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The Ordered Universe

The Ordered Universe. Chapter 2. Why do planets appear to wander slowly across the sky?. Newton’s laws of motion and gravity predict the behavior of objects on Earth and in space. The Night Sky. Movement of stars, planets, sun Physical events are quantifiable and therefore predictable.

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The Ordered Universe

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  1. The Ordered Universe Chapter 2 Why do planets appear to wander slowly across the sky? • Newton’s laws of motion and gravity predict • the behavior of objects on Earth and in space

  2. The Night Sky • Movement of stars, planets, sun • Physical events are quantifiable and therefore predictable

  3. Stonehenge • Started in 2800 B.C. in south England: Built over long time by different people, none had a written language, some even lacked metal tools. Marks passage of time, specifically the seasons. Still functions today. • The largest stone, about 10 m in length, weighted 50,000 kg (100,000 lb), were moved 30 km (20 miles).

  4. Stonehenge: How to build it by people then?

  5. The Discovery of the Spread of Disease of Cholera In nineteenth century, John Snow: Observation, identified a pattern, made a suggestion (hypothesis), proved the prediction.

  6. The Birth of Modern Astronomy Historical Background: Ptolemy & Copernicus • Ptolemy • 2nd century A.D. • First planetary model • Earth at center, stationary • Stars and planets revolved around earth • Copernicus • Ideas published in 1543: On the Revolutions of the Spheres • Sun at center: Is it possible to construct a model of the heavens whose predictions are as accurate as Ptolemy’s, but in which the Sun, rather than the Earth, is at the center?

  7. Observations: Tycho Brahe & Johannes Kepler • Tycho Brahe (1546-1601) • Observed and discovered a new star • Designed and used new instruments • Collected accurate data on planetary movement • Johannes Kepler (1571-1630) • Kepler’s Law of Planetary Motion: • 1. Planets all move in elliptical orbits about the Sun, with the Sun at one focus of the ellipse. • 2. The radius vector drawn from the sun to the planet sweeps out equal areas in equal times. • 3. The cube of the average radius about the sun for each planet is proportional to the square of the period of the orbit.

  8. The Birth of Mechanics Galileo Galilei (1564-1642) • Mechanics: motions of material objects • Galileo • Invented many practical devices such as thermometer, pendulum clock, compass, etc. • Was the first to record observations of the heavens with a telescope • The Heresy Trial of Galileo

  9. Speed, Velocity, and Acceleration • Speed: distance traveled over time • Velocity: speed with direction • Equation for speed or velocity: • Acceleration: rate of change of velocity • Equation for acceleration:

  10. The Founder of Experimental Science • Galileo • Relationship among distance, time, velocity and acceleration • Found objects accelerate while falling

  11. Falling Objects • Constant acceleration • Balls on a plane with a slope: • v=at d=½at2 • Freefall • Constant acceleration at g • g=9.8 m/s2 = 32 feet/s2 • Velocity v=gt • Distance traveled • d=½gt2

  12. Examples • Ex2-1. If your car travels 30 miles per hour, how many miles will you go in 15 minutes? • Ex2-2. A sprinter accelerates from the starting blocks to a speed of 10 meters per second in one second. Answer the following questions about the sprinter’s speed, acceleration, time, and distance. In each case, answer the question by substituting into the appropriate motion equation. • 1. What is his acceleration? • 2. How far does the sprinter travel during this 1 second of acceleration? • 3. Assuming the sprinter covers the remaining 95 miters at a speed of 10m/s. What will be his time for the event? • Ex2-3. The tallest building in the United States is the sears Tower in Chicago, with a height of 1454 feet. Ignoring wind resistance, how fast would a penny dropped from the top be moving when it hit the ground?

  13. Isaac Newton and the Universal Laws of Motion • A moving object will continue moving in a straight line at a constant speed in the same direction, and a stationary object will remain at rest, unless acted upon by an unbalanced force. • Examples • Uniform motion and acceleration • Force • Inertia The first Law

  14. The Second Law • The acceleration produced on a body by a force is proportional to the magnitude of the force and inversely proportional to the mass of the object • Equation: F=ma • Example: What is the force needed to accelerate a 75 kg sprinter from rest to a speed of 10 m/s in a half second?

  15. The Third Law • For every action there is an equal and opposite reaction. • Equation: F1 = -F2 • Examples:

  16. Newton’s Law at Work

  17. Examples • Ex2-4. What is the force needed to accelerate a 75 kg sprinter from rest to a speed of 10 meters per second (a very fast run) in a half second?

  18. Momentum • Momentum depends on mass and velocity • Linear momentum: p=mv • Conservation of linear momentum • Examples (Ex2-5): A baseball with mass 0.3 kg moves to the right with a velocity of 30 m/s. What is the momentum?

  19. Angular momentum An object that is rotating will keep rotating unless a twisting force acts to change it. The twisting force is called a torque. Object with more mass, or with mass located farther away from the central axis of rotation have greater angular momentum. Conservation of Angular momentum, Examples

  20. The Universal Force of Gravity • Gravity • Newton’s law of universal gravitation • F=Gm1m2/d2

  21. The Universal Gravitational Constant, G • G: universal constant • First measured by Henry Cavendish • G=6.67 x 10-11m3/s2-kg or 6.67 x 10-11N-m2/kg2 The measurement of the G is equivalent to the measurement of the mass of the Earth.

  22. Weight and Gravity • Weight • The force of Gravity acting on an object. • Weight depends on where you are • Different on earth vs. moon • Mass is the amount of matter, which stays the same wherever you are

  23. Big G and Little g • Closely related: • Weight on Earth = (G x mass x ME)/RE2 • Weight on Earth = mass x g • Setting equations equal: g= (G x ME)/RE2 The mass of the Earth is 6.02x 1024 Kg, and its radius is 6370 km.Plug in numbers, g = 9.8m/s2 • Example (Ex2-6) : The mass of moon is 7.18x 1022 Kg, and its radius is 1738 km. If your mass is 100 kg, what would be you weight on the moon?

  24. Problems (p47) 1. If a person weighs 150 pounds, what does he weight in Newtons? 2. If your car goes from 0 to 60 miles per hour in 6 seconds, what is your acceleration? If you step on the brake and your car goes from 60 miles per hour to 0 in 3 seconds, what is your acceleration? 3. How much force are you exerting when you lift a 50-pound dumbbell? What unit will you use to describe this force? 4. What would you weight on Venus? On Saturn?

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