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Chapter 8
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Motion
What is motion?
If I threw a ball from here to there, can
you tell me when the ball is in motion
and when it isn't?
Motion = ∆ location
• In math, ∆ means "change in"
• What could affect the motion of the
ball?
–How hard I throw the ball… I can
change the speed.
• Change in speed:
– Faster means it has to go the same
distance in a shorter time.
– Slower means it has to go the same
distance in a longer time.
• Think about when you're running to class:
Gym - - - - - - - - - - - - - - - - - - - - - -Classroom
– When you are late to class… you run
through the halls
– When you are early… you strut down the
halls
Speed
Speed = ∆ Distance
∆ Time
Various speeds:
To be
measured
Turtle
Miles per
hour
0.25
Mile per
second
0.00006
Feet per
second
0.3
Rifle bullet
2045
0.57
3,000
Columbia
shuttle
Earth's orbit
12,000
3.3
17,598
40,000
11.1
58,666
• These are all different numbers that have the same
values… they have different units of measure.
• Note: Always pay close attention to units of measure,
your units should always agree with what's asked for
in a question.
• Speed = how fast something is moving
– on average = over time = AVERAGE
SPEED
–at an exact moment =
INSTANTANEOUS SPEED
Average speed = Total Distance traveled
Time taken to travel Distance
• Average speed = The average overall
speed on a trip
–Example: 2 hours in the car to travel a
distance of 100 miles
–Equation 100 miles = 50 MPH
2 hours
• Instantaneous speed = The speed you
are traveling at that exact moment
–Example: During a 2 hour trip over
100 miles
• stop at a red light = 0 MPH
• speed at 75 MPH on the highway
• slowly driving at 25 MPH past a
school
Image for remembering equations for
speed math problems
Velocity
Velocity = Speed and direction
–Measured by a speedometer and a
compass
• Velocity = ∆ Distance + direction of movement
∆ Time
• In this class we will use the terms
interchangeably… and imply the direction.
• However:
CONSTANT SPEED ≠ CONSTANT
VELOCITY
The car can be traveling at the same speed,
but has changes in direction
• Changes in velocity can have different
causes:
– ∆ V = same speed + ∆ direction
– ∆ V = ∆ speed + same direction
– ∆ V = ∆ speed + ∆ direction
Mathematical – Graphic
Representations of Velocity
• If we know the average speed, we can plot the
time and distance along a trip:
Distances Traveled (miles)
Time
(hours)
Car A at
15 MPH
Car B at
30 MPH
Car C at
60 MPH
0.5
7.5
15
30
1
15
30
60
1.5
22.5
45
90
2
30
60
120
Car Speed
140
120
Dist. miles
100
80
Car A
Car B
Car C
60
40
20
0
0
0.5
1
1.5
Time (hours)
2
2.5
• What do you notice about the 3 lines
on the Car Speed graph?
–Steepness of line = greater the
slope of the line
–the greater the slope, the faster the
speed of the car
– slope = ∆ Y or rise
∆X
run
– If distance is placed on the y-axis
and time is placed on the x-axis,
Velocity = ∆ D = ∆ Y = Slope of line
∆T ∆X
• So, Velocity = Slope of line
Car A Slow
Gradual line
Car B Medium
Medium
Car C Fast
Steep line
Graphing Velocity (Average
Speed)
What can you tell from different graphs?
• 3 Different objects
moving at 3
different speeds
D
T
• Stopped Object:
Time passes but
distance does
not change
• No movement
D
T
D
T
• Backward moving
object…
• The distance is
decreasing, so
there is movement
towards the source
• Circular Motion:
Time passes
as the same
distances are
revisited: like a
race track
D
T
• Series of motions
D
T
• Rest-forward-restbackward-rest
• Note: does not
represent the
profile of the
terrain
Velocity Graphs and Profiles of
Terrain
3
1
D
4
2
5
T
• What do we know
about movement?
• 1 – rest
• 2 – gradual
movement forward
• 3 – rest
• 4 – backward
movement
• 5 – rest
Velocity Graphs and Profiles of
Terrain
3
1
D
4
2
5
T
• What could be a
possible
explanation: pulling
a wagon uphill?
• 1 – You are halfway up a
hill, at rest holding a wagon.
• 2 – You start moving uphill
• 3 – You take a rest
• 4 – The wagon handle slips
out of you hand and travels
backward down the hill.
