Download Science of Motion

Science of Motion
• Early Ideas (Greeks)
• Galileo
• Newton
©2013 Robert Chuckrow
Ancient-Greek Ideas
1. The earth is the center of the universe.
2. The earth is spherical.
3. The earth neither rotates nor moves.
4. The heavier an object is, the faster it falls.
5. It takes a force to keep an object in motion.
1. Ancient Greeks Thought that the Earth
is the Center of the Universe.
They thought that the sun, moon, planets, and stars
circle the earth once per day. We now know that (a) a
force toward the center is required for an object to
move in a circle, and such a large force could not be
supplied; and (b) the stars are so distant that they
would be moving faster than the speed of light, which
is impossible.
2. Ancient Greeks thought that the
earth is spherical.
Ancient Greek scientists correctly thought that the
earth was spherical because: (a) During an eclipse of
the moon, the shadow of the earth is always circular
whether the moon is on the horizon or overhead. (b)
Ships leaving port were seen to disappear below the
horizon. (c) Rays from the sun to the surface of the
earth at different latitudes are at different angles at
the same time of day. Eratosthenes used this fact to
measure the circumference of the earth in 250 B.C.
3. Ancient Greeks thought that the
earth neither rotates nor moves.
The Greeks Incorrectly Thought the Following:
• If the earth were not stationary, there would be huge
winds.
• If the earth were not stationary, a dropped object
would not fall directly to earth but slantingly to the
side, opposite to the earth’s motion.
• A huge force would be required to keep the earth
moving.
4. Ancient Greeks thought that the heavier
an object is, the faster it falls.
Aristotle (384 BC–322 BC), who espoused this
incorrect idea, believed in the power of the mind and
logic and did not think that statements needed to be
physically tested. Today, it is understood that air
resistance (friction), which often affects lighter objects
more than heavier ones, determines the rate of
falling. Aristotle did not understand friction.
5. Ancient Greeks thought that a force is
required to keep an object in motion.
The Greeks did not understand friction, which slows
down moving objects, so when friction is present, a
force is required to keep an object moving. We now
know that in the absence of friction (nearly so in the
case of the motion of the earth), no force is required
to keep an object moving. Actually, a force toward the
center of the circular motion (the gravitational force of
the sun) is required to prevent the earth from moving
in a straight line.
Galileo (1564–1642)
Galileo’s Discoveries
• By dropping different masses off the Leaning Tower of Pisa,
Galileo discovered experimentally that all bodies fall at the same
rate in the absence of friction.
• Using a telescope, he discovered four of the moons of Jupiter.
• He discovered that an object will move at constant speed in a
straight line in the absence of a force.
• Using a telescope, he also discovered and observed sun spots
and mountains on the moon.
• He studied pendulums and used them in timing experiments.
• He espoused the idea that the earth revolved around the sun
rather than that the sun revolved around the earth. He was
forced to recant this belief by the Church and spent his
remaining years under house arrest.
Galileo’s Thought Experiment
In the late 1500s, people still believed Aristotle’s idea of using
logic and rejecting experimentation. Consequently, they were
not interested in Galileo’s demonstration of dropping masses off
the Leaning Tower of Pisa. Therefore, he came up with the
following thought experiment: Imagine dropping two masses of
different weights, joined by a string. The combination is heavier
than the heavier weight, so it should fall even faster than the
heavier weight. But if it is true that the lighter weight falls more
slowly, it will act as a drag on the heavier weight and cause it to
fall more slowly. That means the combination will fall more
slowly than the heavy weight. Thus, the idea that the heavier a
weight is, the faster it falls leads to a contradiction.
Light and Heavy Falling Bodies: A Contradiction
Galileo’s Discovery of Mountains on
the Moon
Galileo looked at the moon through his telescope and
saw irregularities in its surface. When he tried to get
others to look through his telescope, they refused,
saying, “There can’t be mountains because all
heavenly bodies must be perfect spheres.” When
they finally saw the mountains, they proposed an
invisible, perfectly spherical spherical surface
extending beyond the mountains (non-verifiable). In
turn, Galileo proposed even-larger invisible
mountains resting on the perfectly spherical surface
(two can play the same game).
