1. Physical Science Unit: Motion

2. Physics:
A branch of Physical science that deals with physical changes of objects.
The models on which Physics is based are most frequently expressed in mathmatical equations that describe the conditions of the real world.
The primary task in studying physics is to understand its basic principles

3. Motion Is a change in position relative to a frame of reference
Motion is measured by distance and time.

4. Frame of reference
The object or point from which movement is determined
Movement can only be measured with reference to something that is assumed to be fixed in place

5. The most common frame of reference is the Earth

6. Are You Moving ? You are sitting down, reading a book….
Object is in motion when its distance from another object is changing.
All depends on the “Point of Reference”
Therefore object is in motion if it changes position relative to a reference point.

7. International System of Units
“SI”
Based on the number 10
Distance (length) uses meter (about 39 inches)
Mass (how much matter) uses gram ( a nickel is about 5 grams)
Volume (how much space)
Liquid volume – uses liter ( a little more than a quart)
Solid volume – uses cm3 ( about the size of a sugar cube)
1 ml = 1 cm3
Weight (affect gravity has on object) uses newton ( an apple weighs about 1 newton) (1 pound is about 4.4 newtons)
Density = Mass / Volume = grms / ml

8. To Amplify the Point Distances can be short or very long.
Basic metric unit of length is the meter.
Metric prefixes are based on the number 10.
10 meters = 1 decameter
10 decameters = 1 hectometer
10 hectometer = 1 kilometer
Therefore : 1 kilometer =1000 meters
And…
There are 10 decimeters in a meter
There are 10 centimeters in a decimeter
There are 10 millimeter in a centimeter
Therefore: 1000 millimeters = 1 meter

9. Metric Stairs
You should be comfortable with converting from [cm] to [m], [mm] to [km], and so on.
Convert: centigrams into hectograms: going four steps up means you move the decimal 4 places to the left. Therefore:
1527 centigrams = hectograms
&
kg = (steps to the right) mg

10. Graphing ( x,y ) coordinates
A graph w/ points (2,3) , (-2,1) & (1.5, -1) plotted:
Remember:
b. The y axis is vertical axis
c. The origin is (0,0)
Remember:
a. the x axis is the horizontal axis

11. More Graphing!
Graph the following points: a) (3, 3) b) (- 2, 3) c) (- 1, - 2) d) (3, 0) e) (0, 0) f) (0, - 4) b a e d c f

12. & Still More Graphing…. What are the coordinates of these points?
Click for the answers…
a. (2, 0) b) (0, 2) c) (4, 3) d) (-1, 3) e) (-3, 3) f) (-1, -3)
g) (-3, -1)
h) (2, -4)

13. Working w/ Units
Determining the correct units in a problem is just as important as getting the number correct.
Remember we can “cancel” numerators & denominators to make the math easier:
24 x 6 x 2 x 9 x 18 = 24 x 6 x 2 x 9 x 18 = 1
12 x 18 x 3 x 3x x 18 x 3 x 3 x 24
We can do the same w/ units….

14. Multiplying & Dividing Units
Do this problem:
5 minutes x 3 feet = 15 minute feet
12 miles miles
3 hours hour
mile x week x dollar x bananas x week x newton x week
dollar x newton x mile x bananas x week x kilogram x week
mile x week x dollar x bananas x week x newton x week week
dollar x newton x mile x bananas x week x kilogram x week kilometer

15. Speed = distance / time Formula: S=D/T
What is the speed of a car that traveled 75 km in 1.5 hr?
S = D / T = 75km / 1.5 hr = 50 km/hr
Since distance is measured in meters or kilometers and time is measured in seconds or hours, the units of speed are meters per second (m/sec) or kilometers per hour (km/hr)
In Physics, distance can be thought of as having a directions. The distance is called displacement.

17. Graphing Acceleration
You can use both a speed - versus - time graph and a distance - versus - time graph to analyze the motion of an accelerating object.

18. Speed - Versus - Time Graph
The slope of a line on a speed - versus - time graph represents acceleration.

19. Distance - Versus - Time Graph
You can also show the motion of an accelerating object with a distance - versus - time graph.

