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Equations of Motion

Equations of Motion. Newton’s First Law of Motion. Every body continues in its state of rest or uniform speed in a straight line unless acted on by a nonzero net force. Preceding defines INERTIA Preceding defines MASS ( m  W). Best when observed in the absence of friction.

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Equations of Motion

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  1. Equations of Motion

  2. Newton’s First Law of Motion Every body continues in its state of rest or uniform speed in a straight line unless acted on by a nonzero net force. Preceding defines INERTIA Preceding defines MASS (m W) Best when observed in the absence of friction.

  3. Newton’s Second Law of Motion The acceleration of an object is directly proportional to the net force acting on it and is inversely proportional to its mass. The direction of the acceleration is in the direction of the net force acting on the object.

  4. Newton’s Third Law of Motion Whenever one object exerts a force on a second object, the second exerts an equal and opposite force on the first.

  5. The Bane of Galileo: Friction Friction is everywhere! There is little wonder why it played such a prominent part in MECHANICS for the ancients (e.g., Aristotle). Galileo recognized friction as separate from motion, so the equations of kinematics could be discovered (using geometry). Friction - treated as a force (though not a vector) - always opposite to the motion - sometimes related to the motion, sometimes not so related

  6. Dynamics of Circular Motion Galileo sez: Circular motion is not natural; straight line motion is natural What is required for an object to move in a circle?

  7. What happens to an object when the centripetal force quits?

  8. A 0.150-kg ball on the end of a 1.10-m cord is swing in a vertical circle. What is the minimum speed that the ball must have to continue moving in a circle?

  9. Banked Curves - Rotations and Inclines

  10. A 1000-kg car rounds a curve on a flat road of radius 50 m at a speed of 50 kph (14 m/s). Will the car make the turn if the pavement is icy and s = 0.25? Ffr FR the car will slide

  11. An airplane traveling at 520 kph attempts to turn around. By banking at an angle of 38, how long will this maneuver take? Need to find radius of curve, then time =  radius / speed

  12. Nonuniform Circular Motion Easiest to describe in terms of the circle. (polar coordinates)

  13. Terminal Velocity For velocity-dependent friction force (e.g., air resistance), the frictional force can equal the motive force.

  14. Newton’s Law of Universal Gravitation In 1687, very controversial law of mechanics action at a distance - no direct contact (first of the force fields) universal - applies to both terrestrial and celestial motion verification required experiments, calculus, and history

  15. Law of Universal Gravitation Every particle in the universe attracts every other particle with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them. This force acts along the line joining the two particles.

  16. What is the force of attraction between a 50-kg person and a 75-kg person sitting 50 cm apart?

  17. Weighing the Earth

  18. What is g on the top of Mt Everest, 8848 m high?

  19. What is g on the moon? mM = 7.35E22 kg rm = 1.74E6 m

  20. What is g in the Shuttle? h = 240 km

  21. What is the effect of the Earth’s rotation on the value of g?

  22. Why is the Space Shuttle weightless?

  23. Kepler’s Laws and Gravitation Kepler found three laws of planetary motion in Brahe’s data. He was looking for celestial music. 1) Planetary orbits are ellipses 2) Equal areas in equal time 3) T2 s3

  24. Kepler’s Third Law from Newton’s Laws

  25. Gravitational Field Force fields are simpler than contact forces. Project action at a distance. Interaction only for pairs of objects. Force depends on the “charge” of an object.

  26. Forces in nature : gravitation - mass electromagnetic - electric charge weak nuclear - electric charge strong nuclear - baryon Electric and magnetic forces combined by Faraday and Maxwell around 1840. Electromagnetic and weak nuclear combined in 1967. Who is next?

  27. Principle of Equivalence Conceptually, the gravitational mass and the inertial mass are different. But, numerically, they are equal to high precision. What about the laws of mechanics?

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