Dynamics Concepts
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Dynamics is the scientific study of forces
that make things move (there is another study of forces, called statics,
that deals with forces that affect things but don't move them). When
physicists began to apply the science of dynamics as developed by Isaac
Newton, it caused a revolution in science and technology. This is
one of the most significant events in the history of civilization.
Consult a history book or teacher for more info.
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A force is a push or a pull.
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Physicists identify four fundamental forces
that affect matter in the universe. Gravity, the electromagnetic
force, the strong nuclear force, and the weak nuclear force.
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Gravity is an attractive force between any
two objects with mass.
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The strong nuclear force holds atomic nuclei
together.
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The weak nuclear force acts in the radioactive
decay of some "weakly-interacting" particles. It has (relatively
recently) been unified with the electromagnetic force.
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The electromagnetic force concerns the attraction
between electrons and protons, and the repulsion between electrons and
electrons, or the repulsion between protons and protons.
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Forces that affect objects in our everyday
experience may be the result of physical contact between two or more objects,
or of non-contact forces. Gravity and the electromagnetic force are
the non-contact forces we discuss most often in this course (the strong
force and the weak force are the other two non-contact forces). Objects
need not be touching for a non-contact force to affect them.
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Kinematics only described the motion of objects;
dynamics explains why things move.
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Newton formulated three laws of motion which
are the foundation of dynamics (and statics, too).
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Newton's first law: An object stays
in a state of constant velocity unless acted on by a force. This
means the object may move in a straight line at constant speed, or may
stay at rest (a state of zero velocity). This is the idea of inertia.
Inertia refers to the tendency of objects to persist in a state of constant
velocity. (Note: be careful with words like force, inertia, momentum,
and energy that are used casually in everyday speech but have a specific
meaning in physics. Many physics students have had to overcome the
belief that they "already know" what these words mean. The upshot:
they didn't know what the words mean in physics).
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If you want to think of inertia as a quantity,
think of it as mass. Changing the motion of an object with a lot
of mass is difficult, so you might say it has a lot of inertia. Note:
You would not be speaking physics. Some physicists distinguish
between gravitational mass and inertial mass. For our purposes, we
will consider them to be the same thing. Gravitational mass is the
mass as measured by the effect of a gravity field on an object. Inertial
mass is the mass as measured by the object's resistance to acceleration.
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Newton's second law relates force to acceleration.
In mathematical terms, we state it as F=ma. That means that acceleration
is the result of a force, and is directly proportional (goes up or
down as does) to the force.
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Newton's third law is stated in plain English
like this: If an object exerts a force on another object, the second
object exerts a force equal in size and opposite in direction on the first
object. A physicist once said: "If you punch the wall, the wall punches
you back, just as hard." Be careful in the way you state this.
As in most physics concepts, the everyday statement of it leaves a lot
to be desired in the precision department.
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When an object is in contact with a surface,
the surface exerts a force perpendicular to itself on the object.
We call that force "normal force." This is because the force is perpendicular
to the surface. Normal means perpendicular in this context.
The normal force is how we experience our weight. If we are not in
contact with a surface (falling), then we accelerate towards the center
of the earth at g, and we feel weightless.
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When a force is exerted on a very strong object
(say a concrete wall), it appears that the object does not move.
But how does the wall "know" to push back with an equal and opposite force?
The answer is in the molecules. The push on the wall deforms the
wall a tiny bit and stretches the molecules, which act like tiny springs.
This tension of the "tiny springs" (molecules) produces force proportional
to the push on the wall. That is how the wall "knows" how hard to
push back. Push harder, and you stretch the molecules more.
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Static or kinetic friction occurs when the
molecules of two objects in contact bond together, or "cold weld."
The amount of friction is different for different combinations of surfaces.
This is because of the different chemical composition (differences in the
arrangements of the electrons and nuclei) of the two materials. Note
that a common way of naming drag is to call it air friction. That
does not mean that drag results when air cold welds with a surface.
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Cold-welding is incomplete. It does
not produce a single, "welded-together" object. In general, this
is because of the interference of dirt, oil, and oxygen in the air.
The dirt and oil are deposited on surfaces and interfere because of their
presence. The oxygen reacts with some surfaces to produce a layer
of chemical on the surface that does not cold-weld very well.
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Sliding (kinetic) friction is a force that
occurs when two surfaces are in contact and one is in motion relative to
the other. It opposes the direction of motion. Note:
not all frictional forces oppose the direction of motion.
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We compare the force of sliding friction between
two different substances by dividing the amount of force it takes to slide
an object on a surface at constant speed by the Normal force on the object.
This leads us to a dimensionless quantity we call mu, or the coefficient
of friction. The higher the mu, the more friction there is between
two surfaces. Many physics books and engineering handbooks contain
tables of coefficient of friction for various combinations of substances.
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Static friction is higher than kinetic friction
for a surface. This is because left over time, the object bonds more
completely to the surface. A common experience is to slide a heavy
object from rest. Once the object is moving, the force you apply
to keep it moving is less than the force to start it.
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Rolling friction is generally very low (this
is the reason ball and roller bearings are used so often). This is
because any point on the wheel always contacts a different point on the
surface. The two surfaces don't slide. The friction results
from the deformation of the surface and the wheel as the wheel moves along.
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Objects moving through the air are subject
to a drag force. When the gravitational force pulling on a falling
object equals the drag force, the object moves at constant velocity.
This velocity is called terminal velocity. The drag force is proportional
to the square of the velocity of the object (and to the cross-sectional
area of the object, the density of the air, and the coefficient of drag).
For
the exact relationship, consult a college physics book.
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The coefficient of drag is analogous to the
coefficient of friction. It is a dimensionless quantity that is a
measure of how "slippery" an object is in air.
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Forces are vectors. They follow the
rules of vectors. See the text and the vectors concepts page for
more info.
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To solve dynamics problems, we follow a time-honored
procedure. First, draw a free-body diagram, depicting all the forces
acting on the object being considered. In general in this unit, most
objects will be subject to a gravitational force and to a force from everything
that touches them. Second, write "sum of the forces" equations for
the forces. Be sure to only add x forces to x forces,
and y forces to y forces. Third, solve the equations
for the desired quantity(ies).
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The sum of the forces is always equal to the
Net Force. This is the single "leftover" force that acts on the object
in the direction under consideration. If there is a non-zero net
force, it is equal to ma (Newton's Second Law), and the object accelerates
in the direction of the net force. A non-zero net force causes acceleration.
The net acceleration is what the thing is observed to do. If the
net force is zero, the object either remains at rest or moves at constant
velocity.
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