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Chapter 12- Universal Gravitation Do question 180, 1-4 and 7-10 after test. It was fairly apparent to people for centuries that the earth, attracted objects on earth to it. Newton knew that since the apple changed speed Gravity must be a force Newton knew that the moon’s velocity changed constantly and therefore there must be a force on it. Might the earth pull on the moon just like the apple? Can Earth’s gravity reach all the way to the moon? Where does it stop???? If the moon is falling to the earth like the apple, then WHY doesn’t it fall Newton realized that the moon and the apple are both falling like projectiles. Cannonballs are shot with increasing speed They are all falling towards the earth gravity free path v Fg Gravity pulls the moon towards the center of the earth providing the CENTRIPETAL Force ___________ to keep it moving in v Fg The tangential velocity is sufficient to keep it from falling into the earth The velocity is always perpendicular to the force of gravity In order to “prove” his theory he wanted to predict the acceleration of the moon and see if it matched observation. He knew an apple on earth accelerates at 9.8 m/s2. But what about the moon out in space? If both the moon and the apple were jus above the surface of the earth. Which would hit the ground first: The massive moon or the tiny apple? Heavy and light objects fall at the same rate on earth, he figured the mass of the moon wouldn’t affect its acceleration But the apple is much closer to the earth than the moon. The apple is a distance 1 earth radius for the center of mass of the earth The moon is 60 earth radii away. The apple is only 1. Note: apple not to scale Newton reasoned that gravity would get weaker the farther away two objects are. Think of 2 magnets For reasons we will see later, He calculated that at a distance 60 times From the center of the earth. 2 9.8 m/s amoon = 602 amoon = .0027 m/s2 After falling for 1 second on earth’s surface an apple would have fallen 4.9 m from a gravity free path 4.9 m it Without falls 1.4 mm gravity each after 1second second the moon would be here His answer matched what we know today But he wasn’t sure if the distance used should be between the centers of the objects and didn’t publish for another 20 years ItWhat would would fall to happen the earth. if the moon The suddenly fall would stopped take about 3.5 hours The earth is constantly falling toward the sun Sun If the earth lost some of its tangential velocity? The objects in our solar system have just the right speed to stay in their orbit. If an object is moving too slow, it falls closer to the sun. As it does it speeds up. What makes the earth and the sun so special that they attract objects to them with an invisible force of gravity? They have MASS What else has mass? Are you attracted to the person sitting next to you? YES!! Its called GRAVITY Newton didn’t discover gravity, He discovered that anything that has mass attracts anything else that has mass. If there was no friction on the table you could pull your pencil to you not by magic but by gravity NEWTON’s Universal Law of Gravitation m1 m2 d Distance between center of masses Fg ~ m1 m2 2 d Proportional to – not equal to This is the force of gravity on EACH Object m1 m2 r Remember Newton 3rd law: When m1 exerts a force on m2 then….. Fg ~ m1 m2 2 r Which feels a greater FORCE from the other The exert EQUAL but opposite forces on each other If the mass of 1 object is doubled, doubles Then Fg ________ m1 r m1 m2 Fg ~ r2 m2 Compare the force of gravity between the earth & 1kg object to earth & 2kg object m1 m2 Fg ~ r2 If the mass of both object is doubled, quadruples Then Fg ________ m1 r m1 m2 Fg ~ r2 m2 If the distance between them doubles, is 1/4 Then Fg ________ m1 r m1 m2 Fg ~ r2 m2 If everything attracts everything else, Why isn’t it more obvious? The mass of the earth is HUGE!!!!! The between earth andbe Howforce big will the attraction abetween 1 kg object only 10 N two is 1 kg objects? m 1 m2 Fg ~ 2 r In order to make this an equation we need a fudge factor. Fg = G m1 m2 2 r If we knew G we could calculate the force between any two objects The In order forcetooffind gravity G, both between masses normal wouldobjects need tothat be can known. be weighed As wellisasVERY the force weak. and distance between them. How to measure? What is so hard about this? Fg = G m1 m2 2 r Henry Cavendish English chemist and physicist who was shy and absent-minded. He was terrified of women, and communicated with his female servants by notes. G = 6.67 -11 10 2 2 Nm /kg G = .0000000000667 A very small number because gravity is a relatively weak force Fg = G m1 m2 2 r A 1 kg object on the surface of the earth has a force of gravity of 9.8 N between it and the earth. The radius of the earth is 6,380,000 m. With G known, they could find the mass of the earth 9.8 N = G 1kg mearth (6,380,000 2 m) Cavendish’s experiment is often said to have weighed the earth in his experiment 5.98 1024 mearth = 5.98 24 10 kg Phillip von Jolly Around 1850 later used a simpler apparatus and got more accurate results What is the force of gravity between a 65 kg student sitting .50 m away from a 75 kg student? G = 6.67 x 10 -11 What is the force of gravity between the earth and the planet mars at their closest approach (which is 1.01x1011 m between centers of mass) mearth = 5.98 1024 kg mmars = 6.41 x 1023 kg Closest approach 101.1 million kilometers 