Exploring Motion and Forces: Frames of Reference and Velocity

1. Motion & Forces Q To me there has never been a higher source of earthly honor or distinction than that connected with advances in science. Isaac Newton

2. Frames of Reference You don't always need to see something move to know that motion has taken place A reference point is needed to determine the position of an object Ever felt like you were slowly moving backwards when a semi truck passed you on the highway?

3. Frames of Reference You have mistakenly made the truck your frame of reference, measuring your motion relative to the truck Both vehicles move forward relative to the stationary tree (the ground is the proper frame of reference) Proper Frame of Reference

4. Describing One-Dimensional Motion • Motion- a change in position, measured by distance and time • The SI unit of length or distance is the meter (m) • Shorter distances are measured in centimeters (cm) • Longer distances are measured in kilometers (km) • The following quantities are used to describe motion: • Speed • Velocity • Acceleration The fastest “thing” travels at ~670,000,000 mph… What is it? Light

5. Change in Position • Suppose a runner jogs to the 50-m mark and then turns around and runs back to the 20-m mark • Distance- quantity that tells you how far something has moved • The runner travels 50 m in the original direction (east) plus 30 m in the opposite direction (west), so the total distance she ran is 80 m

6. Change in Position • Sometimes you may want to know not only your distance but also your direction from a reference point, such asfrom the starting point • Displacement- the distance AND direction of an object’s position relative to a starting point • Adding displacement: 50 m east, turn around and run 30 m west = 20 m east total displacement

7. Speed • Speed- the distance traveled by a moving object over a period of time • Kilometers/sec, miles/hour, meters/min

8. D = SXT S = D/T T = D/S Example: A rifle bullet travels 1200 meters in 4 seconds. What is the speed of the bullet? Step # 1 Step # 2 Step # 3 Speed Formula S = 300 m/sec. S = D / T S = 1200m/4 sec.

9. SPEED! BABY! SPEED!

10. Constant Speed • A moving object that doesn’t change its speed travels at constant speed • Constant speed- equal distances are covered in an equal amount of time (i.e. 25 miles/hour) • This results in a linear position vs. time graph

11. Changing Speed • Usually speed is not constant • Usually the speed will change for any number of reasons (wind, stop lights, etc.)

12. Instantaneous speed • Instantaneous speed-speed at any instant which the word “speed” alone is representing • “My speed is 60 miles/h” is referring to your speed at that particular moment, but likely to change

13. Average Speed Instantaneous speeds A car travels at 50 km/h, slows down to 0 km/h, and speeds up again to 60 km/h Its average speed over the whole journey: overall distance travelled = total time of travel

14. Graphing Motion • On a distance (or position)-time graph, the distance,or position, is plotted on the vertical axis and the time on the horizontal axis • Each axis must have a scale that covers the range of number to be plotted • The slope on a distance-time graph is equal to speed

15. Check for Understanding • What is the difference between distance and displacement?

16. Check for Understanding • __________ is the distance an object travels per unit of time. A. acceleration B. displacement C. speed D. velocity

17. Check for UnderstandingName two observations you can make about the cars speed from looking at the graph.Calculate the speeds of both cars from the graph by choosing two points on each line.

18. Check for UnderstandingCalculate the average speed of the car below:

19. direction magnitude (speed) Velocity • Velocity- a speed in a given direction • It’s possible for two objects to have the same speed, but different velocities Has direction! velocity

20. Earth’s speed at the equator: 1670 km/h Earth’s velocity at the equator: 1670 km/h to the East

21. Velocity • Velocity depends on direction as well as speed, so the velocity of an object can change even if the speed of the object remains constant • The speed of this car might be constant, but its velocity is not because the direction of motion is always changing

22. Velocity and Momentum • A moving object has a property called momentum that is related to how much force is needed to change its motion • Momentum (p) takes into consideration not only an object’s velocity AND mass • Mass- the amount of matter (atoms) in an object (kg)

23. Velocity and Momentum • Momentum is given the symbol p and can be calculated with the following equation p = mass (kg) X velocity (m/s) • The unit for momentum is kg · m/s. Notice that momentum has a direction because velocity has a direction.