• 5 – The wagon stops
moving at the bottom of the
hill.
Dimensional Analysis – Unit
Analysis
In your head, you can probably convert…
… inches to feet
sure, 12 in = 1 ft
… inches to yards
okay, 3 ft in 1 yd = 36 in
… inches to miles
um, probably not
• FAQ: When I convert from inches to yards
or yards to inches, when do I multiply and
when do I divide?
• The easiest way to approach these unit
conversions is by using dimensional
analysis.
There are 4 rules:
1. If you use only one unit to start, put it over a
1.
2. Determine the conversion factors. (Ex: 12
inches = 1 ft) and put into a fraction.
3. Properly place the conversion factors in an
equation.
4. Check cancellations of units so that you are
left with the unit you were looking for on the
top of a division bar. The units that are
canceled should be on opposite sides of the
division bar.
Example 1: How many feet in 13 in? 1 1/12 or 1.083 ft
Step 1… starting with 13, so… 13 inches
1
Step 2… conversion factors:
1 foot
or 12 inches
12 inches
1 foot
Step 3… place factors: 13 inches
1
x
1 foot
12 inches
Step 4… check cancellations: 13 inches
1
13 inches = 1.083 ft
x
1 foot
12 inches
Example 2: Convert 13 inches into yards.
Step 1… starting with 13, so… 13 in
1
Step 2… conversion factors:
1 ft
12 in
1 yd
3 ft
Step 3… place factors: 13 in x 1 ft x 1 yd =
1
12 in
3 ft
Step 4… check cancellations: 13 in x 1 ft x 1 yd
1
12 in 3 ft
13 in = 0.36 yd
Example 3: Convert 2 years into seconds.
2 yrs x 365 days x 24 h x 60 min x 60 sec
1
1 yr
1 day
1h
1 min
2 yrs = 63,072,000 sec
Example 4: Convert 4 decades into minutes.
4 dec x 10 yrs x 365 days x 24 h x 60 min
1
1 dec
1 yr
1 day
1h
4 decades = 21,024,000 m
Example 5: I am 5’ 3” or (5 x 12) + 3 = 63 inches
tall. How many cm tall am I?
63 in x 2.56 cm =
1
1 in
63 in = 160.1 cm
Dimensional Analysis Worksheet
1. In New Jersey, students in public schools go to
school for 4 years. How many minutes are
students enrolled in high school?
4 years x 365 days x 24 h x 60 min
1
1 yr
1 day
1h
4 yrs = 2,102,400 min
2. Alayna’s dog is 3 ft tall. What is the dog’s
height in mm?
3 ft x 12 in x 2.54 cm x 10 mm
1
1 ft
1 in
1 cm
3 ft = 914.4 mm
3. Brian and Jesse were on a bus trip going 50
MPH. For some extra fun, they decided to
convert the bus’s speed into km/h. What should
their answer be?
50 miles x 1.61 km
1 hr
1 mile
50 MPH = 80.5 km/h
4. Driving home from practice, Alex’s mother was
driving at a speed of 30 m/s. What was their
speed in km/h?
30 m x 1 km x 60 s x 60 min
1 s 1000 m 1 min
1h
30 m/s = 108 km/h
5. Saskia was riding her bike down the road at a
speed of 5 km/h. What was her speed in m/s?
5 km x 1000 m x 1 hr x 1 min
1h
1 km
60 min 60 s
5 km/h = 1.39 m/s
Class experiment:
1. Determine how tall you are in inches.
2. Using the conversion factor: 1 mile =
1.61 km, determine how tall you are in
cm.
3. Check your answer with a meter stick.
Acceleration
When you accelerate, what are you doing?
Speeding up… accelerating
When you slow down, what are you doing?
Decelerating
In physics, we use the same term, “acceleration”
for both speeding up and slowing down. We
distinguish between the two by assigning
positive or negative values.
