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 ~ m1m2 / 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.

F1/F2 = (r2/r1)2

Eighteenth Century• The size of solar system• Parallax • Transit of Venus• Henry Cavendish

(1731 - 1810) – Discovered hydrogen

• Solved F = G m1m2 / r²for G:

• G = F r² / m1m2

• 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 – h1) = mgh2 – mgh1

• W = Δ (mgh) = Δ PE = change in potential energy

• F = ma• 2a s∙ = vf²-v0²

• 2ma s∙ = m(vf²-v0²)

• F s∙ = ½ m(vf²-v0²)

• W = ½ mv∙ f² - ½ mv∙ 0²• 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.”