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Acceleration due to gravity (Earth)

Acceleration due to gravity (Earth). Acceleration due to gravity (Earth) Treated as a constant near the Earth 9.81 m/sec^2 = 981 cm/sec^2. Displacement, velocity, and time. Units?. m/sec = m/sec. What does the slope mean?. Velocity, acceleration, and time. m/sec = m/sec -2 * sec.

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Acceleration due to gravity (Earth)

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  1. Acceleration due to gravity (Earth)

  2. Acceleration due to gravity (Earth) • Treated as a constant near the Earth • 9.81 m/sec^2 = 981 cm/sec^2

  3. Displacement, velocity, and time Units? m/sec = m/sec

  4. What does the slope mean?

  5. Velocity, acceleration, and time m/sec = m/sec-2 * sec m/sec-2 = m/sec / sec

  6. Assume constant acceleration

  7. What is happening here? What does the slope mean? What is the linear relationship?

  8. Displacement, acceleration, and time

  9. Assume constant acceleration

  10. What could affect this curve for a falling object?

  11. What could affect the curve of displacement vs time?

  12. What could affect the curve of displacement vs time? • Initial displacement? • Initial velocity? • Wind resistance? • Mass? • Size?

  13. 22. An object shot straight up rises for 7.0 sec before it reaches its maximum height. A second object falling from rest takes 7 sec to reach the ground. Compare the displacements of the objects.

  14. 23. Describe the changes in the velocity of a ball thrown straight up into the air. Describe the changes in the acceleration.

  15. 24. The value of g on the moon is 1/6 of its value on Earth. Will a ball dropped by an astronaut hit the surface of the moon with a smaller, equal, or larger speed than that of a ball dropped the same height on Earth?

  16. 26. One rock is dropped from a cliff, the other thrown upwards from the top of the cliff. They both land at the bottom of the cliff. Which has a greater velocity at landing? Which has a greater acceleration? Which arrives first?

  17. Given: A ball, initially at rest, is dropped. Assuming it is near the surface of the earth, how far does it fall in 2 seconds? 4? 10? 100? What is its final velocity?

  18. Given: A ball, initially at rest, is dropped. Assuming it is near the surface of the earth, how far does it fall in 2 seconds? 4? 10? 100? d = ½ a t^2, where a = 9.8 m/sec^2 What is its final velocity?

  19. Given: A ball, initially at rest, is dropped. Assuming it is near the surface of the earth, how far does it fall in 2 seconds? 4? 10? 100? d = ½ * a * t^2, where a = 9.81 m/sec^2 What is its final velocity? V = a * t, where a = 9.81 m/sec^2 and t is found above

  20. A ball falls from rest for a distance of 6m. How far will it fall in the next 0.1sec?

  21. A ball falls from rest for a distance of 6m. How far will it fall in the next 0.1sec? • Find t from d = (1/2)at^2 • Find d from d = (1/2)a(t+0.1)^2

  22. Displacement, velocity, acceleration, and time

  23. Optional: Displacement, velocity, and time

  24. Velocity, acceleration, and time m/sec = m/sec-2 * sec m/sec-2 = m/sec * sec

  25. Displacement, acceleration, and time

  26. Displacement, acceleration, velocity, and time

  27. Displacement, acceleration, and velocity Position, velocity and acceleration when t is unknown. vf2 = vi2 + 2 * a * d

  28. Example 1: Calculating Distance • A stone is dropped from the top of a tall building. After 3.00 seconds of free-fall, what is the displacement, d of the stone?

  29. Example 1: Calculating Distance • Since vi = 0 we will substitute g for a and get: d = ½ gt2 d = ½ (-9.81 m/s2)(3.00 s)2 d = -44.1 m

  30. Example 2: Calculating Final Velocity • What will the final velocity of the stone be?

  31. Example 2: Calculating Final Velocity • Again, since vi = 0 we will substitute g for a and get: vf = gt vf = (-9.81 m/s2)(3.00 s) vf = -29.4 m/s • Or, we can also solve the problem with: vf2 = vi2 + 2ad, where vi = 0 vf = [(2(-9.81 m/s2)(44.1 m)]1/2 vf = -29.4 m/s

  32. Example 3: Determining the Maximum Height (per 6) • How high will the coin go?

  33. Example 3: Determining the Maximum Height • Since we know the initial and final velocity as well as the rate of acceleration we can use: vf2 = vi2 + 2ad • Since Δd = Δy we can algebraically rearrange the terms to solve for Δy.

  34. Example 4: Determining the Total Time in the Air • How long will the coin be in the air?

  35. Example 4: Determining the Total Time in the Air • Since we know the initial and final velocity as well as the rate of acceleration we can use: vf = vi+ aΔt, where a = g Solving for t gives us: • Since the coin travels both up and down, this value must be doubled to get a total time of 1.02s

  36. Position Position Position Position Time Time Changing Velocity Constant Velocity What information does the shape of the curve provide? • Straight curve = constant velocity. • Changing curve = changing velocity (i.e. acceleration).

  37. Sample Problems A horse rounds the curve at 11m/s and accelerates to 17.3m/s. His acceleration is 1.8m/sec^2. How long does it take him to round the curve and what distance does he travel?

  38. Sample Problems A car slows from 15.6m/sec to 0.9m/sec over a distance of 29m. How long does this take and at what acceleration?

  39. Sample Problems Natara is running a 1km race, and during the second half of the race suddenly increases her speed from 9.3m/s to 10.7m/s over a 5.3second interval. What was her acceleration and how far did she run while accelerating?

  40. Sample Problems Alex, while driving through the parking lot, brakes at 3m/sec^2 over a distance of 47m. What is his final velocity? For how long did he brake?

  41. Sample Problems A train traveling at 5.2m/sec accelerates at 2.3m/sec^2 over a 4.2sec period. What is its final velocity? How far does it travel while accelerating?

  42. Sample Problems Connor throws a bowling ball out the window of Planet WeirdPicture with a downward velocity of 14.9m/s. The ball falls 32m in 9.3s. What is its final velocity and the acceleration due to gravity on planet WeirdPicture?

  43. Sample Problems

  44. Sample Problems

  45. Sample Problems

  46. Sample Problems

  47. Sample Problems

  48. Position Position Time Position Position Time Position Position Position Position Time Time What information does the shape of the curve provide? Negative Acceleration Positive Acceleration Decreasing Velocity Increasing Velocity

  49. E D C Position B A Position Time Characterize the motion of the object from A to E. Constant velocity in the positive direction. Decreasing velocity. Stationary. Increasing velocity. Constant velocity in the positive direction.

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