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Transcript
Newton’s Universal Law of Gravitation Newton’s conceptual leap in understanding gravity was his realization that the same force governs the motion of a falling object on Earth & the motion of the Moon in its orbit around the Earth. Universal Force Universal Law of Gravitation • Every mass attracts every other mass through gravity. • The force of attraction between any 2 objects is directly proportional to the product of their masses. • Doubling the mass of 1object doubles Fg between the 2 objects. Gravity and Weight • Definition: The weight of an object is a measure of the Fg one object feels in the presence of another. • Weight Fg = mg. Where g is known. Mass can be measured in 2 ways • Inertial mass - the mass of a body as determined by its momentum, as opposed to gravitational mass. How it accelerates • m = Fnet/a • Gravitational mass -the mass of a body determined by its response to the force of gravity. 1. Show that the acceleration of gravity g = GM/r2, where M is the mass of a planet or star r is its radius. Fg = m2g = GM1m2. r 2. g = GM1 is accl due to gravity r 2. Mass of the object cancels out. Acceleration depends only on the mass of the planet (or star). Questions: Raise Hands. • Is heavier body attracted to the Earth with more force than a light body. •Does the heavier object free fall faster? •Explain. Newton’s Universal Law of Gravitation • Fg = GMm. R2. Describes Force btw point masses. What is a point mass? Gravitational Field deals with space around the large mass. Gravitational Field Strength/Intensity Force per unit mass experienced by a small “test mass” in space. Gravitational Field Lines drawn in direction of acceleration of small mass. Gravitational Field = g. The value for acceleration, g, is also called the gravitational field. Set the weight equal the Fg. The units of the gravitational field are N/kg. Since mg = GMm. r2. Grav Field The small mass m cancels g = GM r2. units N/kg. Use to find acceleration or gravitational field. 2. What is the gravitational field strength due to Earth at a point 450 km above the surface? • g = GM r2. • (6.67 x 10-11)(6 x 1024kg) (6.4 x 106m + 450 x 103m)2. • 4 x 1014. (6 850 000)2. • 4 x 1014. 4.7 x 1013. 8.5 N/kg Combining Fields All fields are vectors. Forces resulting from more than 1 field is the sum of the field strengths. Write the equation for grav field strength that involves planets mass and distance> 3. Two spheres lie along a straight line. The sphere on the left has m = 1000-kg, and the right on the right has m = 100-kg. The distance between their centers is 5-m. Point A lies between the spheres at 2.5-m from the center of each. Point B lies 1 m to the left of m = 1000kg. Calculate the field strength at A and B. B A 9.63 x 10 – 9 N/kg left 6.69 x 10-8 N/kg Satellites in freefall not beyond grav field = apparent weightlessness. The orbit is maintained by gravity. Newton’s Cannon Animation http://waowen.screaming.net/revision/force&motion/ncananim.htm 4. Derive an equation to express the minimum velocity a satellite must have to stay in orbit. Fg keeps the satellite in orbit. Set Fc equal to gravitational force. Fg = GMem r2 v= Fc = mv2. r (GMe)1/2. (r) 1/2. 5. What is the velocity needed for a satellite to stay in orbit 200 km above the Earth’s surface? • First find dtot between their centers – r: • 2.0 x 105 m + 6.57 x 106m • 6.57 x 106m v= (GMe)1/2. (r) 1/2. (6.67x10-11)(5.98x1024 kg)1/2 (6.57 x 106m )1/2. 7800 m/s. Einstein vs. Newton 9.5 min • http://www.youtube.com/watch?v=4yyb_R NJWUM Squeeze water in freefall • http://apod.nasa.gov/apod/ap130424.html • Squeeze water in space Rd Hamper 127 – 129 do pg 129 - 131. Purple boxes #1 – 5. Show all work. Einstein vs. Newton 9.5 min • http://www.youtube.com/watch?v=4yyb_RNJWUM http://www.phy.ntnu.edu.tw/java/pro jectileOrbit/projectileOrbit.html • Newton’s Cannon Launch Satellite • Apparent weightlessness. Satellites are in freefall around the Earth! That is why astronauts appear weightless. They are constantly falling toward Earth. Their rate of fall is balanced by their tangential momentum. The universe season 2 Gravity, Roller Coasters, Space Travel & PEg. https://www.youtube.com/watch?v=Eilj zeDL0co 45 minutes