Gravity

1. Gravity • Galileo’s observations on gravity led to Newton’s Law of Gravitation and the three Laws of Motion • Objects fall at the same rate regardless of mass because more massive objects have more inertia or resistance to motion • Fgrav = G (m1 x m2) / r2 • Force of gravity between two masses is proportional to the product of masses divided by distance squared  ‘inverse square law’

2. Newton – Three Laws of Motion • Inertia • F = ma • Action = Reaction

3. Newton’s Laws of Motion • Law of Inertia: A body continues in state of rest or motion unless acted on by an external force; Mass is a measure of inertia • Law of Acceleration: For a given mass m, the acceleration is proportional to the force applied F = m a • Law of Action equals Reaction: For every action there is an equal and opposite reaction; momemtum (mass x velocity) is conserved

4. Velocity, Speed, Acceleration • Velocity implies both speed and direction; speed may be constant but direction could be changing, and hence accelerating • Acceleration implies change in speed or direction or both • For example, stone on a string being whirled around at constant speed; direction is constantly changing therefore requires force

5. Ball Swung around on a String: Same Speed, (in uniform circular motion) Changing Direction (swinging around the circle)

6. Ball Swung around on a String: Same Speed, (in uniform circular motion) Changing Direction (swinging around the circle)

7. Acceleration Force Donut Swung around on a String

8. Acceleration Force Donut Swung around on a String

9. Conservation of momemtum:action equal reaction • The momemtum (mv) is conserved before and after an event • Rocket and ignited gases: M(rocket) x V(rocket) = m(gases) x v(gases) • Two billiard balls: m1 v1 + m2 v2 = m1 v1’ + m2 v2’ v1,v2 – velocities before collision v1’,v2’ – velocities after collision • Example – you and your friend (twice as heavy) on ice!

10. Conservation of momemtum:action equal reaction • The momemtum (mv) is conserved before and after an event • Rocket and ignited gases: M(rocket) x V(rocket) = m(gases) x v(gases) • Two billiard balls: m1 v1 + m2 v2 = m1 v1’ + m2 v2’ v1,v2 – velocities before collision v1’,v2’ – velocities after collision • Example – you and your friend (twice as heavy) on ice!

11. Force = (apple’s mass)  (acceleration due to gravity) Action = Reaction Equal and Opposite Force from the Table Net Force is Zero, No Net Motion

12. Force = (apple’s mass)  (acceleration due to gravity) Action = Reaction Equal and Opposite Force from the Table Net Force is Zero, No Net Motion

13. Acceleration due to gravity • Acceleration is rate of change of velocity, speed or direction of motion, with time  a = v/t • Acceleration due to Earth’s gravity : a  g g = 9.8 m per second per second, or 32 ft/sec2 • Speed in free-fall T (sec) v (m/sec) v (ft/sec) 0 0 0 1 9.8 32 2 19.6 64 3 29.4 96 60 mi/hr = 88 ft/sec (between 2 and 3 seconds)

14. Galileo’s experiment revisited • What is your weight and mass ? • Weight W is the force of gravity acting on a mass m causing acceleration g • Using F = m a, and the Law of Gravitation W = m g = G (m MEarth) /R2 (R – Radius of the Earth) The mass m of the falling object cancels out and does not matter; therefore all objects fall at the same rate or acceleration g = GM / R2 i.e. constant acceleration due to gravity 9.8 m/sec2

15. Galileo’s experiment on gravity • Galileo surmised that time differences between freely falling objects may be too small for human eye to discern • Therefore he used inclined planes to slow down the acceleration due to gravity and monitor the time more accurately v Changing the angle of the incline changes the velocity v

16. ‘g’ on the Moon g(Moon) = G M(Moon) / R(Moon)2 G = 6.67 x 10-11 newton-meter2/kg2 M(Moon) = 7.349 x 1022 Kg R(Moon) = 1738 Km g (Moon) = 1.62 m/sec/sec About 1/6 of g(Earth); objects on the Moon fall at a rate six times slower than on the Earth

17. Escape Velocity and Energy • To escape earth’s gravity an object must have (kinetic) energy equal to the gravitational (potential) energy of the earth • Kinetic energy due to motion K.E. = ½ m v2 • Potential energy due to position and force P.E. = G m M(Earth) / R (note the similarity with the Law of Gravitation) • Minimum energy needed for escape: K.E. = P.E. ½ m v2 = G m M / R Note that the mass m cancels out, and • v (esc) = 11 km/sec = 7 mi/sec = 25000 mi/hr The escape velocity is the same for all objects of mass m

18. Object in orbit  Continuous fall ! Object falls towards the earth at the same rate as the earth curves away from it

21. Angular Momentum Conservation of angular momentum says that product of radius r and momentum mv must be constant  radius times rotation rate (number of rotations per second) is constant

22. Angular Momentum • All rotating objects have angular momentum • L = mvr ; acts perpendicular to the plane of rotation • Examples: helicopter rotor, ice skater, spinning top or wheel (experiment) • Gyroscope (to stabilize spacecrafts) is basically a spinning wheel whose axis maintains its direction; slow precession like the Earth’s axis along the Circle of Precession

