1
The Acceleration Due to Gravity
Introduction:
Acceleration is defined as the rate at which the velocity of a moving object changes
with time.
Accelerations are always caused by forces.
In this laboratory we will
investigate the acceleration due to the force of gravity.
Theory:
In its simplest form, Newton's law of force relates the amount of
force
on an
object to its
mass
and
acceleration
.
F
=
m
a
(1)
or force = mass times acceleration.
Therefore, to impart an acceleration to an object, one
must impart a force.
One of the most obvious (and the weakest) of all forces in nature is the
gravitational
force
.
Newton's
Universal Law of Gravitation
describes the gravitational
force
(F
g
)
as follows:
F
g
=
Gmm'
r
2
(2)
This equation states that the force between the two masses
m
and
m'
is equal to the
product of their masses (
mm'
) multiplied by a constant (
G
) and divided by the distance
between them squared (
r
2
).
The constant (
G
) is called the
gravitational constant
.
To compute the gravitational force between the Earth and an any object, we
substitute the mass of the Earth (
M
E
) and the distance from the object to the center of the
Earth (
r
).
When the objects are on or near the Earth's surface, this distance can be
approximated by the value for the radius of the Earth
*
(
R
E
) so that Equation (2) becomes:
*
We can approximate this because in the scale of the size of the Earth (many hundreds of kilometers)
the
value for
r
at the top of our lab table is virtually equal to the value of
r
at the floor.
Algebraically this is shown by:
R
E
2245
R
E
+
D
R
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F
g
=
GmM
E
R
E
2
(3)
in which we see that the force only depends on the mass of the object, because
G
,
M
E
, and
R
E
are all
constants .
This force (measured at the Earth's surface) is called the
weight
of
the object.
Now looking at Equation (1) and equating
F
to the gravitational force
(F
g
)
, we see
that:
ma
=
GmM
E
R
E
2
=
mg ,
(4)
where
g
=
GM
E
R
E
2
.
In this last equation, we see that
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 Spring '09
 ham
 Mass, General Relativity, Standard gravity, Newton's law of universal gravitation

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