+ acceleration as in speeding up  positive
- acceleration as in slowing down  negative
Acceleration = the change in velocity over time
- measured in m/s or m/s2
s
Acceleration = ∆ Velocity
∆ Time
Acceleration =
∆ Distance + Direction
∆ Time
∆ Time
Given an object moving in a circle
- ∆ velocity due to a ∆ direction
- if ∆ velocity, the ∆ acceleration as well
- circular motion = ∆ D = ∆ V = ∆ A
Graphing Acceleration
A = ∆ V and slope = ∆ Y
∆T
∆X
Acceleration = ∆ V = ∆ Y = Slope of line
∆T ∆X
So, Acceleration = Slope of line
Steep slope = fast movement
Gradual slope = slow movement
V
V
T
Acceleration
T
Deceleration
Steepness of the line indicates the degree of
acceleration
V
T
Comparing Velocity and
Acceleration
Velocity = ∆ Distance
∆ Time
D
Acceleration = ∆ Velocity
∆ Time
V
T
T
These two lines indicate the exact same
thing the same rate of acceleration
•
Acceleration = + slope
•
Deceleration = - slope
- slope
V
+ slope
T
When object is a rest  Velocity is zero
If ∆ Distance = 0, then ∆ Velocity… so
Acceleration = 0
V
D
0
T
T
When acceleration equals zero
A= ∆ V  no change in velocity
∆ T  Time will always pass
No change in velocity
- no velocity – V = 0 then object is at rest
- constant velocity - ∆ V = Vfinal – Vinitial
Vf = 50 miles/h and Vi = 50 miles/h
Then ∆ V = 0
If acceleration = zero, you are either stopped
or on cruise control
To determine which, you must find if there is
a change in distance.
How it all fits together
From Motion  Acceleration only one variable is
added at a time
1. Motion = ∆ Distance
2. Speed = ∆ Distance
∆ Time
3. Velocity = ∆ Distance + Direction
∆ Time
4. Acceleration = ∆ Distance + Direction
∆ Time
∆ Time
Momentum
When an object is in motion, we think
velocity. However, we must not forget
Momentum – which is also acting on the
object.
Momentum = a quantity defined as the
product of an object’s mass and its
velocity.
- In a formula, P = momentum.
- momentum moves in the same direction
as the velocity
P = Mass x Velocity
- Measured in kg·m/s
Momentum and ∆ Velocity
- large momentum, difficult to change
velocity
- small momentum, easier to change
velocity
Class Experiment: Red light, green light
Stationary objects have momentum of zero
Why?
No motion = no speed = no
velocity = no momentum
Momentum is directly proportional to mass…
momentum increases as mass increases.
P
Mass (kg)
Force
Force = the cause of acceleration or a
change in velocity
- force is measured in units called
Newtons
Net force = the combination of all the forces
acting upon an object.
• The size of the arrow represents the amount of
force…
• The arrows are the same so there is no movement.
Friction
Friction = the force between two objects in
contact that opposes the motion of either
object.
Pretend you are in a helicopter looking down
on a ski slope in early spring…. The ice is
melting…. Patches of dirt and gravel begin
to show…
**********
How much friction?
Skis + snow = little friction… skis move
over snow
Skis + dirt = a lot of friction… skis do not
move over dirt
Air resistance is a type of friction.
Gravity
Gravity = Force of attraction between 2
objects due to their masses.
The force of gravity is different on different
planets, moons etc.
On earth: g = 9.8m/s2
Gravity depends upon the masses as well
as the distance between objects.
Newton’s Laws of Motion
Newton’s 1st Law- the law of inertia
An object at rest remains at rest and an
object in motion remains in motion unless
it experiences an unbalanced force.
• Example 1: Whiplash – Person B is stopped at a
traffic light. Person A is not paying attention, and
rear-ends Person B.
• Result: Person B moves forward suddenly… Their
head snaps back as it attempts to “remain at rest.”
Their body, attached to the seat moves forward…
their head snaps forward to catch up with the
body resulting in whiplash.
Example 2: Bus ride - The bus driver does
not like children. Every time, they get too
loud, he slams on the breaks. Why does
he do this?
Inertia = The tendency of an object to
remain at rest or in motion with a constant
velocity. All objects have inertia because
they resist changes in motion.
Trivia: If two people on a space ship (in
space) get into a physical fight, which will
win?
Person A
Person B
Even though they are weightless… there
is no gravity Person A has a greater mass,
therefore, a greater inertia.
Newton’s 2nd law of Motion- the law of
acceleration
• The unbalanced force acting on an object
equals the object’s mass times its
acceleration.
• Force = Mass x Acceleration
Example: pushing a cart
The greater the mass, the more force
needed to cause acceleration.
Bumper cars
Newton’s 3rd law of Motion- the law of
interaction
• For every action, there is an opposite and
equal reaction force.
• Forces occur in pairs
Example: Holding up a wall