• F ~ 1/r² ratio of acceleration apple:moon = 3600 moon is 60 times farther from center of earth
• F = mg on earth (g=9.8 N/kg)
– On Earth F ~ m
• The Tide
• Every 12.5 hours
• Every day about an hour later
• Complete cycle 24 days  27 days
• Third Law:
If the earth pulls the moon, then moon pulls the earth
• F ~ m
1 m
2
/ r²
• Using calculus he showed that the path of a planet is an ellipse.
F
1
/F
2
= (r
2
/r
1
) 2
Every particle in the universe attracts every other particle with a force that is directly proportional to the product of the masses and inversely proportional to the square of the distance between the particles.

• The size of solar system
• Parallax moon = .5°
• Transit of Venus
• Henry Cavendish
(1731 - 1810)
– Discovered hydrogen
• Solved F = G m
1 for G: m
2
/ r²
• G = F r² / m
1 m
2
• G = 6.67x10
−11 (SI units)
Minilab (prob set 41)
A 1 kg mass feels a force of gravity of 9.8 Newtons at the surface of the earth, The radius of the earth is 6400 km. Calculate the mass of the earth from this data.

• Work = F∙s = mg ∙ (h
2
– h
1
) = mgh
2
– mgh
1
• W = Δ (mgh) = Δ PE = change in potential energy
• F = ma
• 2a∙s = v f
²-v
0
²
• 2ma∙s = m(v f
²-v
• F ∙ s = ½ m(v f
0
²)
²-v
• W = ½∙mv f
0
²)
² - ½∙mv
0
²
• Work = Δ ( ½ mv² ) = change in (vis viva)
• Work = Δ KE = change in kinetic energy

• Newton never knew about “Energy”
• James Watt
(1736 – 1819)
– Improved steam engine
– “Horse Power”
• Heat engines
• James Joule
(1818 – 1889)
– Showed that heat was a form of energy equivalent to mechanical energy
Law of Conservation of Energy:
“Energy can be neither created nor destroyed. It can be transformed.”