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 Development of Mechanics
Aristotle vs. Galileo

4. He said that we must first understand why objects move.
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. 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. Stationary things react to pushes and pulls.
Mechanics
the study of motion
Dynamics
Kinematics
Statics
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.
Question

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

12. everything outside of the system
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. your frame of reference
What’s the difference?
your frame of reference

17. you (How self-centered!)
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. Frame of Reference The frame of reference you choose
Sun
Earth
North Pole
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. non-physical continuum that orders the sequence of events
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. Question What is another name for a coordinate axis? fulcrum
space-time continuum
number line
reference frame
Question

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

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

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

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

33. Kinematics: Describing Motion

34. 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 x v
0 cm
1 cm
2 cm
3 cm t1 t2 t3

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

36. the overall change in position during a time interval
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 distance d speed (v) = = time Δt
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. using the speed triangle:
distance
speed =
time

41. using the speed triangle:
distance
time =
speed

42. 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?
d = s × t
d = 100 km/h × 5 h
d = 500 km

47. rate of motion over a time interval
Average Speed
rate of motion over a time interval
V1 + V2 2
V =
This is only true in cases of uniformly accelerated motion, in the context of the one-dimensional motion discussed in Chapter 4.

48. rate of motion at a specific time
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 = = 54.2 km/h = 54 km/h 2 Sig Digs allowed d 19 km
Known:
time interval (Δt) = 0.35 h distance (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

51. Velocity technically different than speed
involves both speed and direction
It is the rate of displacement.
Example: The car is traveling east at 65 mph.

52. Velocity
Velocity is called a vector measurement because it includes how fast and which direction.
Speed is called a scalar measurement because it only involves how fast.

53. Scalars and Vectors Scalars Vectors Scalars Vectors distance (d)
displacement (d)
speed (v)
velocity (v)
Scalars
Vectors
distance (d)
displacement (d)
speed (v)
velocity (v)
Remember, vectors can be positive or negative, but scalars are only positive.

54. Scalars and Vectors Vfuel cell Vhybrid −45 m/s +30 m/s West (−)
East (+)

55. Acceleration
Acceleration is an increase in velocity in a given space of time (speeding up).
Deceleration is a decrease in velocity in a period of time (slowing down).

56. Acceleration Formula = = Δv Acceleration Δt change in velocity
change in time
The Greek letter delta (Δ) stands for “change in.” Δv
Acceleration = Δt

57. Acceleration Units The units for velocity are distance/time.
Since acceleration is velocity/time, the units must be distance/time/time.

58. Acceleration Units This is rewritten distance/time2.
Actual units could be miles/sec2. a v
West (−)
East (+)

59. Sample Problem 3
A car moving at +5.0 m/s smoothly accelerates to m/s in 5.0 s. Calculate the car’s acceleration. North is positive.
Known:
car’s vi = +5.0 m/s
car’s vf = m/s
time interval (Δt) = 5.0 s
Unknown:
acceleration (a)

60. Sample Problem 3 = = Known:
car’s vi = +5.0 m/s car’s vf = m/s time interval (Δt) = 5.0 s
Unknown:
acceleration (a)
vf − vi
(+20.0 m/s) − (+5.0 m/s) = = a Δt
5.0 s

61. Sample Problem 3 = = = = = vf − vi (+20.0 m/s) − (+5.0 m/s) a Δt 5.0 s
+3.0 m/s/s a
5.0 s =
3.0 m/s2 north

62. Sample Problem 4
A car moving at m/s smoothly slows to a stop (0 m/s) in 6.0 s. Calculate the car’s acceleration. East is positive.
Known:
car’s vi = m/s
car’s vf = 0.0 m/s
time interval (Δt) = 6.0 s
Unknown:
acceleration (a)

63. Sample Problem 4 = = Known:
car’s vi = m/s car’s vf = 0.0 m/s time interval (Δt) = 6.0 s
Unknown:
acceleration (a)
vf − vi
(0.0 m/s) − (+20.0 m/s) = = a Δt
6.0 s

64. Sample Problem 4 = = = = = vf − vi (0.0 m/s) − (+20.0 m/s) a Δt 6.0 s
-3.3 m/s/s a
6.0 s =
-3.3 m/s2 west

65. What is acceleration? going a distance the direction you travel
how fast you move
a change in how fast you move

66. If a car takes 5 seconds to change speed by 40 m/s, what is its acceleration?

67. A car going 40 m/s takes 10 s to speed up to 140 m/s
A car going 40 m/s takes s to speed up to 140 m/s. What is its acceleration?
400 m/s2
10 m/s2
1,400 m/s2
4 m/s2

68. Which of the following are possible units of acceleration?
seconds
feet
feet / second
feet / second2

69. Two and Three Dimensional Motion
These examples had motion in only one dimension.
Two dimensional motion is common also.
An example is a car rounding a corner.

70. Two and Three Dimensional Motion
Three dimensional motion is not unusual.
An example is a car rounding a corner on a hill.
This type of motion uses “spatial” dimensions, so called because 3 dimensions enclose a volume or space.

71. Two and Three Dimensional Motion
A car rounding a corner is changing its direction.
Direction is part of velocity, so the car is accelerating even if its speed is constant.

72. Two and Three Dimensional Motion
When a car repeatedly comes to a stop from the same speed—as in a busy downtown with red lights—its acceleration is closer to zero if it takes longer to stop.