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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?

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Chapter 7: Circular Motion and Gravitation

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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 Object moving in a circle is accelerating

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Tangential speed (v t ) – speed of an object in circular motion When v t is constant = uniform circular motion Depends on distance

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Centripetal Acceleration Centripetal Acceleration – acceleration directed toward the center of a circular path (center-seeking) Centripetal Acceleration a c = v t 2 /r Centripetal Acceleration = (tangential speed) 2 /radius of circular path

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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/s 2, what is the car’s tangential speed?

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Tangential acceleration – acceleration due to the change in speed

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Centripetal Force – net force directed toward the center of an object’s circular path Centripetal Force F c = mv t 2 /r Centripetal Force= mass x (tangential speed) 2 /radius of circular path Example: Gravitational Force – keeps moon in its orbit

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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 1.89x10 4 N. What is the plane’s mass?

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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 10 4 N. A. What is the mass of the car? B. What is the coefficient of friction?

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

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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/s 2 and the cord has a length of 0.34m, what is the tangential speed of the keys?

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Gravitational Force – mutual force of attraction between particles of matter Newton’s Law of Universal Gravitation F g = G m 1 m 2 r 2 Gravitational Force= constant x mass1 x mass2 (distance between masses) 2 G = 6.673x10 -11 Nm 2 kg 2

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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.

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

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Field Force Gravitational force is an interaction between a mass and the gravitational field created by other masses Gravitational Field Strength g = F g /m g = 9.81m/s 2 on Earth’s surface

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Weight changes with location Weight = mass x free-fall acceleration or ● Weight = mass x gravitational field strength F g = Gmm e / r 2 g = F g /m = Gmm e /m r 2 = Gm e / r 2

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

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Bellringer 11/15 A 7.55x10 13 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?

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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.

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Example Earth has a mass of 5.97x10 24 kg and a radius of 6.38x10 6 m, while Saturn has a mass of 5.68x10 26 kg and a radius of 6.03x10 7 m. Find the weight of a 65.0kg person at the following locations a.On the surface of Earth b.1000km above the surface of Earth c.On the surface of Saturn d.1000 km above the surface of Saturn

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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.

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

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

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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

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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

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Kepler’s Laws of Planetary Motion - Third Law: The square of a planet’s orbital period (T 2 ) is proportional to the cube of the average distance (r 3 ) between the planet and the sun Planet Period (s) Average Dist. (m) T 2 /R 3 (s 2 /m 3 ) Earth3.156 x 10 7 s 1.4957 x 10 11 2.977 x 10 -19 Mars5.93 x 10 7 s2.278 x 10 11 2.975 x 10 -19

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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

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Period and Speed of an object in circular motion T = 2π r 3 v t = G m Gm r T = Orbital period r = mean radius m = mass of central objectv t = 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

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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?

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

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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 3.98x10 31 kg, what is the star’s radius?

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

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Weight and Weightlessness Weightlessness – sensation when all contact forces are removed

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

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Example Otis’ mass is 80kg. a.What is the scale reading when Otis accelerates upward at 0.40m/s 2 b.What is the scale reading when Otis is traveling upward at a constant velocity at 2.0m/s c.Otis stops at the top floor and then accelerates downward at a rate of 0.40m/s 2

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