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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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**Circular Motion – motion of an object about a single axis at a constant speed**

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 (vt) – speed of an object in circular motion**

When vt 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 ac = vt 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/s2, 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= mass x (tangential speed)2 /radius of circular path**

Centripetal Force – net force directed toward the center of an object’s circular path Centripetal Force Fc = mvt 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 1.89x104 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 104 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/s2 and the cord has a length of 0.34m, what is the tangential speed of the keys?

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**Newton’s Law of Universal Gravitation (distance between masses) 2**

Gravitational Force – mutual force of attraction between particles of matter Newton’s Law of Universal Gravitation Fg = G m1m2 r2 Gravitational Force= constant x mass1 x mass2 (distance between masses) 2 G = 6.673x N•m 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 8.92x N.

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

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**Gravitational Field Strength**

Field Force Gravitational force is an interaction between a mass and the gravitational field created by other masses Gravitational Field Strength g = Fg /m Gravitational field strength equals free fall acceleration Masses create a gravitational field in space…. g = 9.81m/s2 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 Fg = Gmme / r2 g = Fg /m = Gmme /m r2 = Gme / r2

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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 7.55x1013 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?

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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 5.97x1024kg 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

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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 Nicolaus Copernicus**

Thought Earth was the center of the universe Nicolaus Copernicus Thought Earth orbits the sun in perfect circles

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**Kepler’s Laws of Planetary Motion**

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 (T2 ) is proportional to the cube of the average distance (r3 ) between the planet and the sun Planet Period (s) Average Dist. (m) T2/R3 (s2/m3) Earth 3.156 x 107 s x 1011 2.977 x 10-19 Mars 5.93 x 107 s 2.278 x 1011 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 r3 vt = 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

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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 3.98x1031 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… 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

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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.**

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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