NEWTON’S LAWS
I. If a balanced force system acts on a
particle at rest, it will remain at rest. If a balanced force system
acts on a particle in motion, it will remain in motion in a straight
line without acceleration.
II. If an unbalanced force system acts
on a particle, it will accelerate in proportion to the magnitude and
in the direction of the resultant force.
III. When two particles exert forces on
each other, these forces are equal in magnitude, opposite in
direction, and collinear.
Fundamental Equation
The basic relation between mass,
acceleration, and force is contained in Newton’s second law of
motion. As applied to a particle of mass, F 5 ma, force 5 mass 3
acceleration. This equation is a vector equation, since the direction
of F must be the direction of a, as well as having F equal in
magnitude to ma. An alternative form of Newton’s second law states
that the resultant force is equal to the time rate of change of
momentum, F 5 d(mv)/dt.
Law of the Conservation of Mass
The mass of a body remains unchanged by
any ordinary physical or chemical change to which it may
be subjected.
Law of the Conservation of Energy
The principle of conservation of energy
requires that the total mechanical energy of a system remain
unchanged if it is subjected only to forces which depend on position
or configuration.
Law of the Conservation of Momentum
The linear momentum of a system of
bodies is unchanged if there is no resultant external force on the
system. The angular momentum of a system of bodies about a fixed axis
is unchanged if there is no resultant external moment about this
axis.
EXAMPLE.
Each of two solid steel spheres 6 in in
diam will weigh 32.0 lb on the earth’s surface. This is the force
of attraction between the earth and the steel sphere. The force of
mutual attraction between the spheres if they are just touching is
0.000000136 lb.
STATICS OF RIGID BODIES
General Considerations
If the forces acting on a rigid body do
not produce any acceleration, they must neutralize each other, i.e.,
form a system of forces in equilibrium. Equilibrium is said to be
stable when the body with the forces acting upon it returns to its
original position after being displaced a very small amount from that
position; unstable when the body tends to move still farther from its
original position than the very small displacement; and neutral when
the forces retain their equilibrium when the body is in its
new position.
External and Internal Forces
The forces by which the individual
particles of a body act on each other are known as internal forces.
All other forces are called external forces. If a body is supported
by other bodies while subject to the action of forces, deformations
and forces will be produced at the points of support or contact and
these internal forces will be distributed throughout the body until
equilibrium exists and the body is said to be in a state of tension,
compression, or shear.
The forces exerted by the body on the
supports are known as reactions. They are equal in magnitude and
opposite in direction to the forces with which the supports act on
the body, known as supporting forces. The supporting forces are
external forces applied to the body.
In considering a body at a definite
section, it will be found that all the internal forces act in pairs,
the two forces being equal and opposite. The external forces act
singly.
General Law
When a body is at rest, the forces
acting externally to it must form an equilibrium system. This law
will hold for any part of the body, in which case the forces acting
at any section of the body become external forces when the part on
either side of the section is considered alone.
In the case of a rigid body, any two
forces of the same magnitude, but acting in opposite directions in
any straight line, may be added or removed without change in the
action of the forces acting on the body, provided the strength of the
body is not affected.
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