Reading and Announcements

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1 Reading and Announcements Read Chapters 7.1 and 7.2 Homework #4 due Thursday, February 14 Quiz #3 Tuesday, February 12 No class Tuesday, February 19 as it s a UMass Monday Exam #1, Tuesday, February 21

2 Gravity What force is responsible for motions in the universe? What force makes objects fall? What keeps us on the rotating Earth? Why don t planets move in straight lines, but orbit around the Sun instead? Why doesn t the moon travel in a straight line? There must be a force acting on it.

3 How did Newton figure out Gravity: if the apple was initially at rest and then started to fall, there must be a force acting on the apple. What force? More importantly, if the force of gravity reaches to the tree, might it not reach even further? In particular, might it not reach all the way to the orbit of the Moon? Newton calculated what the Earth s gravity would be at the position of the Moon. And found that it is what would be required to keep the Moon in its orbit.

4 Why doesn't the earth fall into the sun? Without gravity the earth would travel in a straight line. It has a velocity and it has inertia! Force of gravity causes change in the direction of velocity --acceleration. The earth is falling towards the sun all the time!

5 so what is an orbit? Suppose you dig a hole through the center of the Earth and pumped out all the air. And then tossed an apple into the hole. Can you visualize the motion of the apple?

6 so what is an orbit? The object will move up and down, periodically, forever. Its speed will be highest when it transits at the center of Earth and the slowest in proximity of the surface, when it stops and reverses its motion. THAT IS AN ORBIT! (with velocity always having the same direction and alternating sign).

7 Now, let s make an orbit whose velocity does change direction. If I do not give the object enough speed, its trajectory will eventually intersect the ground. V=8km/s At the right speed, namely the ORBITAL VELOCITY, the vertical downward motion and the horizontal outward motion combine to produce a circular orbit.

8 Suppose you shrink Earth keeping the same mass. Now the trajectory of even the slowest moving object does not intersect the ground. That is an elliptic orbit! A circular orbit is only a special case of an orbit where the speed is always the same. V=8km/s

9 Gravity We can summarize the universal law of gravitation with the following statements: Every mass attracts every other mass through the force of gravity. If mass #1 exerts force on mass #2, and mass #2 exerts force on mass #1, the force must depend on both masses and the force of attraction is directly proportional to the product of the two masses. The force of attraction is inversely proportional to the square of the distance between the masses.

10 The Universal Law of Gravity d M1 F g =G M1 M2 d M2 2 G = 6.67x10-11 m3/kg/s2 G is the Universal constant of gravity

11 The Universal Law of Gravity Any two bodies with mass are attracted to each other through gravitation, with a force proportional to the product of their masses and inversely proportional to the square of their distance: F=-G Mm r2 (G is the Universal constant of gravity.)

12 How did Newton calculate Earth s gravity at the position of the Moon? F ~ 1/D2 To calculate Earths gravity on the Moon, Newton assumed that Gravity obeys the inverse square law.

13 M 1M 2 Fg G d2 Two equal masses, m, separated by a distance, d, exert a force, F, on each other owing to their gravitational attraction. How large is the gravitational force between an object of mass m and an object of mass 2m separated by the same distance d? Survey Question ¼F ½F F 2F 4F

14 Survey Question F g =G M1 M2 d 2 Two equal masses, m, separated by a distance, d, exert a force, F, on each other due to their gravitational attraction. How large would their gravitational attraction be if the distance between them was doubled? ¼F ½F F 2F 4F

15 Remember these two very important concepts: 1) Your mass decides the total force of gravity acting on you Both you and a truck have the same distance to the center of earth. The force of gravity on the truck is bigger 2) Your acceleration = force/mass In other words, when objects fall under gravity, they all have the same acceleration, regardless of their mass, and hence fall at the same speed.

16 In a vacuum all objects fall at the same speed.

17 Tides Tides occur because of the gravitational pull of the Moon on the Earth. The Moon pulls more strongly on the closer side of Earth than the one further away. It literally stretches the Earth. Water (and air) get stretched much more easily than rock. This makes tides. Note that the Sun does the same thing.

