ARISTOTELIAN PHYSICS
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Aristoteles (Aristotle) (384-322 BC) had very strong influence on
European philosophy and science;
n
everything on Earth made of (mixture of) four elements: earth, water,
air, fire
n
every element has a “natural place”:
u
earth at center of Earth,
u
water above earth,
u
air above water,
u
fire above air;
n
celestial bodies (stars, planets, Moon) made from fifth element, “ether”,
which also fills space between them; ether is perfect, incorruptible,
weightless;
n
two kinds of motion of things on Earth: “
natural
” and “
violent
” motion
n
natural motion
: things tend to move towards their natural place - natural
motion happens by itself, needs no push/pull (e.g. stone falls).
n
violent motion
: = motion contrary to natural motion; needs effort
(external push or pull)
n
celestial motion
= natural motion of ether;
natural motion of bodies made from ether is circular motion, regular and
perpetual
Problems with aristotelian physics:
●
Galileo Galilei's thought experiments and real experiments:
n
falling bodies:
u
according to Aristoteles, heavy bodies (contain more earth element)
fall faster than lighter bodies
u
observation: fall equally fast if they have same shape and size
u
Galilei: difference in speed of differently shaped falling bodies due
to air resistance
n
thought experiment about two falling bodies - “
reductio ad absurdum
”:
u
consider two bodies, one light (L), one heavy (H)
Aristoteles: L falls more slowly than H
L put under H should slow
down fall of H;
H with L under it should fall more slowly than H
alone; but (L + H) heavier than H alone
should fall faster than H
alone
contradiction.
n
pendulum: ball suspended on string reaches same height as that to which
it was lifted to set it in motion (not quite; - due to friction);
height independent of path (pendulum with shortened string)
n
ball rolling on inclined plane:
u
ball rolling down inclined plane speeds up;
u
ball rolling up slows down; rate of slowing down depends on
steepness of incline: less steep
longer distance travelled;
extrapolation to zero slope of incline: ball will go on forever
GALILEI'S NEW SCIENCE
●
Galileo Galilei (1564 - 1642) -- founder of modern science;
n
new methods introduced by Galilei include:
u
controlled experiments designed to test specific hypotheses
u
idealizations to eliminate any side effects that might obscure main
effects
u
limiting the scope of enquiry - consider only one question at a time;
u
quantitative methods - did careful measurements of the motion of falling
bodies.
n
from observations and thought experiments, generalizes to two new laws:
●
LAW OF INERTIA
:
n
without external influence (force) acting on it, a body will not change its
speed or direction of motion; it will stay at rest if it was at rest to begin
with.
n
inertia = property of bodies that makes them obey this law, their ability to
maintain their speed (or stay at rest)
●
LAW OF FALLING
:
n
if air resistance is negligible, any two objects that are dropped together
will fall together; speed of falling independent of weight and material.
NEWTONIAN MECHANICS
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Starting from law of inertia (René Descartes, Galileo Galilei), Isaac
Newton developed a new way of looking at nature.
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Principia Mathematica Philosophiae Naturalis (1687) (Mathematical
Principles of Natural Philosophy):
n
based on a small number of concepts and principles,provide a clear and
quantitative explanation of a vast array of phenomena.
n
give a unification of our view of nature - the first major synthesis of
science
n
explain: motion of bodies on Earth and in heaven (falling bodies, Moon,
planets, comets,...
n
key concepts:
u
velocity
u
acceleration,
u
force
u
inertial mass, gravitational mass
n
key principles:
u
law of inertia (Newton's 1st law of motion)
u
law of motion (forces) (Newton's 2nd law of motion)
u
law of force pairs (action=reaction) (Newton's 3rd law of motion'')
u
law of gravity
FORCE
n
law of inertia: no force
no acceleration;
n
if acceleration - there must be force;
n
we say:
body exerts force on another if it forces the other body to
accelerate;
n
note there is some circularity in this definition, but definition is justified by
its usefulness and predictive power;
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force is not a property of a body;
n
if more then one force acting
effects add
forces add -- “net force”;
n
acceleration is in direction of net force; two or more forces can compensate
(“balance”) each other (e.g. two equally strong forces acting in opposite
directions)
n
kinds of forces:
u
push, pull, shove, kick, tap
u
friction, air resistance
u
gravity
u
electric
u
magnetic
n
Aristotelian view
:
forces cause velocity
(force necessary to maintain uniform motion).
n
Newtonian view
:
forces cause acceleration
(force necessary to change motion)
Forces,
Newton’s
2nd law
●
Observations:
n
stronger force
larger acceleration
n
more “massive” object
smaller acceleration
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apply more than one force
net force determines acceleration
n
inertia = resistance of object against being accelerated;
(inertial) mass = measure of amount of inertia,
observed to be proportional to amount of matter -- set them equal;
n
unit of mass = kilogram = kg (original definition: = mass of 1 liter of water)
●
observations can be summarized by:
Newton's 2nd law:
F = k m a
n
k = proportionality constant; by choice of units, can make k = 1
n
note that F, a are vectors, and acceleration a is in direction of force F
n
unit of force = newton; 1 newton = 1 kg m s
-2
n
in English system: unit of force = pound = 4.448 N
n
note: the mass m in Newton's 2nd law is the “inertial mass”
●
weight vs mass:
n
mass of object = quantity of its inertia;
n
weight of an object = net gravitational force on an object; depends on
environment;
n
our weight on the Moon is 1/6 of that on the surface of the Earth;
n
our weight on a high mountain is smaller than at sea level;
n
our weight in a satellite in orbit around Earth = 0;
n
our mass is always the same.
Newton’s 3rd law (Law of force pairs - action and reaction)
•
“actio = reactio'’
n
when a body exerts a force on a second body, the second body exerts an
equally strong force on the first body, directed opposite to the first force;
●
examples:
n
apple and Earth:
u
Earth exerts force on apple
apple exerts force on Earth;
u
Earth's large mass
Earth's acceleration very small
n
book on table: 2 pairs of forces:
u
Earth exerts gravitational force on book, book exerts gravitational force
on Earth.
u
book exerts force (= its weight) on table; table exerts equal and
opposite force on book (“contact force”, “normal force”)
u
net force on book = 0
book stays at rest on table (does not fly away,
does not fall through table)
u
(contact force caused by interaction of electrons in atoms of book with
those in table)
n
walking: exert force on ground
ground exerts force on you;
rowing, driving, recoil of a gun, rocket propulsion
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Note:
n
Newton’s 3rd law closely related to
momentum conservation