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MSTC Physics 2

MSTC Physics 2. Chapter 7 Section 6. Johannes Kepler. Formulated 3 empirical laws from observational data gathered over a 20 year period by Tycho Brahe Laws were initially applied only to Mars First 2 laws announced in 1609 3 rd law announced 10 years later. Johannes Kepler.

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MSTC Physics 2

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  1. MSTC Physics 2 Chapter 7 Section 6

  2. Johannes Kepler • Formulated 3 empirical laws from observational data gathered over a 20 year period by Tycho Brahe • Laws were initially applied only to Mars • First 2 laws announced in 1609 • 3rd law announced 10 years later

  3. Johannes Kepler • Took Kepler 15 years to derive his laws from observed data • Today they can be derived theoretically in a page or two of calculations • Laws apply to planets and any 2 body system composed of a body revolving about a much more massive body

  4. Kepler’s First Law • Law of orbits • Planets move in elliptical orbits, with the Sun at one of the focal points • In reality, most of the planets orbit in a path closer to a circle than an ellipse

  5. Kepler’s Second Law • Law of areas • A line from the sun to a planet sweeps out equal areas in equal lengths of time • Tells us that the orbital speed of a planet varies in different parts of its orbit • Speed is greater when it is closer to the sun

  6. Kepler’s Third Law • Law of periods • The square of the orbital period of a planet is directly proportional to the cube of the average distance of the planet from the Sun; that is, T2 α r3 • Can we derive it?

  7. Loose Ends

  8. Centripetal Force Lab • Why was it important to make sure that the stopper was traveling in a horizontal circle? • to make sure we had uniform circular motion

  9. Vertical Circles • A small sphere of mass m is attached to the end of a cord of length R, which rotates under the influence of the gravitational force in a vertical circle about a fixed point. Determine the tension in the cord at various locations.

  10. Sample Problem A car of mass m passes over a bump in a road that follows the arc of a circle of radius R. What force does the road exert on the car as the car passes the highest point of the bump if the car travels at a speed v? What is the maximum speed the car can have as it passes this highest point before losing contact with the road?

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