Physical Science Unit: Motion

1
Physical ScienceUnit 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.
• Are you moving?
• 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 1527 centigrams into hectograms going
four steps up means you move the decimal 4 places
to the left. Therefore 1527 centigrams .1527
hectograms 9.8712345 kg (steps to the right)
9871234.5 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 pointsa) (3, 3)b) (- 2,
  3)c) (- 1, - 2)d) (3, 0)e) (0, 0)f) (0, - 4)

a
b
d
e
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 24 12 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
• Do this problem
• 12 miles 4 miles
• 3 hours hour
• Do this problem
• 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 SD/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.

16
(No Transcript)
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 37.5
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 17.5 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
  sprinters 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 8.45
  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
Velocity
Velocity is speed with a direction

• Written like 125 miles/hour east or 83
  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 19.5 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 Earths
  rotational speed work together to break the
  Earths 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
Whats 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
0 5 m/sec2 0 m/sec
1 5 m/sec2 5 m/sec
2 5 m/sec2 10 m/sec
3 5 m/sec2 15 m/sec
4 5 m/sec2 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
587.5 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

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.

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.

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.

52
Example problems Momentum

• A motorcycle has a mass of 250 kg and a velocity
  of 68 m/s, what is its momentum?
• Solution
• Momentum mass x velocity
• 250 kg x 68 m/s 17000kg 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) kgm/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 28000 kgm/s?
• Solution
• (answer 12.72 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 Galileos work and developed the 3 laws
  of motion