Introduction to Mechanics

1. Introduction to Mechanics

2. Mechanics • It has nothing to do with the people you call when your car needs to be repaired. • It is the study of motion.

3. Historical Developmentof Mechanics Aristotle vs. Galileo

4. Aristotle He said that we must first understand why objects move.

5. Aristotle • Things move because they “desire” to do so. • Light things “desire” to rise to the heavens. • Heavy things “desire” to sink to earth. • In short, objects have a natural tendency.

6. Aristotle Early scientists like Aristotle were called natural philosophers.

7. Galileo Galileo said that we should first study how things move, and then we should describe why they move.

8. Dynamics Kinematics Statics Mechanics the study of motion Why?cause How? Stationary things react to pushes and pulls.

9. Mechanics is the study of • life. • motion. • work. • systems. Question

10. T/F Aristotle believed that we should first determine why things move. T Question

11. System an artificial boundary used to isolate an object or objects

12. Surroundings everything outside of the system

13. Systems Scientists are free to select any system as they study the motion of objects. Examples: you, your desk, the floor you and your desk

14. Frame of Reference • When a car zooms by you, it is moving.

15. Frame of Reference • But if you are in the car, it seems that the car is standing still and everything else is speeding past the windows.

16. Frame of Reference What’s the difference? your frame of reference

17. Frame of Reference What is THE frame of reference? you (How self-centered!) the earth the sun the galaxy

18. Frame of Reference • There is no “THE frame of reference.” • Choose the best frame of reference for the problem being solved.

19. Sun NorthPole Earth Frame of Reference The frame of reference you choose determines how the motion will be described.

20. Kinds of Reference Frames • Fixed—the reference frame is stationary, but the system moves. • Accelerated—the reference frame accelerates with the system. • Rotational—the reference frame accelerates, but the system is stationary.

21. Coordinate Axis Number Line • Zero is the origin. • Negative numbers are to the left of the origin. • Positive numbers are to the right of the origin.

22. Time non-physical continuum that orders the sequence of events

23. Time • sometimes called the space-time continuum • created by God • Before time was, God is. “I AM.”

24. Time • Any event that happens must occur within a span of time. • The start of that time span is called the initial time (ti). • The end of that time span is called the final time (tf).

25. Time • The difference between the initial and final time is the time interval. • It is called Δt (“delta tee”) and is found by subtracting the initial time from the final time.

26. What is another name for a coordinate axis? • fulcrum • space-time continuum • number line • reference frame Question

27. Scalar measurement that has a magnitude (amount) with no direction indicated Examples: 13 m 47 km/h

28. Scalar Since the smallest measurement is zero, scalars never have a negative magnitude. This paper has a measurement of 215.7 mm.

29. Vectors measurement that has both a magnitude and a direction Examples: 13 m forward 47 km/h ENE

30. Vectors The magnitude part of a vector is considered to be a scalar.

31. Vectors • Vectors are shown on the coordinate axis by an arrow. • The length indicates the magnitude. • The arrowhead indicates the direction. force (F) weight (w)

32. T/F Scalar measurements have magnitude and direction. F Question

33. Kinematics:Describing Motion

34. x 0 cm 1 cm 2 cm 3 cm v Motion • a change of position during a time interval • It can be in one, two, or three dimensions. X1 = 0.5 cm X2 = 1.5 cm X3 = 2.5 cm t1 t2 t3

35. Distance a positive scalar quantity that indicates how far an object has traveled during a time interval

36. Displacement the overall change in position during a time interval (how much it moved)

37. Displacement • Displacement is a vector quantity. • The distance is the magnitude of the displacement vector.

38. X X

39. Speed • the rate at which an object changes position • the distance traveled in a period of time • As an equation: distance d speed (v) = = time Δt

40. Speed d s t using the speed triangle: distance speed = time

41. Speed d s t using the speed triangle: distance time = speed

42. Speed d s t using the speed triangle: distance = speed × time

43. Sample Problem 1 If a motorcycle travels 540 km in 2 hours, what is its speed? distance 540 km speed = = time 2 h = 270 km/h

44. What does speed equal? • time / distance • the rate at which an object changes time • the amount of time traveled over a distance • distance / time

45. If a car travels 400 km and the trip takes 5 hours, how fast is the car traveling? • 405 km/h • 395 km/h • 2000 km/h • 80 km/h

46. If an object is traveling at 100 km/h for 5 hours, how far does it travel? • 500 km • 20 km • 105 km • 95 km d = s × t d = 100 km/h × 5 h d = 500 km

47. V1 + V2 V = 2 Average Speed rate of motion over a time interval

48. Instantaneous Speed rate of motion at a specific time

49. Sample Problem 2 It takes a fast cyclist 0.35 h (20.85 min) to cover the 19 km stage of a European biking race. What is his average speed in km/h? Known: time interval (Δt) = 0.35 h distance (d) = 19 km Unknown: speed (v)

50. Sample Problem 2 Known: time interval (Δt) = 0.35 hdistance (d) = 19 km Unknown: speed (v) d 19 km v = = = 54.2 km/h Δt 0.35 h = 54 km/h 2 Sig Digs allowed