2.51 x 1016 N What is the force of gravity between the earth and 5.0 kg object which 12,760,000 m (2 earth radii) above the surface of the earth? mearth = 5.98 1024 kg rearth = 6,380,000 m Add to questions page 180 11, 15, 16, 17, 19, 20, 21, 22 If you increase the separation of two objects by 3 times, why doesn’t Fg decrease by 3 instead of decreasing by________ 9 How much more pizza do you get when you go from a pizza which is 1 m in radius to one that is 2 m Area = 2 pr When a light shines it spreads out as a sphere getting dimmer as you go further Picture a hollow sphere with the light bulb in the middle. If the sphere was doubled in radius, the same amount of light is spread out over 4 times the area. a sphere = So itArea is 4 oftimes dimmer 4 p r2 Picture a butter gun It shoots out the same amount of butter each time The further away, the more it can cover with 1 shot 1 inch thick 1m 2m 3m Many things follow this law: Gravity, Light, Sound, Magnets, Radioactivity…… What is the distance from? What happens to your weight as you climb a mountain? Compare weights when you are halfway up a mountain vs. at the top? Did the distance double? How far away from the surface of the earth would you need to be to have your mass reduced to ¼. rearth rearth Your weight is just a special case of gravitational force Your mass also attracts the earth Which is stronger the: Fg,you,earth Fg,earth,you Your mass also attracts the earth and everything else in the universe When you wave your hand the rest of the universe feels it The shuttle orbits the earth at 200,000 m above it surface. How strong is gravity there? Let’s put things to scale 6,380 km Shuttle 6,580 km Gravitational pull is still 94% at that height. astronauts is space astronauts training in an airplane If an astronaut still has ~94% of earth’s gravity on them, why do they “feel” weightless The feeling of weight is most closely related to the Normal Force exerted on us by the floor or seat etc… 600 N 500 N 400 N Still accelerating up accelerating down If the cord is cut FREE FALL An astronaut is in Free Fall towards the Earth, Why don’t they crash? Book problems page 181 29, 32, 33 Why did all planets turn out pretty round? Planets and suns condensed from clouds space “dust” Picture a square cloud of space “dust” . Any corner gets pulled in. Even other planets pull on the earth causing “perturbations” The furthest “planet” Pluto was discovered because it was causing Uranus to wobble a bit in its orbit Newton showed us that the same laws of physics on earth apply to the rest of the universe Two galaxies crashing What is concerning about the fact that everything in the universe attracts everything else? The universe about 15,000,000,000 years ago. Then the big bang But this is sort of like throwing a rock into the air, as it gets further up it slows As it expands its speed slows, then Strangely enough the universe does not seem to be slowing down as it expands, but rather speeding up. This is like throwing marker in the air and having it…… Move upward faster and faster instead of slowing down and coming back An object is located equal Find the net force on itdistances using thefrom two 1 kg masses. Compare the magnitude parallelogram method. and direction of the forces it feels 1 kg 1 kg An object located equal from a 1 Findisthe net force ondistances it using the kg and 2 kg masses.method. Compare the parallelogram magnitude and direction of the forces it feels 2 kg 1 kg Chapter 13- Gravitational Interactions There are 2 types of forces which can pull on another object without touching it that you are familiar with. (there are less familiar ones electric charge, strong force, weak force) Gravity Magnets Gravity Magnets Exert a force without contact through a vacuum That really bugs me. A mass creates a Force FIELD, and the field exerts a force on objects in it Gravitational Field Electric, Magnetic, and Gravitational Fields are FORCE FIELDS The arrows field is represented the direction bywhere imaginary a to mass The Where field is lines thepoint field areinclosest strongest, close the field the would accelerate (to lines the or center the earth) surface of isfield the the earth strongest farofaway? AA 1How kg 2 kg object toobject measure onatthe the the surface same strength location feelsofathe force infield? theoffield 10 N feels a force of 20 N. The field isn’t any stronger, only the force on the object What is the gravitational field strength at the location of the red object Field Strength = m1 m2 FG m Since, F = m a Field Strength = mFa m The gravitation Field Strength at a location, is just the acceleration of an object there. Field Strength = FG m1 G m1 m2 FG = r2 m1 m2 G m1 Field Strength = r2 Compared the acceleration due to gravity at the surface of the earth, how would the acceleration compare on a planet that…. had was hadthe 5the twice times same same the asmass mass, mass massive, but but and3same and 1/2 times as 1/10 radius radius bigthe size Field Strength = GM r2 Sure,What you wouldWould accelerate happen youif fall? you toward drilled the acenter hole through of mass the earth of theand earth jumped in? What would happen to the Force of gravity and your acceleration as you fell? Do Some You youof are still the earth closerpulls the accelerate at g CM you the orofup. earth, Which but… more stronger or the up or down? less Consider this, what happens when you are at the center of the earth? Do Half youpulls stop at you the center up, & of half the earth pulls youthen? down. What is the net force? Going back what happened to the acceleration half way down? g g/2 ? 