Announcements

1
Announcements

• First quiz will be given on 26 February
• Review on 24 February
• HW 5 will be posted this eve due 24 February
• HW 4 due this Thursday, 19 February

2
Spectacular News this week!

• First DNA first draft (63) of a Neanderthal,
  our closest relatives!
• Using bones from Croatia, they find that
  Neanderthals share 99.5-99.9 of our DNA
  sequence.
• Neanderthals share the same mutation of the
  FOXP2, the language and speech transcription
  factor unlike chimps, our closest living
  relative.
• No evidence for interbreeding of modern humans
  and Neanderthals.
• Archeology indicates that Neanderthals became
  extinct 30,000 yrs ago.
• Their DNA indicates that their evolution branch
  split from ours 300,000 yrs ago.
• Can they be cloned? Highly debateable.

- NY Times
3
Newtons Laws of Motion

• An object remains at rest or in constant velocity
  unless acted on by a force.
• Force equals mass times acceleration
• Each action has an equal and opposite reaction.

4
In-class Assignment
Behavior of all things F ma Circular motion
of constant speed a v2/R Speed distance /
time v 2? R / P Substitution a v2/R
(2? R / P)2 / R 4 ?2R / P2 Use Keplers Law
P2 k R3 a 4 ?2 / kR2
Brahes observations as interpreted by Kepler
indicate
The force experienced by planets is proportional
to their distance to the sun squared. F C/R2
5
Philosophy Inverse Square Law
At R2 the light is spread out over 4 times the
area, so it is 4 times less intense. At R3 the
light is spread out over 4 times the area, so it
is 9 times less intense. The intensity of light
depends dims by 1/R2 just like gravity
Area 4 ? 1
Area 4 ? 4 4 times bigger
Area 4 ? 9 9 times bigger
The area of a circle is Area 4 ? R2
6
What if the Sun was emitting particles
The number of particles reaching say a planet
falls off as 1/R2 too! Maybe light and gravity
is just made up of particles
7
Galileos inclined plane experiment
Objects fall with a nearly constant acceleration
with height. Thus they experience a nearly
constant force. (F ma) Objects fall with the
same acceleration regardless of mass. The force
is such that F/m constant.
Keplers laws
The force experienced by planets is proportional
to their distance to the sun squared. F C/R2
Newtons hypothesis
The force that makes objects fall is the same
force that causes planets to orbit the Sun.
8
Newtons Law of Gravity

• All bodies exert a gravitational force on each
  other.
• The force is proportional to the product of their
  masses and inversely proportional to the square
  of their separation.
• F GmM/R2
• where m is mass of one object, M is the mass
  of the other, and R is their separation.
• G is known as the constant of universal
  gravitation.

9
Gravity
F m1a
m1a
10
Motion of a planet around a star
11
A planet in circular orbit
Cancel out m1 v2/r Gm2/r2
Multiply both sides by r v2 Gm2/r
The speed of the planet depends on the mass of
the Sun and the planet-Sun distance in a precise
way.
m1 planets mass, m2 Suns mass, r
planet-Sun distance, v speed of planet
12
Derivation of Keplers 3rd Law

• Begin with Newtons law a GM/r2
• We assume a circular orbit a v2/r
• Velocity of planet v 2pr/P
• Velocity of an object in circular motion about a
  mass, M, a distance r away
• v2/r GM/r2
• v2 GM/r
• Thus (2pr/P) 2 GM/r
• And r3 / P2 GM/4p2
• Which is a constant.
• It equals 1 for our Sun in units of year AU.

13
Newton Explains Galileo
1. The acceleration does not depend on m!
Bodies fall at the same rate regardless of
mass. 2. Bodies fall with constant acceleration
with height
14
Next Class

• We calculate the motion of bodies in motion on
  Earth. We will be able to calculate the speed and
  position (with time) of an apple as it drops from
  a tree. After a lot of examples of Newtons
  ideas, we begin a new topic, and define energy
  and power.