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Barry Latham Bloom High School Conceptual Physics, Hewitt, 1999. CH 12: UNIVERSAL GRAVITATION 12.1: The Falling Apple Newton is credited with the idea of the falling apple to prove gravity. Probably never happened. If no outside forces are present, an object continues on a straight line path forever. Inertia! What keeps the Moon in orbit then? RQ 1-2 12.2: The Falling Moon The Moon really is falling toward the Earth! We just keep getting out of the way! If we fire a cannonball from Earth, we get the same results. Image: Fire a cannonball with faster and faster velocities. Faster velocities mean that the cannonball will farther and farther. Eventually it will go all the way around! Tangential Velocity Tangent- “perpendicular to” Gravity tries to pull the Moon toward the Earth, the tangential velocity keeps it from crashing into us The only difference that matters for the apple vs. Moon is the distance from the Earth. If the Moon is 60 times further away than an apple at 1s… (Transparency 19, p. 170) The apple will fall 4.9m in the first second The Moon will only fall 1.4mm RQ 3-6 12.3: The Falling Earth The Moon is “falling” toward the Earth The Earth is then “falling” toward the Sun Why don’t we crash into the Sun? RQ 7 12.4: Newton’s Law of Universal Gravitation Universal Gravitation: Everything is gravitationally attracted to everything else! F=ma Only for local objects or those in an independent frame of reference F=Gm1m2/r2 F=force of attraction (N) m1=mass of first object (kg) m2=mass of second object (kg) r=distance separating centers of m1 and m2 (m) G=gravitational constant (6.67x10-11 Nm2/kg2) Makes the units cancel out correctly Measurement of G “G” was measured by Cavendish 150 years AFTER Newton “discovered” gravity Device measured a small twist in a quartz wire due to attraction between two Pb spheres A small value of G means that gravity is very weak! Scientific Notation Review Scientific notation is needed when working with F because the numbers are SO big! 6.67x10-11 is way easier to write than 0.0000000000667 every single time. The equatorial radius of the Earth is 6,370,000 m Keep dividing by 10 until you get to the one’s place Use the number of 10’s as your exponent 6.37x106 m One billion examples Meters: Earth-Moon distance Kilograms: mass of Earth’s oceans Seconds: 31.7 years (Mr. Latham in 09/2008) Minutes: 1903 years Years ago: no Humans on Earth People: Population of China Atoms: enough to make the dot on a printed “i” Weigh the Earth (without a scale or balance) Using Fg=mg and F=Gm1m2/r2 we can find the mass of the Earth! mg=(mobject)(g on Earth) Gm1m2/r2 =(G)(mobject)(mEarth)/(rEarth)2 Set them equal to each other (mobject)(g on Earth)=(G)(mobject)(mEarth)/(rEarth)2 Solve for (mEarth) (rEarth)2(g on Earth)/(G)=(mEarth) Plug & Chug (scientific calculator needed!) (rEarth)2(g on Earth)/(G)/=(mEarth) (6.4x106 m)2(9.80 m/s2)/(G)=(mEarth) (mEarth)=6.02x1024 kg RQ 8-10 12.5: Gravity & Distance: The Inverse Square Law The quantity varies as the inverse square of the distance, keeping masses constant (p. 175) F≈1/d2 If distance doubles, Force decreases by 1/22 (or 1/4) If distance triples, Force decreases by 1/32 (or 1/9) Inverse Square & Weight As distance increases, F decreases P. 176 (Transparency 20) CD 12-1 worksheet Inverse Square Law 1. Complete the areas and thicknesses 2. Complete the areas 3. How does depth perception help us? Mislead us? RQ 11-12 12.6: Universal Gravitation Applications Most celestial objects are a sphere because gravity pulls equally in all direction. Because all objects also pull on each other, the planets change their orbits when they come close enough to each other Perturbation Uranus displayed perturbations Neptune was calculated to exist before it was seen Pluto was also calculated to exist before it was seen RQ 13-14