0 As What youhappens fall towards as you thepass center you center speed of the up, Let’s complete our the journey but your acceleration earth? decreases. g g/2 0 What You will willbegin your to speed accelerate be when butyou which reach way? the other side? g g/2 0 g/2 g You will If you begin weren’t to accelerate able to jump but which out???way? g g/2 0 g/2 g Video link to earth hole bungee jumping So the Net Force of Gravity (or gravitational field) increases as you get closer to the center of mass of an object until… You get inside the object Decreasing Increasing BLACK HOLES How do we know they are there if we can see them? BLACK HOLES Stars orbiting very quickly around a dark region How do they form? As they run Stars out“burn” of fuel, hydrogen they start to cool. BLACK HOLES As they cool, the atoms slow and the star collapses under its own gravity What happens to the mass of the star as it collapses? The of tothe hole is just the Whatmass happens theblack mass of a slice of bread if you squish it? star that same as the mass of the made it (or less)!!!! What makes them so SCARY If they don’t have any more mass than a big star does, why is their gravitational field so strong? Consider a Sun and a Black hole of the same mass Decreasing Increasing But remember the strength increases with the square of the distance. So this isn’t quite an accurate representation Increasing It would be a little more like this Increasing When a sun collapses into black hole, most scientists believe it becomes infinitely small. But let’s say that our sun collapses into a same mass black hole which is 1 trillionth the size (109). Compare the gravitational field strength of the surface of each. Field Strength = GM r2 What would happen to the earth, if the sun collapsed into a black hole? Field Strength = GM r2 Nothing, except we would freeze! Book problems page 196-197 #’s 1, 3-6, 8, 25-28, 30 What causes the tides? The Fg the earth feels from the moon is not equal on all sides 59 Rearth 61 Rearth Where is it stronger? The Fg the earth feels from the moon is not equal on all sides Fg vs distance If the pull of gravity from the moon is stronger on your head than your feet, what is it doing to you? Fg vs distance Because the water is able to move around the earth it moves towards the moon. Because the water is able to flow around the earth, it moves towards the moon. Which has a greater effect on the earths It is the DIFFERENCE in the force of tides? gravity on the opposite sides of the planet Sun or Moon which cause the tides. (note the force of gravity on the earth from the sun is MUCH stronger than from the moon) Not really to scale Compare the force of gravity on opposite sides of the planet Fg Fg 4 1m 2m Different by a factor of 4!! Compare the force of gravity on opposite sides of the planet Fg Fg 2.25 2m 3m Different by a factor of 2.25!! What happens to the difference in gravity as the planets separate? THE MOON it is closer to earth’s the earth Which has abecause bigger impact on the there is a greater difference on the sides of tides? the earth!!!!!!! Not really to scale The earth spins on its axis once a day, So different parts of the earth are closest to the moon once a day. So how many High Tides should there be in one day But there are actually 2 high tides and 2 Low Tides per day. Because What causes the earth the other actually one?????? has two bulges, one closest to the moon and one furthest If the moon simply rotated around the earth, there would only be one Where is the center of mass about for an earth / moon system As the moon revolves around the earth, The earth “wobbles” As the moon revolves around the earth, The earth “wobbles” The inertia of the water causes it to bulge away from the moon slightly BrainPop tides movie An object that goes in a circle never speeds up even though a force is constantly applied. Why? Only a force that is parallel to motion can do Work If the earth traveled in a perfect circle it would never speed up or slow down because. Sun If the earth was given a extra speed it would Now it would start to slow Sun Get further away from the sun Slowest, PE- KE v Fg Sun Fastest, PE- KE Which How components does other ofofthe component forcesdo dono effect work the ononthe earth? earth? Where does thethe force gravity work the earth v F F Sun F Elliptical orbit applet applet #2 Planet travel in elliptical orbits with the sun at one focus Is The there more a speed KE isatstarts which with thethe object morewould PE it never ends with (before come back it fallsdown? back down) Escape Velocity The further you get from the earth, the weaker the force of gravity gets. At an infinite distance the force approaches zero If you shoot an object upward and there is no friction at 11,200 m/s. It will never fall back to earth, it will just move Slower and slower but never stop. Escape velocity is 11,200 m/s for earth Inverse Square Law Many things follow this law: Gravity, Light, Sound, Magnets, Radioactivity…… totopredict of gravity AInIn 1order kg object theforce surface oftothe order findon it the they would have between any two objects ain fudge factor know every variable the of equation earth has a other force of gravity 9.8 N was needed between it and the earth. The radius Why isn’t this easy. of the earth is 6,380,000 m. What’s missing? Fg = G m1 m2 2 r