Bellringer 11/12
description
Transcript of Bellringer 11/12
![Page 1: Bellringer 11/12](https://reader033.fdocuments.net/reader033/viewer/2022061514/56816293550346895dd304e8/html5/thumbnails/1.jpg)
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?
![Page 2: Bellringer 11/12](https://reader033.fdocuments.net/reader033/viewer/2022061514/56816293550346895dd304e8/html5/thumbnails/2.jpg)
Chapter 7: Circular Motion and Gravitation
![Page 3: Bellringer 11/12](https://reader033.fdocuments.net/reader033/viewer/2022061514/56816293550346895dd304e8/html5/thumbnails/3.jpg)
• 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
![Page 4: Bellringer 11/12](https://reader033.fdocuments.net/reader033/viewer/2022061514/56816293550346895dd304e8/html5/thumbnails/4.jpg)
• Tangential speed (vt) – speed of an object in circular motion When vt is constant = uniform circular motion Depends on distance
![Page 5: Bellringer 11/12](https://reader033.fdocuments.net/reader033/viewer/2022061514/56816293550346895dd304e8/html5/thumbnails/5.jpg)
Centripetal Acceleration
• Centripetal Acceleration – acceleration directed toward the center of a circular path (center-seeking)
Centripetal Accelerationac = vt
2/rCentripetal Acceleration = (tangential speed)2 /radius of
circular path
![Page 6: Bellringer 11/12](https://reader033.fdocuments.net/reader033/viewer/2022061514/56816293550346895dd304e8/html5/thumbnails/6.jpg)
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?
![Page 7: Bellringer 11/12](https://reader033.fdocuments.net/reader033/viewer/2022061514/56816293550346895dd304e8/html5/thumbnails/7.jpg)
• Tangential acceleration – acceleration due to the change in speed
![Page 8: Bellringer 11/12](https://reader033.fdocuments.net/reader033/viewer/2022061514/56816293550346895dd304e8/html5/thumbnails/8.jpg)
• Centripetal Force – net force directed toward the center of an object’s circular path
Centripetal ForceFc = mvt
2/rCentripetal Force= mass x (tangential speed)2 /radius of
circular path
Example: Gravitational Force – keeps moon in its orbit
![Page 9: Bellringer 11/12](https://reader033.fdocuments.net/reader033/viewer/2022061514/56816293550346895dd304e8/html5/thumbnails/9.jpg)
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?
![Page 10: Bellringer 11/12](https://reader033.fdocuments.net/reader033/viewer/2022061514/56816293550346895dd304e8/html5/thumbnails/10.jpg)
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?
![Page 11: Bellringer 11/12](https://reader033.fdocuments.net/reader033/viewer/2022061514/56816293550346895dd304e8/html5/thumbnails/11.jpg)
Centripetal vs Centrifugal
• Centrifugal – center fleeing – away from the center/outward DOES NOT EXIST!!!! Fake force!
![Page 12: Bellringer 11/12](https://reader033.fdocuments.net/reader033/viewer/2022061514/56816293550346895dd304e8/html5/thumbnails/12.jpg)
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?
![Page 13: Bellringer 11/12](https://reader033.fdocuments.net/reader033/viewer/2022061514/56816293550346895dd304e8/html5/thumbnails/13.jpg)
• Gravitational Force – mutual force of attraction between particles of matter
Newton’s Law of Universal GravitationFg = G m1m2
r2
Gravitational Force= constant x mass1 x mass2(distance between masses) 2
G = 6.673x10 -11 N•m 2 kg 2
![Page 14: Bellringer 11/12](https://reader033.fdocuments.net/reader033/viewer/2022061514/56816293550346895dd304e8/html5/thumbnails/14.jpg)
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.
![Page 15: Bellringer 11/12](https://reader033.fdocuments.net/reader033/viewer/2022061514/56816293550346895dd304e8/html5/thumbnails/15.jpg)
Gravity’s Influence
• Tides – periodic rise and fall of water
![Page 16: Bellringer 11/12](https://reader033.fdocuments.net/reader033/viewer/2022061514/56816293550346895dd304e8/html5/thumbnails/16.jpg)
Field Force
• Gravitational force is an interaction between a mass and the gravitational field created by other masses
Gravitational Field Strengthg = Fg /m
g = 9.81m/s2 on Earth’s surface
![Page 17: Bellringer 11/12](https://reader033.fdocuments.net/reader033/viewer/2022061514/56816293550346895dd304e8/html5/thumbnails/17.jpg)
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
![Page 18: Bellringer 11/12](https://reader033.fdocuments.net/reader033/viewer/2022061514/56816293550346895dd304e8/html5/thumbnails/18.jpg)
Weight
• Gravitational field strength depends only on mass and distance – your distance increases, g decreases…your weight decreases
![Page 19: Bellringer 11/12](https://reader033.fdocuments.net/reader033/viewer/2022061514/56816293550346895dd304e8/html5/thumbnails/19.jpg)
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?