How Galileo Dealt With those who
Proposed an Invisible Spherical Surface
Galileo’s Thought Experiment
Involving Rolling Bodies
Galileo’s Principle
A body moving on a level surface will continue in the
same direction at constant speed unless disturbed.
Galileo’s principle contradicts the Aristotelian view
that a force is necessary for keeping an object
moving.
Newton (1642–1726)
Newton’s Discoveries
Newton adopted Galileo’s principle and expanded it
(Newton’s three laws of motion). Also, Newton
mathematically explained the motion of the planets
(their elliptical motion around the sun and the nature
of gravity), provided a theory of gravitation,studied
lenses and came up with a system of analyzing their
properties, and studied light and found a way of
demonstrating the wave aspect of light (he didn’t
believe that light could act like a wave but thought
that light consists of particles—another aspect of
light).
Newton’s First Law
In the absence of a net force, if a body is at rest, it
will remain so, and if a body is moving, it will continue
to move at constant speed in a straight line. (Thus if a
body is at rest, there is no force on it or, if there are
multiple forces, they add to zero.
In the above example, the net force on the 2-kg
block would be 12 – 4 = 8 Newtons to the right.
Can you guess the tension in each
string?
Newton’s Second Law
If a force F acts on a mass m, it will have an
acceleration* a given by the equation F = ma. The
acceleration is always in the same direction as that of
the force.
If more than one force acts on a mass, its acceleration is given by the equation F = ma, where F is
the net force.
*Acceleration is defined as an object’s change in
speed divided by the time for that change.
Can you guess the tension in each
string?
Newton’s Third Law
If object A exerts a force on object B, then B will exert
an equal and opposite force on A. Note that action
and reaction are (a) always equal and opposite, (b)
never on the same body, and (c) always of the same
type of force (electrical, gravitational, or nuclear).
An Example of Newton’s Third Law
Consider the situation below:
(a) The force of the hand on the eraser is equal
and opposite to that of the eraser on the hand.
(b) The force of the table on the eraser is equal
and opposite to that of the eraser on the table.
(c) The gravitational force of the earth the on the
eraser is equal and opposite to that of the eraser
on the earth.
Conditions for Action and Reaction
For two forces to be an action-reaction pair,
the following four conditions must all hold:
1.
2.
3.
4.
The two forces must be equal and opposite.
The two forces cannot be on the same object.
The two forces must be of the same type (gravitational,
electrical, or nuclear).
If one force is removed, the other force must also disappear.
Why are the two forces below not action and reaction?
The downward gravitational force of the earth on the eraser
and
The upward force of the table on the eraser.
1.
2.
3.
The downward gravitational force of the earth on
the eraser and the upward force of the table on the
eraser are equal and opposite (why?). However,
they are not an action-reaction pair for three
reasons:
The force of the table on the eraser is electrical, not
gravitational.
If the table were removed, gravity would still act on
the eraser (it would fall to the ground).
Both of these forces are on the same object!
Question:
What is the reaction to the gravitational force on the
eraser?
Answer:
The reaction to the gravitational force on the eraser is
the gravitational force of the eraser on the earth.
Question:
If the gravitational force of the earth on the eraser is
equal in magnitude to the force of the eraser on the
earth, then why don’t we see the earth and the eraser
move toward each other the same distance when the
eraser is released and allowed to fall?
Answer:
Whereas the forces are the same, the mass of the
earth is very much greater than that of the eraser.
Consider the equation F = ma for each object: For a
given force, the larger the mass, the smaller the
acceleration. The earth has a much larger mass than
the eraser and, therefore, a much smaller
acceleration. Thus, any movement of the earth is
unobservable.