Transcript PowerPoint Presentation - 5. Universal Laws of Motion

Sir Isaac Newton
and Astronomy
Newton, as he
appeared on the last
day of his life, in
1727. He was born
the year Galileo died
(but no, not the same
day).
Describing Motion:
Examples from Daily Life
Structure your notes—these are the goals:
• Distinguish between speed, velocity, and
acceleration.
• What is the acceleration of gravity?
• How does the acceleration of gravity
depend on the mass of a falling object?
Objects in Motion
Objects in motion can be
described as possessing…
• speed – rate at which an object moves i.e.,
the distance traveled per unit time [m/s;
mi/hr]
• velocity – an object’s speed in a certain
direction, e.g. “10 m/s moving east”
• acceleration – a change in an object’s
velocity, i.e. a change in either speed or
direction is an acceleration [m/s2]
The Acceleration due to
Gravity
As objects fall,
they accelerate.
The acceleration
due to Earth’s
gravity is 10 m/s*
each second, or
g = 10 m/s2.
The higher you
drop the ball, the
greater its velocity
will be at impact.
*ok, it’s really 9.8 m/s, we’ll
use 10 and note the lowercase g
The Acceleration of Gravity (g)
Galileo demonstrated that g is the same for all objects,
regardless of their mass!
This was confirmed by the Apollo astronauts on the
Moon, where there is no air resistance.
Apollo 15 landed and
performed the experiment
Galileo could only do in his mind.
Forces
Forces - change the motion of objects.
momentum – the (mass x velocity) of an object
force – anything that can cause a change in an object’s
momentum
As long as the object’s mass does not change, the force
causes a change in velocity, or an…
a brief note about force(s)…
Whenever you see this f-word used in a scientific context,
you should toggle the same mental switch you would for the
word theory. That is, a force is anything that causes a push
or a pull on objects. This action results in a change of
motion and a change in position.
Let’s also take the opportunity to introduce the scientific
symbol for change. It is the Greek letter, delta or Δ. Thus, a
change in velocity would be written as Δv.
Is Mass the Same Thing as
Weight?
mass – the amount of matter in an object
weight – a measurement of the force which acts
upon an object
Recall Kepler's Laws:
Kepler's First Law:
Each planet’s orbit around
the Sun is an ellipse, with the
Sun at one focus.
Kepler's Third Law: The squares of
the periods of the planets are
proportional to the cubes of their
semi-major axes:
Kepler's Second Law: Line
joining planet and the Sun
sweeps out equal areas in equal
times
p2 = r3
Newton’s Laws of Motion
Our goals for learning:
• What are Newton’s three laws of
motion?
• Why does a spinning skater spin
faster as she pulls in her arms?
Sir Isaac Newton (1642-1727)
Perhaps the greatest
genius of all time
Invented the reflecting
telescope
Invented calculus*
Connected gravity and
planetary forces
Philosophiæ
Naturalis Principia
Mathematica
*ok, ok, here you go…
Newton: Laws of Motion
1 A body at rest or in motion at a
constant speed along a straight line
remains in that state of rest or motion
unless acted upon by an outside force.
Newton’s Laws of
Motion
2 The change in a body’s velocity due to
an applied force is in the same direction
as the force and proportional to it, but
is inversely proportional to the body’s
mass.
F/ m = a
F=ma
Newton’s Laws of
Motion
3 For every applied force, a
force of equal size but opposite
direction arises.
Newton’s Laws of Motion
© 2004 Pearson Education Inc.,
publishing as Addison-Wesley
Angular Momentum
angular momentum – the momentum involved in
spinning /circling = mass x velocity x radius
torque – anything that can cause a change in an
object’s angular momentum (twisting force)
Conservation of Angular Momentum
In the
absence of a
net torque,
the total
angular
momentum
of a system
remains
constant.
The Force of Gravity
Our goals for learning:
• What is the universal law of
gravitation?
• What types of orbits are possible
according to the law of gravitation?
• How can we determine the mass of
distant objects?
Newton’s Universal
Law of Gravitation
Isaac Newton discovered that it is
gravity which plays the vital role of
determining the motion of the planets concept of action at a distance.
…and seriously freaked some people out.
So, what was gravity?
For Newton’s contemporaries, it seemed a very
troubling prospect, almost like a form of “magick”.
How could the action of one physical body affect
another without them ever touching?
Still, it became a law. Scientific laws tell us what
nature will do given certain variables. A law also
implies that you will get the same answer every
single time you run the experiment or conduct the
observation.
Every. Single. Time.
What about the theory of
gravity?
Theories tell us why something happened. A theory will
explain the essential nature of the phenomena being
investigated.
Laws are the rules by which theories operate.
"Two objects always attract in direct proportion of their
masses and in inverse proportion of the square of the distance
between them."
Newton’s Universal Law of
Gravitation
Between every two objects there is an attractive
force, the magnitude of which is directly
proportional to the mass of each object and
inversely proportional to the square of the distance
between the centers of the objects.
Newton’s Universal Law of
Gravitation
G=6.67 x 10-11 m3/(kg s2) this is the value of G, the
gravitational constant. We call it “Big G.” Little g is for the
pull of gravity on a particular planet or mass.
On Earth, g = 9.8 m/s2 On the Moon, g = 1.6 m/s2 On Jupiter,
if there were a solid surface you could stand on, you would
experience g as 21.9 m/s2. This extra force would turn your
100 lbs into 236 lbs.
Why is there a need for G?
Short answer, no one knows but it is found in physical
science where there is a constant of proportionality (such
as here, inverse-square) between phenomena.
It makes each side of the equation equal.
The actual value would be determined by Cavendish
some 80 yrs after Newton’s death. Physicists are still
fine-tuning their understanding still today.
•How does the acceleration of gravity depend
on the mass of a falling object?
•It does not. All falling objects fall with the same
acceleration (on a particular planet).
•Now see why…
•F = ma and on Earth acceleration due to gravity denoted
“g” so F=mg or g=F/m
•If mass of earth is ME then Fg=GMEm/d2
•mg=GMEm/d2
g=GME/d2
To summarize,
•Every mass attracts every other mass through the
force called gravity
•The strength of the gravitational force attracting any
two objects is proportional to the product of their
masses
•The strength of gravity between two objects
decreases with the square of the distance between
their centers