18 We have two high tides because of the stretching action Moon The Moon exerts a stronger gravitational pull on the near side of the Earth than on the far side of the Earth. This difference in pull causes the Earth to stretch!

19 Tides low tide high tide Looking down on the Earth low tide high tide Moon Exaggerated view of tides

20 Spring and Neap Tides Spring tides The Sun also produces tidal effects, about half as strong as the Moon. Near Full and New Moon, those two effects add up to cause spring tides. Neap tides Near first and third quarter, the two effects work at a right angles, causing neap tides.

21 What is light? Light is electromagnetic radiation. Technically, light is the part of electromagnetic (e.m.) radiation that humans (and other animals) see. Although incorrect, we usually call light all types of electromagnetic radiation, like X-ray light or UltraViolet light. Light is made of energy. Light always travels at the speed of light: c. Light is a wave.

22 What is Electromagnetic Radiation? Made of propagating waves of electric and magnetic fields. It carries energy with it. Sometimes called radiant energy. Think solar power, photosynthesis, photo-electric cells, a fireplace

23 What is an electromagnetic wave? It is electricity and magnetism moving through space. So, when we say the speed of light is c what we really mean is that the speed of the electromagnetic wave is c, regardless of its frequency.

24 Light as a wave Waves you can see: e.g., ocean waves. Waves you cannot see: sound waves. electromagnetic waves. Light is an electromagnetic wave.

25 Properties of Waves Wavelength the distance between crests (or troughs) of a wave. Frequency the number of crests (or troughs) that pass by each second. Speed the rate at which a crest (or trough) moves. For light in general: speed = c = d/t = λ λ =c λ = c/ wavelength frequency speed of light = 3x108 m/s in vacuum

26 Light as a Wave Wavelengths of light are measured in units of nanometers (nm) or Ångström (Å): 1 nm = 10-9 m 1 Å = m = 0.1 nm Visible light has wavelengths between 4000 Å and 7000 Å (= nm).

27 Wavelengths and Colors Different colors of visible light correspond to different wavelengths.

28 Visible Light Shorter Wavelength Longer Wavelength

29 Remember: visible light isn t the whole story. It s just a small part of the entire electromagnetic spectrum. Short Wavelength Long Wavelength (high frequency) (high energy) (low frequency) (low energy)

30 Wavelengths and the size of things Roy G. Biv

31 Reminder #1: E.m. Radiation generally contains bundles of waves of different wavelengths (colors). How much of each color is present in a given bundle of e.m. radiation, i.e. the distribution of intensity of each wavelength, is called the spectrum. Here is an example of optical (visible) light:

32 The Multi-wavelength Sun Radio optical infrared X-ray

33 Optical Sky

34 Near-infrared sky Boldt et al.

35 Radio Sky

36 Soft X-ray Sky

37 Different wavelengths carry different types of information Visible light: the glow of stars (dust blocks the light). Infrared: the glow of dust. Visible light (top) and infrared (bottom) image of the Sombrero Galaxy.

38 Light as particles Light comes in quanta of energy called photons little bullets of energy. Photons are massless, but they have momentum and energy.

39 Wave-particle duality All types of electromagnetic radiation act as both waves and particles. The two views are connected by the relation Energy= E = h = h c / h is the Planck's constant, c is the speed of light, is the frequency, and is the wavelength The energy of a photon does not depend on the intensity of the light!!!

40 Intensity A photon's energy depends on the wavelength (or frequency) only, NOT the intensity. But the energy you experience depends also on the intensity (total number of photons).

41 In Summary: properties of Light All light travels through (vacuum) space with a velocity = 3x108 m/s. The frequency (or wavelength) of a photon determines how much energy the photon has (E=h ). The number of photons (how many) determines the intensity. Light can be described in terms of either energy, frequency, or wavelength.

42 Compared to visible light, radio waves have: higher energy and longer wavelength. higher energy and shorter wavelength. lower energy and longer wavelength. lower energy and shorter wavelength. all light has the same energy.

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