23. Conservation of Angular Momentum • Very important in physical phenomena observed in daily life as well as throughout the Universe. For example, • Varying speeds of planets in elliptical orbits around a star • Jets of extremely high velocity particles, as matter spirals into an accretion disc and falls into a black hole

24. Relativistic1 Jet “From” Black Hole 1. “Relativistic velocities are close to the speed of light

26. Quiz 1 • Each quiz sheet has a different 5-digit symmetric number which must be filled in (as shown on the transparency, but NOT the same one!!!!!) • Please hand in both the exam and the answer sheets with your name on both • Question/answer sheets will be handed back on Wednesday after class • Please remain seated until we begin collecting (20-25 minutes after start) • Class after quiz

28. Stars and Galaxies: Galileo to HST • http://thenextdigit.com/16961/nasa-telescopes-new-panoramic-view-andromeda-resolves-stars/

29. Why is the sky blue ? The atmosphere scatters the blue light more than red light

30. Light and Matter • Light is electromagnetic energy, due to interaction of electrical charges • Matter is made of atoms – equal number of positive and negative particles • An atom is the smallest particle of an element; natural element H to U • Atom  Nucleus (protons + neutrons), with ‘orbiting’ electrons • No. of protons in nucleus = Atomic Number • Science of light  Spectroscopy

31. Radiation and Spectroscopy • Light is electromagnetic energy • Propagates as both particles and waves • Photons – particles of light • Wavelength = Velocity / Frequency

32. Light is electromagnetic wave;Does not require a medium to propagate, unlike water or sound Wavelength is the distance between successive crests or troughs

33. Wavelength () Speed (c) WAVES: Frequency, Wavelength, Speed Frequency (f) (# waves/second) Frequency ‘f’ is the number of waves passing a point per second Speed = wavelength x frequency c = l f

34. Units of wavelength and frequency • Frequency is the number of cycles per second • Since speed of light is constant, higher the frequency the shorter the wavelength and vice-versa • Wavelengths are measured in Angstroms: 1A = 1/100,000,000 cm = 1/10 nanometer (nm) • The higher the frequency the more energetic the wave • Wavelength (or frequency) defines radiation or color

35. White Light Spectrum Prisms disperse light into its component colors: Red-Violet Prism

36. Visible light spectrum: Each color is defined by its wavelength, frequency or energy Red - Blue 7000 - 4000 Angstroms ( 1 nm = 10 A, 1 A = 10-8 cm) Blue light is more energetic than red light Light also behaves like ‘particles’ called photons Photon energy, frequency, wavelength: E = h f = hc/l Planck’s Law(‘h’ is a number known as Planck’s constant)

37. Visible Light • Forms a narrow band within the electromagnetic spectrum ranging from gamma rays to radio waves • Human eye is most sensitive to which color? • Yellow. Why?

38. Light: Electromagnetic SpectrumFrom Gamma Rays to Radio Waves Gamma X-Ray UV Visible Gamma rays are the most energetic (highest frequency, shortest wavelength), Radio waves are the least energetic.

39. Decreasing Wavelength OR Increasing Frequency

40. Matter and Particles of Light: Quantum Theory • Light (energy) and matter in motion behave both aswaves and particles • Wave-Particle Duality - Quantum Theory • Energy particles: quanta or photons: E = hf = hc/l • Photons of a specific wavelength l may be absorbed or emitted by atoms in matter • Matter is made of different natural elements: lightest Hydrogen (1 proton), heaviest Uranium (92 protons) • Smallest particle of an element is atom, made up of a nucleus (protons and neutrons), and orbiting electrons • Electrons and protons attract as opposite electrical charges, NOT gravitationally like planets and Sun

42. The simplest atom: Ordinary Hydrogen Resemblance to planets orbiting the Sun is superficial ! Electrons also move both as particles and waves p – positively charged e – negatively “ One proton in the center (nucleus) and one electron in orbits of definite energy; Ordinary H has no neutrons, but ‘heavy hydrogen’ has one neutron in the nucleus

43. Absorption of a quantum of energy photon by H-atom

44. Emission of a quantum of energy photon by H-atomphoton energy color

45. Absorption and emission of quanta of energy photons by H-atom An electron may absorb or emit light photons at specific wavelength Wavelength (n = 3  n = 2): 6562 Angstroms (RED Color) Energy of the photon must be exactly equal to the energy difference between the two ‘orbits’

46. Continuum n= n=1 (Ground State) n=3 (2nd excited state) n=2 (1st excited state) n=4 n=5 Energy Level Diagram of 1H

47. 26 25 24 n=23 n=6 n=1 (Ground State) n=3 (2nd excited state) n=2 (1st excited state) n=4 n=5 Photons of all other energies (wavelengths) are ignored and pass on by unabsorbed.

48. 62 52 42 n=32 n=6 n=1 (Ground State) n=3 (2nd excited state) n=2 (1st excited state) n=4 n=5 Larger Jump = More Energy = Bluer Wavelength

49. Series of spectral lines of Hydrogen

50. Wavelengths of series of lines from Hydrogen