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Foundations-Copernican Revolution
Lecture 4:
Newton: Gravity and the Laws of Motion
Newton (1642-1727)
Kepler's laws were basically playing with
mathematical shapes and equations and seeing
what worked.
Newton's work based on experiments of how
objects interact.
His three laws of motion and law of gravity
described how all objects interact with each other.
Clicker Question:
Why didn’t my hand get crushed by the hammer?
A: My bones are actually stronger than steel.
B: The plate has a lot of inertia
C: The plate is very strong
D: The force of gravity kept the plate from moving
1.4 Newton’s Laws
Newton’s laws of motion explain how objects interact
with the world and with each other.
Newton’s first law:
An object at rest will remain at rest, and an object will
move in a straight line at constant speed if and only if
the sum of forces that act on it are balanced.
Newton's Second Law of Motion
When a force, F, acts on an object with a mass, m, it produces an
acceleration, a, equal to the force divided by the mass.
Fnet
a=
m
or Fnet = ma
acceleration is a change in velocity or a change in
direction of velocity.
Newton's Third Law of Motion
To every action there is an equal and opposite reaction.
Or, when one object exerts a force on a second object, the
second exerts a force on first, that is:



Equal in magnitude
Opposite in direction
Of the same type
Newton's Third Law of Motion
DEMO: CART
DEMO: Force Probes
A.
B.
C.
D.
Cart 1 will exert a larger force on Cart 2 than Cart 2
exerts on Cart 1
Cart 2 will exert a larger force on Cart 1 than Cart 1
exerts on Cart 2
The carts will exert forces of equal magnitude on each
other
Not possible to determine
Newton's Law of Gravity
For two objects of mass m1 and m2, separated by a
distance R, the force of their gravitational attraction is
given by:
F=
G m1 m2
R2
F is the gravitational force.
G is the "gravitational constant".
An example of an "inverse-square law".
Your "weight" is just the gravitational force
between the Earth and you.
1.4 Newton’s Laws
Gravity
For two massive objects,
the gravitational force is
proportional to the product
of their masses divided by
the square of the distance
between them.
1.4 Newton’s Laws
Gravity
On Earth’s surface,
the acceleration due
to the force of gravity
(Newton’s 2nd Law)
is approximately
constant, and
directed toward the
center of Earth.
Falling Objects
DEMO: paper and ball
Movie: Hammer and Feather
1.4 Newton’s Laws
Gravity
The gravitational pull
of the Sun keeps the
planets moving in their
orbits.
Newton’s Laws and Gravity
Massive objects actually orbit around their
common center of mass; if one object is much
more massive
than the other, the
center of mass is not far
from the center of the
more massive object.
For objects more equal
in mass, the center of
mass is between the two.
1.4 Newton’s Laws
Kepler’s laws are a
consequence of
Newton’s laws.
The orbit of a planet around the Sun
has the common center of mass
(instead of the Sun) at one focus.
Escape Velocity
Velocity needed to completely escape the gravity of a planet.
The stronger the gravity, the higher the escape velocity.
Examples:
Earth
Jupiter
Deimos (moon of Mars)
11.2 km/s
60 km/s
7 m/s = 15 miles/hour
Consider Helium Gas at room temperature (300 K)
E = kT = 4.1 x 10-14 erg
E = 0.5 m v2 = 4.1 x 10-14 erg
so v = 1 km/sec on average, but sometimes more