Transcript Aristotle`s Laws of Motion

Aristotle’s Laws of Motion
1. Objects in Motion will
eventually come to a rest.
2. Heavier objects fall
faster than light objects.
Galileo Showed the Error of the
Second Law of Aristotle
When dropped, these
two different masses
will fall with the same
acceleration.
The Error of the First Law was
Corrected by Isaac Newton
If no external forces act on
a moving object, then its
motion will continue on
without changing.
Aristotle’s Mistake was in Not Taking
Into Account the Effect of Friction
An initial push gets this box moving.
It eventually comes to a stop.
On a frictionless surface such as ice, though, it keeps moving.
An Object Weighs Less on the Moon
150 lbs!
25 lbs!
However, the mass is always the same!
The More Mass Something Has, the
Harder it is to Get Significant Motion.
Applied
Force
Same
Applied
Force
Resulting
Velocity
Much
Lower
Resulting
Velocity
Newton’s Second Law of Motion
Takes This Into Account
If a force F is applied to
an object of mass m, a
non-zero acceleration a in
the direction of the
applied force is the result:
a = F/m
If There are More Than Two Forces,
They are Added Together as Vectors
Force 1
Resultant Force due to
Force 1 and Force 2
Mass m
Force 2
The resultant force is the net force acting on the object.
Newton’s Third Law of Motion
For every applied force,
there also occurs a force of
equal magnitude acting in
the opposite direction at
precisely the same point.
Newton’s
rd
3
Law in Action
The force the person exerts on the heavier
boulder is equal in magnitude but opposite
in direction to the force the boulder exerts
on the person--EVEN IF THE BOULDER
IS BEING PUSHED UPHILL!!!
How do we reconcile this?
Force of man on boulder
Force of boulder
on man
Force of ground on man
Force of man on ground
As the man pushes on the ground, the ground responds by
pushing on the man. It is this force that pushes both the man
and the boulder up the hill!
The Universal Law of Gravitation
Near the Earth’s Surface, Gravitational
Acceleration is Nearly Constant
At the top of Mt. Everest,
objects accelerate down
at a rate of 9.78 m/s2
At sea level,
objects accelerate
down at a rate of
9.81 m/s2
The Acceleration Due to Gravity Must
Significantly Decrease With Distance
If it didn’t the Moon would
orbit the Earth once every
hour instead of once a month!
So, What if the Object is Far Away?
acceleration < 9.8 m/s2
Acceleration must drop off as
you get further from the Earth.
By how much does it do so?
Isaac Newton Figured Out the
Force Between Two Masses
It made sense to him that as either one
(or both) of the masses increases, then
the force between both masses would
increase.
It also made sense to him that the
further the separation between the two
masses, the less the force between them.
Newton Had the Information
Provided by Johannes Kepler and
Tycho Brahe to Help Him
Tycho Brahe (1550 - 1605)
Johannes Kepler (1575 - 1624)
Brahe’s Observations and
Kepler’s Calculations Showed
Planets Orbit the Sun in Ellipses
Sun
Mars
(Ellipse exaggerated for clarity--these orbits are actually almost circular.)
From the Results of Kepler and
Brahe, Newton Used His Own
Expectations to Show:
The Force due to Gravity is proportional
to each mass involved, both m1 and m2
The Force due to Gravity is proportional
to the SQUARE of the separation
between the two masses, r.
Gm1m2
F=
r2
G is the “Gravitational Constant of
the Universe”; Newton couldn’t
determine its actual value.