F
G
m1m2
r2
lbm
ft2
slug2
NEWTON'S LAWS OF MOTION
Force and Motion
CP-03
Page 2
Rev. 0
Newton's third law of motion states "if a body exerts a force on a second body, the second body
exerts an equal and opposite force on the first." This law has also been stated as, "for every
action there is an equal and opposite reaction."
The third law is basic to the understanding of force. It states that forces always occur in pairs
of equal and opposite forces. Thus, the downward force exerted on a desk by a pencil is
accompanied by an upward force of equal magnitude exerted on the pencil by the desk. This
principle holds for all forces, variable or constant, regardless of their source.
One additional law attributed to Newton concerns mutual attractive forces between two bodies.
It is known as the universal law of gravitation and is stated as follows.
"Each and every mass in the universe exerts a mutual, attractive gravitational
force on every other mass in the universe. For any two masses, the force is
directly proportional to the product of the two masses and is inversely
proportional to the square of the distance between them."
Newton expressed the universal law of gravitation using Equation 3-2.
(3-2)
where:
F
=
force of attraction (Newton = 1Kg-m/sec or lbf)
2
G
=
universal constant of gravitation (6.673 x 10 m /kg-sec or 3.44 x 10
-11
3
2
-8
)
m
=
mass of the first object (Kg or lbm)
1
m
=
mass of the second object (Kg or lbm)
2
r
=
distance between the centers of the two objects (m or ft)
Using this universal law of gravitation, we can determine the value of g (gravitational acceleration
constant), at the surface of the earth. We already know this value to be 9.8 m/sec (or 32.17
2
ft/sec ), but it can be calculated using Equation 3-2.
2
Calculation:
First, we will assume that the earth is much larger than the object and that the object
resides on the surface of the earth; therefore, the value of r will be equal to the radius of
the earth. Second, we must understand that the force of attraction (F) in Equation 3-2
for the object is equal to the object's weight (F) as described in Equation 3.1. Setting
these two equations equal to each other yields the following.
