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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 F grav = G (m1 x m2) / r 2
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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’
Newton – Three Laws of Motion • Inertia • F = ma • Action = Reaction
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
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
Ball Swung around on a String: Same Speed, (in uniform circular motion) Changing Direction (swinging around the circle)
Ball Swung around on a String: Same Speed, (in uniform circular motion) Changing Direction (swinging around the circle)
Acceleration Force Donut Swung around on a String
Acceleration Force Donut Swung around on a String
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!
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!
Force = (apple’s mass) (acceleration due to gravity) Action = Reaction Equal and Opposite Force from the Table Net Force is Zero, No Net Motion
Force = (apple’s mass) (acceleration due to gravity) Action = Reaction Equal and Opposite Force from the Table Net Force is Zero, No Net Motion
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)
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
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
‘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
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
Object in orbit Continuous fall ! Object falls towards the earth at the same rate as the earth curves away from it
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
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
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
Relativistic1 Jet “From” Black Hole 1. “Relativistic velocities are close to the speed of light
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
Stars and Galaxies: Galileo to HST • http://thenextdigit.com/16961/nasa-telescopes-new-panoramic-view-andromeda-resolves-stars/
Why is the sky blue ? The atmosphere scatters the blue light more than red light
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
Radiation and Spectroscopy • Light is electromagnetic energy • Propagates as both particles and waves • Photons – particles of light • Wavelength = Velocity / Frequency
Light is electromagnetic wave;Does not require a medium to propagate, unlike water or sound Wavelength is the distance between successive crests or troughs
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
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
White Light Spectrum Prisms disperse light into its component colors: Red-Violet Prism
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)
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?
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.
Decreasing Wavelength OR Increasing Frequency
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
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
Emission of a quantum of energy photon by H-atomphoton energy color
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’
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
26 25 24 n=23 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.
62 52 42 n=32 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