This preview shows pages 1–2. Sign up to view the full content.
27
Experiment III:
Centripetal Force
Goals
•
Learn the procedure for determining the exponents in a power law
•
Experimentally determine the relationship between the centripetal force and the mass,
radius, and speed for an object in uniform circular motion
Introduction and Background
Centripetal Force
:
Those of you who have tied an object to a string and whirled it in a horizontal
circle no doubt have noticed that you have to pull on the string, and therefore, on the object in a
direction toward the center of the circle in order to keep the object in the circular path. If you do not
pull on the string, the object will simply fly off. This pull or force, as you learned in class, is called
a centripetal force. You may also have noticed that you have to pull harder if the mass increases, or
the speed increases, or the radius decreases, which is consistent with theoretical relationship
between centripetal force (F) and the mass (M), speed (V), and radius (R) you have learned in class.
In this lab, however, we will pretend that we know nothing about the relationship and try to
determine it through some designed experiments.
Determination of a Power Law
:
A power law is a functional form as shown below:
n
x
C
y
×
=
(31)
where
C
is a constant and
n
is the exponent; namely,
y
is proportional to the
n
th power of
x
. We can
take the logarithmic of both sides of Equation 31:
C
x
n
y
log
log
log
+
×
=
(32)
Therefore, a plot of log
y
versus log
x
should be a straight line whose slope is the exponent
n
. Many
relationships in physics take some form of a power law and very often we need to determine the
exponents in these power laws. To do this experimentally we would generate a set of data points of
(y, x) and plot log(
y
) versus log(
x
) on linear scales to determine the slope and thus the exponent.
In case multiple variables are involved, ie
c
b
a
x
x
x
C
y
3
2
1
×
×
×
=
(33)
we would determine the exponents one at a time. For example, to determine
b
, we would keep
x
1
and
x
2
constant in the experiment and we would have
)
log(
log
log
3
1
2
c
a
x
x
C
x
b
y
×
×
+
×
=
(34)
where the last term is just a constant and the slope of log
y
versus log
x
2
yields the exponent
b
.
Exponents in Centripetal Force
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 11/10/2011 for the course PHY 2053 taught by Professor Lind during the Fall '09 term at FSU.
 Fall '09
 LIND
 Physics

Click to edit the document details