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Announcements

Announcements. No office hours with Prof. Steinmetz this week [he is out of town]. Lecture 6 Newton’s laws: The foundation of modern science. Better data Final touch-up of the model Promotion of the new model. Tycho Brahe Johannes Kepler Galileo Galilei.

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Announcements

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  1. Announcements • No office hours with Prof. Steinmetz this week [he is out of town] Astronomy 201 Cosmology - Lecture 6

  2. Lecture 6Newton’s laws: The foundation of modern science Astronomy 201 Cosmology - Lecture 6

  3. Better data Final touch-up of the model Promotion of the new model Tycho Brahe Johannes Kepler Galileo Galilei Still missing: someone to put the pieces together in order to form a coherent physical theory in the modern sense  Sir Isaac Newton Astronomy 201 Cosmology - Lecture 6

  4. Sir Isaac Newton (1643-1727) • Fundamental contributions in optics, physics and mathematics: • invented calculus (independently: Leibnitz) • invented the mirror telescope • discovered than white light is composed of colored light • Theory of mechanics • Theory of gravity • demonstrated that Kepler’s laws are a consequence of the theory of mechanics and gravity: Principia Astronomy 201 Cosmology - Lecture 6

  5. Newton’s three laws of motion Newton’s first law: A body at rest or in the state of uniform motion will remain at rest or in uniform motion, unless acted upon by a net external force. Astronomy 201 Cosmology - Lecture 6

  6. Consequences of Newton I • Following Galileo, a force is required to change motion, but not to maintain it. • Change in motion means • moving faster • moving slower • changing the direction Astronomy 201 Cosmology - Lecture 6

  7. Question: How many accelerators has a car ? • The accelerator (speeding up) • The break (slowing down) • The steering wheel (changing direction) Answer: three ! Astronomy 201 Cosmology - Lecture 6

  8. Short math excursion:Scalars and Vectors • Scalar: a quantity, which can be completelyspecified by one single number • Vector: a quantity, which in addition requires the specification of a direction • Examples: • Scalar: volume, temperature, weight • Vector: velocity, acceleration, force Astronomy 201 Cosmology - Lecture 6

  9. Newton’s three laws of motion Newton’s second law (law of interia): The acceleration of an object is equal to the net force applied to it, divided by its mass. F = m  a Astronomy 201 Cosmology - Lecture 6

  10. Example: Why can you throw a baseball farther than a bowling ball? • The force you apply to both balls is the same • The bowling ball has a larger mass [inertia] the acceleration is smaller Answer: Astronomy 201 Cosmology - Lecture 6

  11. Newton’s three laws of motion Newton’s third law: For every action, there is an equal and opposite reaction. Astronomy 201 Cosmology - Lecture 6

  12. Examples: • Recoil of a gun • Jump from a boat onto the shore • two ice skater pushing each other • rocket in space Astronomy 201 Cosmology - Lecture 6

  13. Crash test: all three laws at work • Initially, car and driver in uniform motion • Car hits wall • Newton 1: wall exerts a force onto the car  car stops • Newton 2: car stops  acceleration is large  forces are large  car deforms • A priori no forces on driver • Newton 1: driver keeps on moving on a straight line at constant speed Astronomy 201 Cosmology - Lecture 6

  14. Crash test: all three laws at work • driver buckled up: seat belt exerts force onto driver, slows him down (Newton 1+2) • driver not buckled up: drivers head exerts force onto windshield, bursts it, flies through windshield, keeps on going until he eventually hits ground (Newton 1) • Newton 3: • car bounces back • buckled driver falls back into his seat • unbuckled driver: windshield exerts force on drivers head, smashes drivers head. Astronomy 201 Cosmology - Lecture 6

  15. Kepler’s three laws, Newton’s three laws, what is the difference ? Astronomy 201 Cosmology - Lecture 6

  16. Kepler’s three laws Kepler’s first law: Planets orbit the Sun in an ellipse, with the Sun at one focus. Kepler’s second law: The line from the Sun to the planet sweeps out an equal area in an equal time. Thus planets move faster if they are nearer the Sun. Kepler’s third law: The square of the period of the orbit is equal to the cube of the semimajor axis of the ellipse. Empirical laws Astronomy 201 Cosmology - Lecture 6

  17. Newton’s three laws Newton’s first law: A body at rest or in the state of uniform motion will remain at rest or in uniform motion, unless acted upon by a net external force. Newton’s second law: The acceleration of an object is equal to the net force applied to it, divided by its mass. Newton’s third law: For every action, there is an equal and opposite reaction. Axioms Astronomy 201 Cosmology - Lecture 6

  18. Announcements • No office hours with Prof. Steinmetz this week [he is out of town] Astronomy 201 Cosmology - Lecture 6

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