20. Constant Speed Speed that does not change.
Slope: The slant of a line connecting 2 points that indicates the change in the y axis as compared to the change in the x axis

21. Graphing line slopes (rise/run)
1. Graph the line which passes through (2, 3) and has a slope of 2/3.
2. Graph the line which passes through (1, 1) and has a slope of -4. (remember - 4 = -4/1) 2 1
(2,3)
(1,1)

22. Graphing points & slope (rise/run)
1. Graph the line which passes through (0, 2) and has a slope of 3. (remember 3 can be written as 3/1)
2. Graph the line which passes through (- 1, 1) and has a slope of – 2/3. 2 1
(0,2)
(-1,1)

23. Notice the difference in the graphs for constant speed and for average speed

24. Average Speed
The measure of speed obtained by dividing the total distance by the total time.
The speed of a moving objet is not always constant
Speed that changes is not constant speed
Dividing the total distance by the total time gives the average speed NOT the actual speed at that instance

25. Average Speed or Average Velocity
Average speed = total distance / total time
What is the average speed after 2 minutes?
total distance is 75m, total time
is 2 minutes.
S = D/T
S = 75m / 2min
S= m/min
What is the average speed between 2 & 4 minutes?
total distance: 110m – 75m = 35m
total time: 4min – 2min = 2minutes total time
S = D/T
S = 35m / 2min
S= m/min

26. Example Problem : Speed
A truck travels to and from a stone quarry that is located 2.5 km to the east. What is its distance? What is its displacement?
Solution:
Distance = 5 km,
Displacement = 0 km

27. Example Problem average acceleration
During a race, a sprinter increases from 5.0 m/s to 7.5 m/s over a period of 1.25 s. What is the sprinter’s average acceleration during this period?
Solution:
(7.5 -5)/ 1.25=
2.0 m/s2

28. Example Problem average speed
A cross-country runner runs 10 km in 40 minutes. What is his average speed?
Solution:
Average speed = total distance / total time
10 km/40 min
= 0.25 km / m

29. Example Problem Speed
James rode his bike 0.65 hours and traveled km. What was his speed?
Solution:
Speed = distance /time
0.65 hr = t
8.45 km = d
s = d/t
s = 8.45/0.65
s = 13 km/hr

30. Example Problem Speed
Brittany drove at a speed of 85 km / hr south for 4 hours. How far did she travel?
Solution:
Speed = distance/ time
85 km / hr = s
4 hrs = t
? = d
s = d/t
85 km/hr = d / 4 hrs
d = 340 km

31. Example Problem Velocity
A dog travels 250 meters east in 8 seconds. What is the velocity of the dog?
Solution:
250 m = d
8 s = t
? = v
v = d/t
v = 250 / 8
v = 2.5 ,/s

32. Example Problem Acceleration
8. A runner went from 6 m/s to 2 m/s in 2 seconds, what was his acceleration?
Solution:
6 m/s = vi
2 m/s = vf
2 s = t
? = a
a = vf - vi / t
a = 2 – 6 / 2
a = -2 m/s2

33. Example Problem Speed
A high speed train travels with an average speed of 227 km/h. The train travels for 2 h. How far does the train travel?
Solution:
d = s ´ t = 227 km/h ´ (2.00 h) = 454 km

34. Example Problem Speed
A dog travels north for 18 meters, east for 8 meters, south for 27 meters and then west for 8 meters. What is the distance the dog traveled and what is the displacement of the dog
Solution:
distance = 61 m
displacement = 9 meters south

35. Example problem
The driver of a pickup truck drove at a velocity of 75.0 km/m for 33 minutes. What distance did the bus travel?
Solution:
75 km / m = v
33 m = t
?= d
v = d/t
d = 75 x 33
d = 2475 km

36. V = D / T = 1623 mi / 83 min = 19.5 mi/min North
Velocity
Velocity is speed with a direction
Written like: 125 miles/hour east or m/sec towards the house
What is the velocity of a jet that traveled 1623 mi North in 83 min?
V = D / T = 1623 mi / 83 min = mi/min North

37. Velocity
The velocities that have the same direction combine by addition:
Ex you are rowing downstream at 6 km/hr and the velocity of the river is 10 km/hr. You are actually moving at 16 km/hr

38. Velocity
Velocities that have opposite directions combine by subtraction
Ex You are rowing upstream at 10km/hr and the velocity of the river is 8km/hr. You are acturally moving at 2km/hr

39. Velocity This idea is important in launching rockets
Rockets are launched in the same direction as the earth rotates ( about 1800 km/hr)
Thus the rocket engines and the Earth’s rotational speed work together to break the Earth’s gravitational force

40. Acceleration The change in speed or velocity over time
In scientific community, the symbol for “change” is the triangle:
Change in velocity is found by subtracting the final speed from the initial speed
Vf - Vi = V
The formula for acceleration is:
A = Vf - Vi = V
time time
Therefore the units for acceleration are going to be a
distance/time/time
Example
ft/min/sec

