Newton and After. Law of Universal Gravitation F ~ 1/r² ratio of acceleration apple:moon = 3600 moon is 60 times farther from center of earth F = mg on.

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Presentation transcript:

Newton and After

Law of Universal Gravitation 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 Third Law: If the earth pulls the moon, then moon pulls the earth F ~ m 1 m 2 / r² Using calculus he showed The path of a planet is an ellipse That the square of the period (T) of the orbit was proportional to the cube of the radius. (semi-major axis) 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. F 1 /F 2 = (r 2 /r 1 ) 2

Eighteenth Century The size of solar system Parallax Transit of Venus Henry Cavendish ( ) – Discovered hydrogen Solved F = G m 1 m 2 / r² for G: 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. moon =.5°

Vis Viva Sometimes the Math Knows 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 0 ²) F ∙ s = ½ m(v f ²-v 0 ²) W = ½∙mv f ² - ½∙mv 0 ² Work = Δ ( ½ mv² ) = change in (vis viva) Work = Δ KE = change in kinetic energy

Watt and Joule 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.”