Forces I
Introduction to Force
Up to now, we have been studying kinematics, which is the quantification of motion without any
consideration of what causes motion to occur. We now move on to dynamics (and statics, a subset)
where we realize that any change in the motion of an object requires an outside influence called a force.
A Brief History of Dynamics
I. Aristotelian Motion
For centuries, humanity’s (at least in Europe) concepts of motion were based on the ideas of
Aristotle (b. 384 BC), a greek philosopher who spent considerable time speculating on all sorts of
subjects, including science, where his ideas were the most basic foundation for the scientific method.
However, he did not prescribe to much of an empirical (or experimental) approach when it came to
physics, as many of his ideas could easily have been disproven with simple experiments. Aristotle
classified motion into two types.
A. Natural Motion
Aristotle was influenced by the Platonic geocentric system in which the earth was the center
of the universe which was comprised of concentric spheres. The four known elements, earth,
water, air and fire each existed within their own spheres, which were arranged in this order.
The natural up or down motion of objects, therefore was due to the object’s innate need to
reach its natural resting place.
For example: a stone, being comprised of earth, falls when dropped so as to return to the
earth sphere. Air bubbles up through water so as to return to its sphere. Fire rises more
aggressively than air as it is naturally found in the furthest sphere. Other objects were
combinations of the 4 elements, for example wood floats on water owing to its composition
of earth and air, similarly, smoke, comprised of air and fire, rises into the air.
The heavens, which were comprised of a fifth element, aither, behaved perfectly, hence
planets and stars moved in a circular motion, which in the minds of the ancient Greeks, was
the perfect shape.
B. Violent Motion
Aristotle conceded that living things could influence the motion of not only themselves, but
also of inanimate objects but imposing a motion upon them and giving them a certain amount
of impetus to move. As such objects moved in a straight line until running out of impetus, at
which point natural motion reasserted itself. For example, throwing a rock would cause it to
move for a time, but it eventually lost its impetus, or desire to move, and then fell back to
earth, its natural resting place.
In general, the Aristotelian view, which was incorporated into the Christian religion, held that the
natural state of motion of objects was to be at rest.
II. Challenges to Aristotelian Motion
Throughout the middles ages, few accomplishments were made in the world of science and the
religious views dominated society in Europe. Debating the Aristotelian system of motion was to go
against the Bible and the Catholic Church, which was very dangerous. As the Renaissance period
approached in the 16th century (or so), various scientists began investigating science again and
slowly chipped away at the Aristotelian system.
A. Copernicus (Polish, 1473 - 1543)
Copernicus realized some flaws with the celestial spheres and geocentrism, partially due to
retrograde motion, in which a planet moves in the opposite direction in the sky, and
advocated, albeit on his deathbed, for a heliocentric model.
B. Galileo (Italian, 1564 – 1642)
Galileo was a true Renaissance man, who pursued many interests including mathematics,
optics, astronomy and physics. Although not the inventor of the telescope, he took good
advantage of its capabilities and observed astronomical phenomenon. He subscribed to a
heliocentric view.
Galileo’s work on motion was accomplished through the use of balls on ramps. He quickly
observed that a ball will roll down an decline and keep rolling up an incline until it reaches
the same initial height. Taking the experiment further, he reduced the incline in angulation
and observed that the length of the ramp did not matter, it was the height was important. He
then extrapolated these findings to the scenario of a ball rolling down a ramp onto a level
surface, and postulated that the ball would roll forever until it could regain its initial height.
He realized that the ball would eventually stop, irregardless, but knew the cause was not due
to a natural tendency of the ball but rather friction, something not considered by Aristotle.
Therefore Galileo effectively dispelled Aristotle’s notion of object naturally being at rest, and
concluded that instead object’s naturally remained doing what they were doing. This concept
in called inertia.
C. Newton (English, 1642 - 1727)
Newton also pondered science and mathematics and was truly able to piece together the
puzzle of motion, gravity and optics (in addition to discovering calculus). He was finally able
to unite the motion of the heavens with motion on earth as following the same set of rules
and realizing that gravity influenced all objects. He formalized these rules into his famous 3
laws of motion.
1st Law: An object at rest will remain at rest; an object in motion will remain in motion with
a constant velocity, unless affected by a net external force.
2nd and 3rd laws to follow.
Forces
A force is any push or pull on an object. There are two types of forces, those which require a contact
between two objects, called a contact force and those which act over a distance, which are called field
forces. Examples of field forces are gravity and electromagnetism.
Forces are measured in Newtons (N) in the SI system and are equivalent to the force required to
accelerate a 1 kg object to 1 meter per second squared.
Forces are vector quantities and the resultant, or net force, on an object must be found from a vector sum
of all forces acting on the object.
Weight is a force due to the pull of gravity on an object. Weight is directed towards the center of the
earth and its magnitue may be found from:
W = mg, where m is the mass of an object and g is the local acceleration of gravity. On earth, g = 9.80
m/s2.