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The Sun produces heat and
light for our solar system by use of all four of the fundamental
forces in nature. Gravitational forces compress the gases
to very high pressures and temperatures at the Sun's center. This
makes it possible for strong nuclear forces to produce
energy from nuclear fusion at the core. Weak nuclear forces
are responsible for much of the energy production that actually
reaches the surface. Finally, electromagnetic radiation
transfers this energy to other bodies in the solar system and beyond.
Typical usage of the word force underscores the need to rely on
definitions with mathematical descriptions or with prescriptions for
measurements that can be associated with the definition in order to
avoid ambiguity.
Physics Lecture 3
In the usual discussion of physics, we would progress quickly from the topic
of kinematics which explains how things move to
dynamics which
explains why things move the way they
do. In mathematics, the essence of dynamics is extremely simple as we shall
see. In natural philosophy, things are not so easy. Some tenets have to be
accepted on faith simply because they work. The great genius of Galileo and
Newton is that they were able to separate out philosophical concerns about
the ultimate source of motion from the practical aspects of dynamics and
thereby make a tremendous leap. This sounds mystical so we need to illustrate
by simply presenting the arguments of Newton (which were founded on the ideas
of Galileo). The considerations are:
- Friction is everywhere - hence to get at the ultimate description of
motion, we have to idealize to a point where no friction is acting.
If we can do this, we quickly see that motion is just as natural for
an object as the lack of motion. In other words, we mostly see
things at rest because of friction. In a frictionless world, most
things would be in constant non-accelerated motion. Hence, we conclude
that the motion of any object is constant unless it is acted
upon by some other object. Exactly what ``acting upon'' means is left
undefined for now.
- To ``act upon'' an object is to change the motion of that object. This
requires an effort. Some objects
require more effort to change their motion than others. We call the
resistance to change in motion inertia. We notice
that objects with the most inertia also weigh the most.
- For any object (say object 1) to ``act on'' another object (object 2),
that object (object 1) must be ``acted upon'' by object 2.
For Newton, Galileo's observation of the first point is logically clear and
unassailable. An object changes its motion only in response to some action
from outside acting upon it. This would be obvious in a frictionless
world. The third item also makes sense. Any object that acts on another must
itself experience something during the interaction. Its not possible to
punch a wall without feeling the wall hit back. The second item was more
troublesome. It was difficult to think of the meaning of ``acted upon'' in
any way which leads to the conclusion of absolute knowledge of what
causes motion (e.g. a ball moves because you kick it, your leg kicks because
of muscles, your muscles move because of ...? There is no obvious endpoint in
this logical chain!). Many philosophers were stumped and ended their
progress here.
Newton recognized, after much thought, that there was no need to
have an ultimate answer of why motion occurs if you just wanted to make
progress in describing motion. He reasoned that whatever the ultimate
cause of motion may be (will of man, natural magic, force of God, etc.),
its net result is mathematically well-defined and
that the mathematical definition is both repeatable and predictive.
It therefore satisfies the criteria of being a scientific law. The ideas
above then lead to his three famous laws of motion:
- Due to the connection between weight and inertia, it makes sense to
``identify'' mass as being the measure of inertia.
- The change in motion of an object is due to the net external
force acting upon it. The description of this change,
as Newton described it is:
where the arrows indicate that the direction of the force,
,
is the same as the direction of the change in mass times velocity
with respect to time. If the mass of the object is constant in time,
then we get the more familiar formula
To specify a force you MUST have 3 pieces of
information: direction, magnitude, and the object upon which the force acts.
- The force that an object A exerts on another object B must
always appear in conjunction with an equal
magnitude, opposite direction force of B acting on A. In mathematical
form, we express this as
This statement says that force from A on B is equal and opposite to
the force from B on A.
It is difficult to believe, but these three laws, along with the defintions
of acceleration, velocity, and displacement, summarize everything of relevance
about motion involving speeds much less than the speed of light and particles
much greater in size than atomic dimensions.