![Page 20: Bellringer 11/12](https://reader033.fdocuments.net/reader033/viewer/2022061514/56816293550346895dd304e8/html5/thumbnails/20.jpg)
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.
![Page 21: Bellringer 11/12](https://reader033.fdocuments.net/reader033/viewer/2022061514/56816293550346895dd304e8/html5/thumbnails/21.jpg)
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
a. On the surface of Earthb. 1000km above the surface of Earthc. On the surface of Saturnd. 1000 km above the surface of Saturn
![Page 22: Bellringer 11/12](https://reader033.fdocuments.net/reader033/viewer/2022061514/56816293550346895dd304e8/html5/thumbnails/22.jpg)
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.
![Page 23: Bellringer 11/12](https://reader033.fdocuments.net/reader033/viewer/2022061514/56816293550346895dd304e8/html5/thumbnails/23.jpg)
Bellringer 11/18
• What is the force of gravity between two 74.0kg physics students that are sitting 85.0cm apart?
![Page 24: Bellringer 11/12](https://reader033.fdocuments.net/reader033/viewer/2022061514/56816293550346895dd304e8/html5/thumbnails/24.jpg)
Motion in Space
• Claudius Ptolemy Thought Earth was the center of the universe
• Nicolaus Copernicus Thought Earth orbits the sun in perfect circles
![Page 25: Bellringer 11/12](https://reader033.fdocuments.net/reader033/viewer/2022061514/56816293550346895dd304e8/html5/thumbnails/25.jpg)
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
![Page 26: Bellringer 11/12](https://reader033.fdocuments.net/reader033/viewer/2022061514/56816293550346895dd304e8/html5/thumbnails/26.jpg)
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
![Page 27: Bellringer 11/12](https://reader033.fdocuments.net/reader033/viewer/2022061514/56816293550346895dd304e8/html5/thumbnails/27.jpg)
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)
AverageDist. (m)
T2/R3
(s2/m3)
Earth 3.156 x 107 s
1.4957 x 1011 2.977 x 10-19
Mars 5.93 x 107 s 2.278 x 1011 2.975 x 10-19
![Page 28: Bellringer 11/12](https://reader033.fdocuments.net/reader033/viewer/2022061514/56816293550346895dd304e8/html5/thumbnails/28.jpg)
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
![Page 29: Bellringer 11/12](https://reader033.fdocuments.net/reader033/viewer/2022061514/56816293550346895dd304e8/html5/thumbnails/29.jpg)
Period and Speed of an object in circular motion
T = 2π r3 vt = G m Gm r
T = Orbital period r = mean radiusm = 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
![Page 30: Bellringer 11/12](https://reader033.fdocuments.net/reader033/viewer/2022061514/56816293550346895dd304e8/html5/thumbnails/30.jpg)
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?
![Page 31: Bellringer 11/12](https://reader033.fdocuments.net/reader033/viewer/2022061514/56816293550346895dd304e8/html5/thumbnails/31.jpg)
Example
• At what distance above Earth would a satellite have a period of 125 minutes?
![Page 32: Bellringer 11/12](https://reader033.fdocuments.net/reader033/viewer/2022061514/56816293550346895dd304e8/html5/thumbnails/32.jpg)
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?
![Page 33: Bellringer 11/12](https://reader033.fdocuments.net/reader033/viewer/2022061514/56816293550346895dd304e8/html5/thumbnails/33.jpg)
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 anythingb. Space is a vacuum and they is no gravity in a
vacuumc. Space is a vacuum and there is no air
resistance in a vacuumd. The astronauts are far from Earth’s surface at a
location where gravitation has a minimal affect
![Page 34: Bellringer 11/12](https://reader033.fdocuments.net/reader033/viewer/2022061514/56816293550346895dd304e8/html5/thumbnails/34.jpg)
Weight and Weightlessness
• Weightlessness – sensation when all contact forces are removed
![Page 35: Bellringer 11/12](https://reader033.fdocuments.net/reader033/viewer/2022061514/56816293550346895dd304e8/html5/thumbnails/35.jpg)
Astronauts in orbit
• Astronauts experience apparent weightlessness No normal force is acting on them
![Page 36: Bellringer 11/12](https://reader033.fdocuments.net/reader033/viewer/2022061514/56816293550346895dd304e8/html5/thumbnails/36.jpg)
Example
• Otis’ mass is 80kg. a. What is the scale reading when Otis
accelerates upward at 0.40m/s2 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/s2