a rotating body and thus determine the
act upon the mass.
centripetal force on the body. This
moving in a circle, the magnitude of
force will then be compared to a
the centripetal force is Fc = mv2/r.
For an object
statically determined value.
In this experiment the centripetal force
Theory
required to stretch a spring a certain
amount
will
be
dynamically
When an object moves in a circle, it
determined and compared to the static
undergoes
("center
force (provided by hanging weights)
seeking") acceleration with magnitude
required to stretch the spring by the
ac = v2/r, where v is the speed and r is
same amount (Figs. 7-1 & 7-2).
centripetal
the radius of the circle. Newton's First
law states that: An object at rest will
Procedure
remain at rest and an object in motion
will continue in motion with a constant
1.
The mass undergoing circular
velocity unless it experiences a net
motion is referred to as a "bob." Turn
external force.
Velocity is a vector
the spring setting on the bob cage until
quantity which has both magnitude and
it is near the zero position (weakest
direction. In this experiment, a mass
setting). Zero the counter on the
undergoes uniform circular motion.
centripetal force apparatus. Switch on
The speed is constant, but the direction
the machine and adjust the speed of the
PHYS221
Experiment 7-Centripetal Force
apparatus so that the needle position
3.
Unplug the apparatus. Turn the
points to the middle of the indicator
rotational apparatus so that it hangs off
located at the axis of rotation (Fig. 7-
the table (Fig. 7-3).
2).
instructor for help if necessary. Attach
Ask your lab
a weight hanger to the string tied to the
If the speed of the bob is too great, the
bob, and carefully place enough slotted
bob will rest against the cage, the
weights on it to cause the needle to
needle will point above the indicator
point to the middle of the indicator.
and the spring will no longer be the
Calculate the weight Mg hanging from
sole source of the centripetal force. If
the spring.
the bob is rotating too slowly, the
hanging from the spring (weight
needle will point below the middle of
hanger, slotted weights and the mass of
the indicator. One method of obtaining
the bob, which is stamped on the
an uncertainty in the number of
bottom of the bob).
Use the total mass M
revolutions (i.e., n) is to run multiple
trials and
to
use the difference
4.
By adding or subtracting a small
(between the high value and the low
amount of mass from the weight
value) divided by two in the results as
hanger, and observing the deflection of
the uncertainty.
the needle, estimate the uncertainty
M of the total hanging mass. The
2.
When the bob is rotating at the
critical speed, turn on the counter and
true value should lie in the interval
M ± M .
count the number of revolutions during
a two minute period. Repeat. Estimate
5.
While the hanging mass has
both the uncertainty n in the reading
displaced the bob to its rotating
of the number of revolutions and the
position, measure the distance from the
uncertainty t of the time.
axis of rotation to the center of mass of
the bob (the line scribed into the bob
marks its center of mass).
This
PHYS221
Experiment 7-Centripetal Force
distance is the same as the radius r of
1.
the circle made by the bob when it was
parts 3 and 7 compare? If these values
rotating. Estimate the uncertainty r
are not approximately the same, check
of the radius.
your calculations. (Did you include all
How did the two values of force in
the mass hanging on the bob? Did you
6.
Using the information in steps 2
and 5, calculate the speed v of the bob.
mismeasure or misread the vernier
This is given by v = distance/time =
caliper when measuring the radius?)
2 rn/t, where r is the radius of the
circle and n the number of revolutions,
and t is the elapsed time.
2.
In what direction is the bob
accelerating when it is rotating at a
constant speed? Draw a force diagram
7.
Calculate the centripetal accel-
for this situation.
eration ac = v2/r. Calculate the cen-
3.
tripetal force mac acting on the bob
uncertainty in this experiment?
What are the major sources of
and compare this value to the weight
Mg hanging from the bob in step 3.
Calculate the percent difference between the centripetal force and the
4.
Show that, in terms of measurable
quantities in this experiment, the
centripetal force is
hanging weight.
8.
4 2 mrn 2
.
F=
t2
Repeat steps 1-7 for the spring
setting 10 (intermediate setting), and
The fractional uncertainty of this value
then at 20 (strongest setting). These
is then
settings should only be approximate.
Questions/Conclusions
2
F (n)
(t )2 (r ) 2 = 4 2 + 4 2 + 2 t
r F n
1/ 2
,
PHYS221
Experiment 7-Centripetal Force
where it is assumed that the uncertainty of mass is negligible.
The
fractional uncertainty of the hanging
weight is
W M
,
=
M
W
where M is the total mass. From these
expressions, compute F and W for
each set of values in the experiment.
On a single horizontal number line,
plot the intervals F ± F and W ± W
for each set of data.
Displace the
intervals vertically so that they can be
clearly visible.
Does F=W within
experimental error?
intervals
predicts?
overlap
That is, do the
as
the
theory