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Bellringer 11/12

Bellringer 11/12. A worker does 25 J of work lifting a bucket, then sets the bucket back down in the same place. What is the total net work done on the bucket?. Chapter 7: Circular Motion and Gravitation. Object is moving tangent to the circle

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Bellringer 11/12

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  1. Bellringer 11/12 • A worker does 25 J of work lifting a bucket, then sets the bucket back down in the same place. What is the total net work done on the bucket?

  2. Chapter 7: Circular Motion and Gravitation

  3. Object is moving tangent to the circle - Direction of the velocity vector is the same direction of the object’s motion – the velocity vector is directed tangent to the circle • Circular Motion – motion of an object about a single axis at a constant speed Object moving in a circle is accelerating

  4. Tangential speed (vt) – speed of an object in circular motion • When vtis constant = uniform circular motion • Depends on distance

  5. Centripetal Acceleration • Centripetal Acceleration – acceleration directed toward the center of a circular path (center-seeking) Centripetal Acceleration ac = vt2/r Centripetal Acceleration = (tangential speed)2 /radius of circular path

  6. Example • A test car moves at a constant speed around a circular track. If the car is 48.2 m from the track’s center and has a centripetal acceleration of 8.05m/s2, what is the car’s tangential speed?

  7. Tangential acceleration – acceleration due to the change in speed

  8. Centripetal Force – net force directed toward the center of an object’s circular path Centripetal Force Fc = mvt2/r Centripetal Force= mass x (tangential speed)2 /radius of circular path Example: Gravitational Force – keeps moon in its orbit

  9. Example • A pilot is flying a small plane at 56.6m/s in a circular path with a radius of 188.5m. The centripetal force needed to maintain the plane’s circular motion is 1.89x104 N. What is the plane’s mass?

  10. Example • A car is negotiating a flat curve of radius 50. m with a speed of 20. m/s. If the centripetal force provided by friction is 1.2 x 104 N. • A. What is the mass of the car? • B. What is the coefficient of friction?

  11. Centripetal vs Centrifugal • Centrifugal – center fleeing – away from the center/outward • DOES NOT EXIST!!!! Fake force!

  12. Bellringer 11/14 • A building superintendent twirls a set of keys in a circle at the end of a cord. If the keys have a centripetal acceleration of 145 m/s2 and the cord has a length of 0.34m, what is the tangential speed of the keys?

  13. Newton’s Law of Universal Gravitation Fg = G m1m2 r2 Gravitational Force= constant x mass1 x mass2 (distance between masses) 2 G = 6.673x10 -11N•m 2 kg 2 Gravitational Force – mutual force of attraction between particles of matter

  14. Example • Find the distance between a 0.300kg billiard ball and a 0.400kg billiard ball if the magnitude of the gravitational force between them is 8.92x10 -11 N.

  15. Gravity’s Influence • Tides – periodic rise and fall of water

  16. Field Force • Gravitational force is an interaction between a mass and the gravitational field created by other masses Gravitational Field Strength g = Fg /m g = 9.81m/s2 on Earth’s surface

  17. Weight changes with location • Weight = mass x free-fall acceleration or ● Weight = mass x gravitational field strength Fg= Gmme / r2 g = Fg/m = Gmme /m r2 = Gme / r2

  18. Weight • Gravitational field strength depends only on mass and distance – your distance increases, g decreases…your weight decreases

  19. Bellringer 11/15 • A 7.55x1013 kg comet orbits the sun with a speed of 0.173km/s. If the centripetal force on the comet is 505N, how far is it from the sun?

  20. Example • Suppose the value of G has just been discovered. Use the value of G and an approximate value for Earth’s radius to find an approximation for Earth’s mass.

  21. Example • Earth has a mass of 5.97x1024kg and a radius of 6.38x106 m, while Saturn has a mass of 5.68x1026 kg and a radius of 6.03x107 m. Find the weight of a 65.0kg person at the following locations • On the surface of Earth • 1000km above the surface of Earth • On the surface of Saturn • 1000 km above the surface of Saturn

  22. Example • A scam artist hopes to make a profit by buying and selling gold at different altitudes for the same price per weight. Should the scam artist buy or sell at the higher altitude? Explain.

  23. Bellringer 11/18 • What is the force of gravity between two 74.0kg physics students that are sitting 85.0cm apart?

  24. Motion in Space • Claudius Ptolemy • Thought Earth was the center of the universe • Nicolaus Copernicus • Thought Earth orbits the sun in perfect circles

  25. Johannes Kepler Kepler’s Laws of Planetary Motion - First Law: Each planets travels in an elliptical orbit around the sun, the sun is at one of the focal points

  26. Kepler’s Laws of Planetary Motion - Second Law: An imaginary line drawn from the sun to any planet sweeps out equal areas in equal time intervals

  27. Kepler’s Laws of Planetary Motion - Third Law: The square of a planet’s orbital period (T2 ) is proportional to the cube of the average distance (r3 ) between the planet and the sun

  28. Example • The moons orbiting Jupiter follow the same laws of motion as the planets orbiting the sun. One of the moons is called Io - its distance from Jupiter's center is 4.2 units and it orbits Jupiter in 1.8 Earth-days. Another moon is called Ganymede; it is 10.7 units from Jupiter's center. Make a prediction of the period of Ganymede using Kepler's law of harmonies. Answer: 7.32 days

  29. Period and Speed of an object in circular motion T = 2πr3vt = G m Gm r T = Orbital period r = mean radius m = mass of central object vt = orbital speed √ √ m is the mass of the central object. Mass of the planet/satellite that is in orbit does not affect the period or speed

  30. Example • During a spacecraft’s fifth orbit around Venus, it traveling at a mean altitude of 361km. If the orbit had been circular, what would the spacecraft’s period and speed have been?

  31. Example • At what distance above Earth would a satellite have a period of 125 minutes?

  32. Bellringer 11/19 • At the surface of a red giant star, the gravitational force on 1.00kg is only 2.19x10-3 N. If its mass equals 3.98x1031 kg, what is the star’s radius?

  33. What is the correct answer? • Astronauts on the orbiting space station are weightless because… • There is no gravity in space and they do not weight anything • Space is a vacuum and they is no gravity in a vacuum • Space is a vacuum and there is no air resistance in a vacuum • The astronauts are far from Earth’s surface at a location where gravitation has a minimal affect

  34. Weight and Weightlessness • Weightlessness – sensation when all contact forces are removed

  35. Astronauts in orbit • Astronauts experience apparent weightlessness • No normal force is acting on them

  36. Example • Otis’ mass is 80kg. • What is the scale reading when Otis accelerates upward at 0.40m/s2 • What is the scale reading when Otis is traveling upward at a constant velocity at 2.0m/s • Otis stops at the top floor and then accelerates downward at a rate of 0.40m/s2

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