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Today’s Lectures:
The Laws of Gravity
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Speed, velocity, acceleration, force
Mass, momentum and inertia
Newton’s three laws of motion
The Force of Gravity
Assigned Reading
• Chapter 5.1
Before Newton
• Kepler understood the phenomenology of
planetary motions, I.e. the three laws, but
never understood *why* planets move the
way they do
– He thought of magnetic force from the Sun
– He even thought (and dismissed) that Angels pull
planets along their orbits
• Galileo understood inertia, force and
acceleration very well, but fell short of
understand the causal relationship between
force and acceleration. He also did not
propose a universal law for the force of
gravity
Describing Motion
• Motion is when the position of an object
changes in time
• If position does not change, the object is
at rest
• The describe motions we need to monitor
position and time
• The rate at which an objects covers a
given amount of space in a given amount of
time is called speed
–
v = s/t
Vectors,
or things with a sense of
direction
• There are physical quantities in nature for
which only one number, their intensity,
tells the whole story: e.g. temperature,
mass, luminosity, color
• Other quantities need both an intensity
and a direction to be fully described: e.g.
speed, force, acceleration.
• These quantities with a “direction” are
called VECTORS
Galileo and the Concept of Inertia
Aristotle held that objects at rest remained
at rest unless a force acted on them, but
that objects in motion did not remain in
motion unless a force acted constantly on
them: F = v
WRONG.
Galileo concluded that an
object in a state of motion
possesses an ``inertia'' that
causes it to remain in that
state of motion unless an
external force acts on it
RIGHT.
Galileo’s Law of Inertia
• But velocity cannot not the whole story: we
need a more general concept to describe
motions: momentum
P = m·v
• An object maintains its “quantity of
motion” (momentum), unless a force is
acted upon it
• Only a force can change the “quantity of
motion” (momentum) of an object, either
by changing its speed, or by changing its
direction of motion, or both
Sir Isaac Newton and the
Unification of Physics & Astronomy
• Newton was by many standards the
most important figure in the
development of modern science.
• He demonstrated that the laws
that govern the heavens are the
same laws that govern the motion
on the surface of the Earth.
• Newton's Three Laws of Motion.
• Theory of Universal Gravitation
(1642-1727)
Newton’s First Law
(really, Galielo’s Inertia Law)
• In the absence of a net force, an object
moves with constant velocity, or it conserves
its momentum.
• (paraphrased) If nothing acts on an object,
the object will keep moving in a straight line
and at a constant speed.
• The same is true for zero velocity.
There must be a force acting
on the apple. What force?
More importantly, if the
force of gravity reaches to
the tree, might it not reach
even further; in particular,
might it not reach all the way
to the orbit of the Moon!
Vocabulary Words
• Speed is the distance traveled in each
second – it’s measured in meters per
second (m/s).
• Velocity is the speed in a particular
direction – it’s measured in meters per
second (m/s).
• Acceleration is the change in velocity in
each second – it’s measured in meters per
second per second (or m/s2)
Acceleration
• An acceleration is a
change in velocity.
• Acceleration occurs when
either the magnitude or
direction of the velocity
(or both) are altered.
• Uniform Circular Motion
is Accelerated Motion
How many ways can your car be accelerated?
Newton’s Second Law
• Acceleration is caused by force but also
related to the mass of the object
Force = Mass x Acceleration
F = m·a
Or
a = F/m
The gravitational force on an object near
the surface of Earth is:
Fgrav = m·g
(g = 9.8m/s2)
Question: How do objects accelerate due
to the force of gravity?
Newton’s Third Law
• For every ACTION (I.e. application of a
force) there is an equal and opposite reACTION
F1 = -F2
Newton’s Third Law
For any force, there always is an equal and
opposite reaction force.
Box pushes down
on table due to gravity.
Table
pushes
back on
box
Example: The Jet Engine
• What makes a jet-propelled airplane move
forward?
Gravity
• What force is responsible for motions in the
universe?
• What force makes objects fall?
• What keeps us on the rotating Earth?
• Why don’t planets move in straight lines, but
orbit around the Sun instead?
Gravity
• We can summarize the universal law of
gravitation with the following statements:
– Every mass attracts every other mass through the
force of gravity.
– If mass #1 exerts force on mass #2, and mass#2
exxerts force on mass#1, the force must depend o
both masses, namely:
– The force of attraction is directly proportional to
the product of the two masses.
– The force of attraction is inversely proportional to
the square of the distance between the masses.
The Law of Gravity
Near Earth’s
surface
M 1M 2
Fg  G
2
d
Fg  gM 2
G = 6.67x10-11 m3/kg/s2
M1
g G 2
d
2
 9.8m/s
d
M1
M2
Mass and Weight
• Mass is a measure of how much material is
in an object.
• Weight is the force exterted by gravity on
a massive body (body with mass), e.g.
placed on the surface of Earth
• Weight is a measure of the gravitational
force exerted on that material.
• Thus, mass is constant for an object, but
weight depends on the location of the
object.
• Your mass is the same on the moon, but
your weight on the surface of the moon is
smaller
M 1M 2
Survey Question Fg  G d 2
Two equal masses, m, separated by a distance,
d, exert a force, F, on each other due to
their gravitational attraction. How large is
the gravitational force between an object of
mass m and an object of mass 2m separated
by the same distance d?
¼F
½F
F
2F
4F
M 1M 2
Survey Question Fg  G d 2
Two equal masses, m, separated by a distance,
d, exert a force, F, on each other due to
their gravitational attraction. How large
would their gravitational attraction be if the
distance between them was doubled?
1) ¼ F
2) ½ F
3) F
4) 2F
5) 4F
… so why don’t planets just fall
into the sun?
M1
M2
… because they miss (that is, they
have enough tangential velocity to
always miss)
v
Fg
Fg
M1
This is the concept of an orbit.
M2
Why doesn't the earth fall to
the sun?
• It has a velocity
and it has
inertia!
• Force of gravity
causes change in
the direction of
velocity --acceleration.
• The earth is
falling towards
the sun all the
time!
V=8km/s
Why don't they fall?
They are circuling Earth at a speed of 8 km/s!