24. Velocity and Momentum • When two objects have the same velocity, the one with the larger mass has the larger momentum • The 1,000-kg car traveling at 20 m/s east has a momentum of 20,000 kg•m/s east. • p = m X v = 1000kg X 20 m/s • What about the truck? • Law of conservation of momentum- the total momentum of a system stays the same before and after an interaction

25. Check for Understanding • Speed or Velocity? • A race car traveling 155 miles per hour turning left on a circular racetrack • A sprinter running 3 meters/sec • A tornado heading west at 15 km/hour

26. Check for Understanding • Speed or Velocity? • A race car traveling 155 miles per hour V turning left on a circular racetrack • A sprinter running 3 meters/sec S • A tornado heading west at 15 km/hour V

27. Check for Understanding • A 1,500-kg car is traveling west at 100 m/s. What is the car’s momentum? A. 1,500 kg•m/s B. 150,000 kg•m/s C. 1,400 kg•m/s D. 1,600 kg•m/s

28. Check for Understanding • A 1,500-kg car is traveling west at 100 m/s. What is the car’s momentum? B. 150,000 kg•m/s

29. Change in Velocity • Velocity rarely stays constant • Accelerationis the rate of change of velocity • When the velocity of an object changes, the object is accelerating • A change in velocity can be either a change in how fast something is moving, or a change in the direction it is moving • Acceleration occurs when an object changes its speed, its direction, or both • Acceleration- the rate at which velocity changes in time (speed OR direction components)

30. Change in Velocity • In a car we can change our velocity 3 ways: • Speed up • Slow down • Change direction • All of these would be considered acceleration

31. Change in Velocity We say that this car is accelerating because its velocity is increasing We say that this car is accelerating because its direction is changing as it turns, which means its velocity is changingeven though its speed stays constant We say that this car is accelerating because its velocity is decreasing. Decreasing velocity is still acceleration, although it is a negative acceleration 30 km/h 60 km/h 60 km/h 60 km/h 60 km/h 30 km/h 0 km/h

32. Change in Velocity • Changing speed changes velocity and is therefore considered acceleration • Positive acceleration speeding up • Negative acceleration slowing down

33. A = Vfinal–Vinitial T Acceleration Formula OR

34. A = Vfinal – Vinitial Time A = 50.0m/s – 0.0m/s 10.0s Example: A cars velocity changes from 0.0m/ssouth to 50.0m/s south in 10.0 seconds. Calculate the cars acceleration Vinitial: 0.0m/s south Given: Vfinal: 50.0m/s south 10.0 seconds Time: acceleration Uknown: Equation: Setup: A = 5.0 m/s/s or m/s2 Solve:

35. Check for Understanding A car traveling at 60 mph accelerates to 90 mph in 3 seconds. What is the car’s acceleration? Given: Uknown: Equation: Setup: Solve:

36. Check for Understanding A car traveling at 60 mph accelerates to 90 mph in 3 seconds. What is the car’s acceleration? Given: Velocity(initial) = 60 mph 90 mph Velocity(final) = Time = 3 seconds Unknown: What is the car’s acceleration? Equation: Acceleration = Velocity(final) - Velocity(initial) time 30 mph 3 seconds Setup: 90 mph - 60 mph 3 seconds = = Solve: = 10 mph/second

37. Check for Understanding A car traveling at 60 mph slams on the breaks to avoid hitting a deer. The car comes to a safe stop 6 seconds after applying the breaks. What is the car’s acceleration? Given: Unknown: Equation: Setup: Solve:

38. Check for Understanding A car traveling at 60 mph slams on the breaks to avoid hitting a deer. The car comes to a safe stop 6 seconds after applying the breaks. What is the car’s acceleration? Given: Velocity(initial)= 6 seconds Time = 60 mph Velocity(finall)= 0 mph Acceleration Unknown: = Velocity(final) - Velocity(initial) time Acceleration Equation: -60 mph 6 seconds 0 mph - 60 mph 6 seconds Setup: = = = Solve: -10 mph/second

39. Velocity vs. Time Graphs The slope of the line on a speed-time graph equals the object’s acceleration Negative acceleration Positive acceleration

40. Change in Velocity • Is the velocity for each car constant or changing? • Which car has the highest velocity?

41. Acceleration Velocity vs. Time Graph Positiveacceleration

42. Acceleration Velocity vs.Time Graph Negative acceleration

43. Acceleration in 2D • The speed of the horses in this carousel is constant, but they are accelerating because their direction is changing • This would be considered centripetal acceleration- acceleration of an object toward the center of a curved or circular path

44. Horizontal & Vertical Motion Are Independent The bullet from the gun keeps going forward while it falls. Gravity makes both bullets fall at the same rate

45. What if the Projectile is Thrown Upward? Projectiles keeps moving forward with the same speed. . Gravity slows projectiles down while going up and speeds them up while going down.

46. Check for Understanding Which is NOT a form of acceleration? A. maintaining a constant speed and direction B. speeding up C. slowing down D. turning

47. Check for Understanding Which is NOT a form of acceleration? A. maintaining a constant speed and direction

48. why? The question is… Why does everything in the universe move?

49. The answer… Big, huge, massive forces! And little ones too.

50. Forces • A force is a pull (an attraction) • Or, a push(a repulsion)