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Linear Motion

Linear Motion. Fast. S peed depends on distance and time Average speed uses total distance and total time Use this when an object travels at different speeds. Scalars vs . Vectors. Scalars : measure the amount (magnitude) ex: distance traveled, temperature, speed limits

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Linear Motion

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  1. Linear Motion

  2. Fast • Speed • depends on distance and time • Averagespeed • uses total distance and total time • Use this when an object travels at different speeds

  3. Scalars vs. Vectors • Scalars: measure the amount (magnitude) • ex: distance traveled,temperature, speed limits • Vectors: measure both amount and direction • vector: scalar with a direction • ex: weight, velocity of a car • In whichdirection is the 10kg weight directed?

  4. Vector or Scalar? Categorize each quantity as being either a vector or a scalar. CategoryQuantity a. ___________________ 5 m b. ___________________ 30 m/s East c. ___________________ 10 mi.North d. ___________________ 20 degrees Celsius e. ___________________ 256 bytes f. ___________________ 4000 Calories Scalar Vector Vector Scalar Scalar Scalar

  5. Distance vs. displacement • distance: total miles traveled (scalar) • displacement: change in position (vector) • distance from start to end • 2a. What is the displacement and distance of runners when they finish a one-mile race on an oval track? 1 mi Distance: 0 mi Displacement:

  6. Distance vs. displacement • distance: total miles traveled (scalar) • displacement: change in position (vector) • distance from start to end • 2b. What is your displacement and distance if you walk 3m north and then 5m south? 3m 3m + 5m = 8m Distance: 5m 3m - 5m = 2m south Displacement:

  7. Speed vs. Velocity • Speed ( v ) = distance / time • Velocity ( ) = displacement / time arrows mean they are vectors distance displacement

  8. Frame of Reference • Speed is Relative • F.o.R. is something to compare speed to • How fast are you moving now? • Earth is rotating at 1,000 mph

  9. Frame of Reference • Earth is orbiting sun at 66,000 mph • Everything in universe is moving

  10. Frame of Reference • So, if you drive 55 mph, you are going 55 mph relative to the earth • But the earth is rotating at 1000 mph! • So, Relative to outer space, you are moving 1055 mph! 55 mph 1000 mph 1055 mph 55 mph 1000 mph 945 mph

  11. Frame of Reference • Is this car moving? • Speed Limit of the Universe: light speed! (3.0 x 108 m/s)

  12. Time to Practice Go to pg. 248

  13. Variable Unit Graphing Rules Distance (m) • Use a ruler (straightedge)! • Label your axes! • (units in parentheses) • time is always the x-axis Time (s)

  14. Distance (m) Time (s) Graphing Rules Distance vs. Time 3.Title the graph! • (Y vs. X)

  15. Graphing Rules 4.SCALE. • Stretch out your axes!

  16. Graphing Rules 5. Use a Pencil!! 6. Do not just connect the dots! Line of best fit curve: smooth line: ruler The line might not touch dots

  17. Distance (m) Time (s) Graphing Rules • Drawing tangent lines • drawn at a point • “balance” ruler on curve • perpendicular with normal Distance vs. Time Ahh. Just right! • make it long enough to find the slope

  18. Graphing: start work! Pg254

  19. Distance vs. Time (x2, y2) (0.15, y1) Distance (m) Time (s) 0.15 s

  20. Movies And now for a short movie

  21. Eureka: Inertia

  22. Eureka: Mass

  23. Eureka: Speed

  24. Acceleration • accelerationthe rate of change of velocity • =final velocity • =initial velocity • refers to speeding up and slowing down or… Velocity Speed Direction arrows mean …

  25. ExampleA car moving at 20 m/s comes to a stop in four seconds. What was the car’s acceleration? Given: Unknown:

  26. Examplesolve for acceleration said “negative five meters per second per second” negative acceleration means… slowing down

  27. Acceleration • You “feel” speed when you accelerate • This includes speeding up, slowing down and • sharp turns at constant speed! • All three are accelerations

  28. Eureka: Acceleration I

  29. Distance vs. Time Graphs Constant speed • Slope • units are • AKA velocity! Distance (m) Time (s) Distance (m) Time (s) Increasing Speed

  30. Speed vs. Time Graphs • Slope • units are • AKA acceleration! • (same answer as example)

  31. Speed vs. Time Graphs • So, to summarize the graphs: • For distance vs. time: • slope = speed • For speed vs. time: • slope = acceleration • areabetween line and x-axis = distance covered

  32. Eureka: Acceleration II

  33. Freefall • freefall  objects moving under only force of gravity • due to gravity = g • g = 9.8 m/s2 • Terminal velocity is the fastest an object can fall • terminal velocity  when air resistance becomes equal to gravity

  34. Freefall • let’s look at the motion of three objects • An objectdropped from rest • An object thrown downwards • An object thrown upwards • All have the sameacceleration! • Allof these motions are types of… freefall!

  35. Eureka: Gravity

  36. Lab: Acceleration due to Gravity pg. 330A-D 1. Make sure the motion detector only “sees” the ball • Not your arms • Not a table or the wire basket 2. Start the motion detector after you hear beeping for 30 s 3. Make sure your graph has a smooth curve

  37. Safety • Don’t stand on things with wheels • Cover the motion detector with a wire basket Lab: Acceleration due to Gravity pg. 330A-D Important! • Turn off your motion detector when you are done gathering data! • Use the data table on the handheld computer to see the data you need to copy

  38. Don’t forget to…. • Label your axis: variable & units • Title your graph: _____ vs. _____ • SCALE your graph

  39. Lab Questions • Displacement, Velocity & acceleration graphs: http://www.youtube.com/watch?v=_ES1JJ7ErzI • Slow Motion Ball: http://www.youtube.com/watch?v=1PyjLXIYMzI&feature=related

  40. Putting it together • Let’s use what we know about graphs to make two more formulas. • Let’s look at the graph from ti to tf

  41. Putting it together • Each time matches up with a velocity • Initial velocity is vi • final velocity is vf vf vi

  42. Putting it together • To find distance: • area between the line and the x-axis • d = area of rectangle + area of triangle vf vi

  43. Putting it together • d = area of rectangle + area of triangle • area of rectangle = • area of triangle = vf vi

  44. Putting it together we now have a connection between a and d

  45. Putting it together • solve for t from first a equation • substitute into second a equation • a little fancy algebra and… nice if you do not have t

  46. Putting it together • use equation 1 only if acceleration is zero • use equations 2-4 only if constant acceleration

  47. Putting it together • notice there are no arrows • However, the variable are ALL still vectors

  48. Putting it together • vectors mean that direction is important • ex. positive represents up, negative for down

  49. ExampleA spear is thrown down at 15 m/s from the top of a bridge at a fish swimming along the surface below. If the bridge is 55 m above the water, how long does the fish have before it gets stuck? y x start -15m/s -55m -9.8m/s2 end

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