In some sense, since the laws are a prescription for describing motion,
they cannot be ``violated''. Whenever we see an object change its motion we
infer that there must be a force acting on it, even if we cannot see the
source of that force ...
Before discussing how to solve problems involving forces, we first need to
catalogue the various forces we see in nature. Although there appear to
be a nearly infinite variety of forces around us, ultimately physicists
recognize only 4 fundamental forces in nature. These
are:
The Strong Nuclear Force - operates only over distances less than
about 10-15 meters. It holds protons and neutrons together
to make nuclei and is responsible for nuclear fusion and fission.
The Electromagnetic Force - responsible for all electrical and
magnetic phenomena, holds electrons in orbit around protons to
make atoms, atoms together to make molecules, etc.
The Weak Nuclear Force - operates only over distances of nuclear
dimensions. It is responsible for radioactive decay.
The Gravitational Force - responsible for ``weight'', holds the
planets in orbit around the Sun, the Sun in orbit around the
center of the galaxy, etc.
The fundamental forces are listed in order of their strength. Only the
electromagnetic and gravitational forces are readily apparent to us because
they have essentially infinite range whereas the nuclear forces (weak and
strong) operate only over ranges far less than those we normally see.
All other forces we observe are really manifestations of the electromagnetic
force. When you press your hand against your desk, you feel the repulsion
of the electrons in the atoms of your hand against the electrons in the atoms
of the desk. Friction is due to repulsive forces operating on microscopic
scales. Stretch a rubber band and you feel the attractive electromagnetic
forces between molecules in the rubber. Light, radio waves, and heat are
all manifestations of the electromagnetic force.
For freshman physics, you will only be responsible for knowing the nature
of a few of the many different forms of the electromagnetic force and
the gravitational force. We briefly list them here:
- Gravitational force - the force exerted by any massive body on another
massive body. Typically we talk about the gravitational force of
the earth on objects near its surface. In this case,
,
where the direction of acceleration,
,
is always straight down towards the center of the earth.
- Spring forces - if you compress or stretch a spring, the force
exerted by the spring is
.
The minus sign
indicates that the direction of the force is opposite to the
direction of pull or push on the spring. If you stretch the spring,
it pulls against the stretch. If you compress the spring, it pushes
against the compression. The constant k is called the spring
constant. It characterizes the strength of the spring by indicating
how much force you get for a given displacement of the spring from
its normal or equilibrium shape.
- Normal forces - these are the reaction forces that result from contact
between two objects. If you lay a book on a table, the force of
gravity pulls the book downward. The book, in turn, presses against
the table. This is the normal force of the book
on the table. By Newton's Third Law, the table has to have a reaction
force which presses against the book. The reaction force is called
the normal force of the table on the book. Any two objects in contact
have normal forces acting between them. Normal forces are always
directed perpendicularly away from the surface which exerts
the normal force.
- Tension - this reaction force is the force of a string or rope on an
object to which the string or rope is attached. The direction of
the tension is always along the rope or string and away from
the surface of the object to which the rope or string is attached.
NOTE: It is important to remember that we always assume a
non-stretching string or rope (unless explicitly told otherwise) so
that the magnitude of the tension is constant along the
string or rope. This enormously simplifies the mathematics of
using the tension by adding important constraints to the solution
of the problem. One of the most important constraints is that the
length of the string or rope is constant.
- Friction - these forces always resist the motion occuring or the
motion that would occur if friction were not present. If we have
time, we will discuss the specific cases of friction later in this
course.
Do problems 2-22
and 2-23.
Next: Force Revisited
Up: DESCRIBING HOW THINGS CHANGE
Previous: The Growth of Populations
The Sun produces heat and
light for our solar system by use of all four of the fundamental
forces in nature. Gravitational forces compress the gases
to very high pressures and temperatures at the Sun's center. This
makes it possible for strong nuclear forces to produce
energy from nuclear fusion at the core. Weak nuclear forces
are responsible for much of the energy production that actually
reaches the surface. Finally, electromagnetic radiation
transfers this energy to other bodies in the solar system and beyond.