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I.A Newtonian Mechanics

I.A Newtonian Mechanics. I.A.1 Kinematics in One Dimension. Mechanics – motion and the forces that cause that motion Kinematics – describes motion without regard to the forces that cause that motion Dynamics – describes the forces that cause the motion. Displacement – change in position.

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I.A Newtonian Mechanics

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  1. I.A Newtonian Mechanics

  2. I.A.1 Kinematics in One Dimension • Mechanics – motion and the forces that cause that motion • Kinematics – describes motion without regard to the forces that cause that motion • Dynamics – describes the forces that cause the motion

  3. Displacement – change in position

  4. Distance and displacement are NOT the same.

  5. Ex. A kitten is thrown straight upward from the edge of a cliff the is 30 m high. The kitten rises 10 m and then falls all the down to the base of the cliff. What is the distance the kitten travels? What is the displacement of the kitten?

  6. Note displacement needs a direction

  7. Speed and Velocity (they are not the same either)

  8. Average velocity and constant velocity (your first boxer)

  9. Example: The initial position of a runner is 50.0 m. 3.00 s later, the runner is at 30.0 m. What is the average velocity of the runner?

  10. Acceleration (also known as “what’s a meter per second per second?”)

  11. A brief and simple, yet fundamentally important comparison of velocity and acceleration.

  12. Average (constant) acceleration(your second boxer)

  13. Example: A car is traveling in a straight line along a highway at a constant speed of 80.0 km/h for 10 s. What is the acceleration of the car?

  14. Example: During the time interval of 9.0 s to 14 s, a drag racer slows (using a parachute – or perhaps by dragging a comatose llama in a burlap bag) from 15.0 m/s to 5.0 m/s. What is the acceleration?

  15. A few notes on signs and acceleration • If acceleration and velocity have the same sign, the object is increasing in speed. • If acceleration and velocity have opposite signs, the object is decreasing in speed.

  16. A few light and humorous moments as Mr. Evans walks across the front of the room.

  17. Concept Check: A car traveling with a constant speed travels once around a circular path. Which of the following is true regarding the car’s motion? • The displacement is zero. • The average speed is zero. • The acceleration is zero.

  18. Kinematics equations for constant acceleration (The Big Four)

  19. Rewriting the equation for acceleration

  20. An equation for displacement

  21. Example: An object with an initial velocity of 4.0 m/s travels along a straight path with constant acceleration. In a time of 3.0 s, the object increases its velocity and travels a distance of 27 m. What is the final velocity of the object?

  22. A second equation for displacement

  23. Wait a minute, I think I see another kinematics equation . . .

  24. Ex. A race car starts from rest and accelerates at –5.00 m/s2. What is the velocity of the car after it has traveled –30.5 m?

  25. Ex. A drag racer starting at x = 50.0 m accelerates from rest at a constant rate of 8.0 m/s2. a) How fast is the car going at t = 10.0 s? b) How far has it traveled at t = 10.0 s. c) What is the average velocity for the time interval from 0-10.0 s?

  26. Freely falling objects

  27. Galileo and an exceedingly impressive demo.

  28. A couple of modifications to the kinematic equations • Since displacement is vertical replace x with y • a = g = –9.81 m/s2

  29. Example: A stone is dropped from a tall building (this is against the law and very unsafe by the way). What is the vertical displacement of the stone after 4.00 s? What is its velocity at this point?

  30. Example: A melon is thrown upward from the top of a tall building with an initial velocity of 20.0 m/s. Find the a) time for the melon to reach its maximum height b) the maximum height c) the time for the melon to return to the thrower d) the time when the melon is 22.5 m below its initial height.

  31. Some notes on freely falling bodies. • Object is not necessarily moving down, but g is downward • Compare v and g for an object tossed upward • An object launched upward and downward with same vo

  32. Concept check: A baseball is thrown upward. What is the magnitude and direction of the ball’s acceleration: • At one-half of it maximum height as the ball rises? • At maximum height? • At one-half of the maximum height as the ball falls?

  33. Graphical Analysis of Velocity and Acceleration

  34. Position vs. time graphs

  35. The slope of a position vs. time graph is velocity.

  36. Describe the velocity for each part of the graph.

  37. Velocity vs. time graphs (slightly, although not intensely, more confusing)

  38. The slope of a velocity vs. time graph is acceleration.

  39. Hmmm, another interesting property of velocity vs. time graphs . . .

  40. The area under the curve for a velocity vs. time graph is displacement.

  41. Some for fun

  42. Kinematics Equations in Two Dimensions The Slow, Painful Death of the AP Physics Student

  43. The spacecraft in flight and the boat crossing the river

  44. This is important – the two velocity vectors in each case are independent of each other.

  45. A couple of demos.

  46. I.A.2 Motion in Two Dimensions

  47. An object launched horizontally (an instructive and illustrative figure)

  48. Concept check: Describe (magnitude and direction) • The horizontal component of an object’s velocity if the object is launched horizontally • The vertical component of an object’s velocity if the object is launched horizontally • The speed of an object that is launched horizontally • The acceleration for an object launched horizontally

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