41. Acceleration For an object to accelerated it must:
Speed up (positive acceleration)
Slow down (negative acceleration a.k.a deceleration )
Change direction of travel 3 1 2
Each of these pictures depicts a type of acceleration:
1: the shuttle is speeding up every sec of the flight into orbit
2. the horse has come to a screeching halt (slowing down)
3. the baseball thrown to the batter is hit into the outfield
(changed direction)

42. What’s it mean? What does a = 5 [m/sec2] mean?
If an object starts at rest, its velocity increases by 5 [m/sec] every second.
Time (sec)
Acceleration
Velocity
5 m/sec2
0 m/sec 1
5 m/sec 2
10 m/sec 3
15 m/sec 4
20 m/sec
Therefore, an object accelerating at 5m/sec2 will be travelling at 20 m/sec after 4 seconds.

43. Acceleration Problems:
Calculate acceleration for the following data:
A = 60km/hr - 20 km/hr = 4 km/hr
10 sec sec
A = 150km/sec - 50 km/sec = 20 km
5 sec sec2
A = 1200km/hr - 25 km/hr = km/hr
2 min min

44. Circular Motion Acceleration is a change in velocity
Remember velocity expresses direction as well as speed
An object in circular motion is accelerating even though its speed may be constant
Acceleration that is directed toward the center of a circular path is called centripetal acceleration

45. Centripetal Acceleration

46. Momentum All moving objects have momentum
Momentum is equal o the mass of an object multiplied by its velocity.
Momentum = mass x velocity

47. Momentum An objects momentum depends on both its mass and velocity
Ex stopping distance of a car is directly related to its momentum ( how fast it is moving and the mass of the car)

48. Momentum Momentum = mass x velocity
For some reason, maybe because mass is designated as “m” in formulas, momentum is designated as “p”.
Therefore: p = mv
The unit for mass is kg, the unit for velocity is meter/second, therefore the unit for momentum is kg m/sec
Conservation of Momentum:
When two or more objects interact (collide) the total momentum before the collision is equal to the total momentum after the collision 48

49. Momentum – 2 moving objects
During this collision the speed of both box cars changes. The total momentum remains constant before & after the collision. The masses of both cars is the same so the velocity of the red car is transferred to the blue car. 49

50. Momentum – 1 moving object
During this collision the speed red car is transferred to the blue car. The total momentum remains constant before & after the collision. The masses of both cars is the same so the velocity of the red car is transferred to the blue car. 50

51. Momentum – 2 connected objects
After this collision, the coupled cars make one object w/ a total mass of 60,000 kg. Since the momentum after the collision must equal the momentum before, the velocity must change. In this case the velocity is reduced from 10 m/sec. to 5 m/sec. 51

52. Example problems: Momentum
A motorcycle has a mass of 250 kg and a velocity of 68 m/s, what is it’s momentum?
Solution:
Momentum = mass x velocity
250 kg x 68 m/s = kg m/s

53. Example problems: Momentum
A 10-kg wagon has a speed of 25 m/s. What is its momentum?
Solution:
10 kg x 25 m/s = 250 kg m/s
Momentum = mass x velocity

54. Example problems: Momentum
A 10.0 kg dog chasing a rabbit north at 6.0 m/s has a momentum of?
Solution:
Momentum = mass x velocity
10kg x 6 m/s = 60 kgm/s

55. Example Problem Momentum
A large truck loaded with scrap steel weighs 14 metric tons and is traveling north on the interstate heading for Chicago. It has been averaging 48 hm/h for the journey and has traveled over 1450 km so far. It has just stopped to refuel. What is its current momentum?
Solution:
0 (zero) kg•m/s
Remember it is not moving

56. Example Problem Momentum
How fast is a car traveling if it has a mass of 2200kg and a momentum of kgm/s?
Solution
(answer m/s)

57. Law of conservation of momentum
The total momentum of any object or group of objects remains the same unless outside forces act on the object.

58. Scientist
Modern scientist understand the relationships between force and motion,
However it took over 2000 years to figure it out

59. Aristotle:
Inaccurately proposed that force is required to keep an object moving at constant speed
This slowed down the study of motion for nearly 2000 years

60. Galileo
Proved thru observations that the Earth is one of many planets, all governed by the same laws of Gravity
Concluded that objects not subjected to friction or any other force would continue to move indefinitely

61. Isaac Newton
Built on Galileo’s work and developed the 3 laws of motion