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Motion I
Kinematics and Newton’s
Laws
Basic Quantities to Describe Motion

Space (where are you)
Basic Quantities to Describe Motion

Space (where are you)

Time (when are you there)
Basic Quantities to Describe Motion

Space (where are you)

Time (when are you there)

Motion is how we move through space as
a function of the time.
Newton’s Definitions:


Space: Absolute space, in its own nature,
without relation to anything external,
remains always similar and immovable.
Time: Absolute true and mathematical
time, of itself, and from its own nature,
flows equably, without relation to anything
external, and by another name is called
duration.
A Brief Review

Vectors
Size
 Direction

Scalars
Size only
A Brief Review

Vectors
Displacement
 Velocity
 Acceleration


Scalars
Distance
Speed
Time
A Brief Review

Speed: Rate of change of distance

v = distance traveled/time for travel

v = x/t
Example
Suppose that we have a car that covers 20 miles
in 30 minutes. What was its average speed?
Speed = (20 mi)/(30 min) = 0.67 mi/min
OR
Speed = (20 mi)/(0.5 hr) = 40 mi/hr

Note: Units of speed are distance divided by time.
A Brief Review

Given the speed, we can also calculate the
distance traveled in a given time.
distance = (speed) x (time)
x=vxt
Example: If speed = 35m/s, how far do we
travel in 1 hour.
x=(35 m/s)(3600 s)=126,000 m
= 126,000m x [1mi/1609m]=78.3 mi
A Brief Review

Velocity: Rate of change of displacement

v = displacement/time of movement

Displacement is a vector that tells us
how far and in what direction

v = x/t
Velocity

Velocity tells not only how fast we are
going (speed) but also tells us the
direction we are going.
Example: Plane Flight to Chicago

Displacement: 133 mi northeast

Time = ½ hr

v = 133 mi northeast/½ hr
 v= 266 mi/hr northeast
EXAMPLE: Daytona 500



Average speed is approximately 200
mi/hr, but what is average velocity?
Since we start and stop at the same
location, displacement is zero
Velocity must also be zero.
Car keeps changing direction so on average
it doesn’t actually go anywhere, but it is still
moving quickly
A Brief Review

Acceleration: Rate of change of velocity

a = velocity change/time of change

a = v/t

We may have acceleration (i.e. a change in
velocity) by
1. Changing speed (increase or decrease)
2. Changing direction
Units of Acceleration = units of speed/time
(m/s)/s = m/s2
(mi/hr)/day
Example: acceleration


A sports car increases speed from 4.5 m/s
to 40 m/s in 8.0 s.
What is its acceleration?
Example: acceleration




vi = 4.5 m/s vf = 40 m/s t = 8.0 s
Dv = 40 m/s – 4.5 m/s
a = Dv/Dt = (40 m/s – 4.5 m/s)/ 8 s
a = 4.4 m/s2
How many accelerators (ways to change
velocity) are there on a car?
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


a) 1
b) 2
c) 3
d) 4
25%
1
25%
25%
2
3
25%
4
Unit Conversion

Essentially just multiply the quantity you want to
convert by a judiciously selected expression for 1.

For example, 12 in is the same as 1 ft

To convert one foot to inches
[1 ft/1 ft] = 1 = [12in/1ft]
So
1 ft x [12 in/1 ft] = 12 in
The ft will cancel and leave the units you want
Convert 27 in into feet.
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
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27 in x [1 ft/12 in] = 27/12 ft = 2.25 ft
Works for all units.
If the unit to be converted is in the numerator, make
sure it is in the denominator when you multiply.
If the unit to be converted is in the denominator, make
sure it is in the numerator when you multiply.
I know that 1.609km = 1 mi. If I want to
find out how many miles are 75 km I would
multiply the 75 km by
50%
1.
2.
50%
[1mi/1.609km]
[1.609km/1mi]
1
2
Convert 65 mi/hr to m/s.

65 mi/hr x [1609 m/1 mi] x [1 hr/60 min] x [1 min/60 s]
= 29 m/s
Find the speed of light in


c = 3 x 108 m/s
3 x 108 m/s x [100 cm/1 m] x [1 in/2.54 cm] x [1 ft/12
in] x [1 furlong/660 ft] x [60 s/1 min] x [60 min/1 hr]
[24 hr/1 day] x [14 day/1 fortnight]
= 1.8 x 1012 furlongs/fortnight
Given that 1 hr=3600 s, 1609 m=1 mi and
the speed of sound is 330 m/s, what is the
speed of sound given in mi/hr?
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a) 12.3 mi/hr
b) 147 mi/hr
c) 738 mi/hr
d) 31858200 mi/hr
25%
1
25%
25%
2
3
25%
4
Newton’s Laws
I
An object won’t change its state of motion
unless a net force acts on it.




Originally discovered by Galileo
Defines inertia: resistance to change
Mass is measure of inertia (kg)
A body moving at constant velocity has zero
Net Force acting on it
II
A net force is needed to change the state of
motion of an object.



Defines force: F = ma
Da given force, a small mass experiences a
big acceleration and a big mass experiences
a small acceleration
Unit of force is the Newton (N)
III
When you push on something, it pushes back
on you.



Forces always exist in pairs
Actin-reaction pairs act on different objects
A statement of conservation of momentum
Units of Force:
 m
F  ma kg 2   ma( N )
 s 

By definition, a Newton (N) is the force that will
cause a 1kg mass to accelerate at a rate of
1m/s2
Example: Rocket pack


A 200 kg astronaut experiences a thrust of
100 N.
What will the acceleration be?
 F = ma  a = F/m

100 N/200 kg = 0.5 m/s2
Force due to Gravity
Near the surface of the earth, all dropped
objects will experience an acceleration of
g=9.8m/s2, regardless of their mass.
 Neglects air friction
 Weight is the gravitational force on a mass
F = ma = mg =W
Note the Weight of a 1kg mass on earth is
W=(1kg)(9.8m/s2)=9.8N

If and object (A) exerts a force on an
object (B), then object B exerts an equal
but oppositely directed force on A.
When you are standing on the floor, you are
pushing down on the floor (Weight) but
the floor pushes you back up so you don’t
accelerate.
If you jump out of an airplane, the earth
exerts a force on you so you accelerate
towards it. You put an equal (but
opposite) force on the earth, but since its
mass is so big its acceleration is very small
3.
When a bug hit the windshield of a car,
which one experiences the larger force?
1.
2.
3.
The bug
The car
They experience
equal but opposite
forces.
33%
1
33%
2
33%
3
1.
2.
3.
When a bug hit the windshield of a car,
which one experiences the larger
acceleration?
The bug
33%
33%
33%
The car
Since they have
the same force,
they have the
same acceleration.
1
2
3
Four Fundamental Forces
1.
2.
3.
4.

Gravity
Electromagnetic
Weak Nuclear
Strong Nuclear
Examples of Non-fundamental forces:
friction, air drag, tension
Example Calculations

Suppose you start from rest and undergo constant
acceleration (a) for a time (t). How far do you go.
Initial speed =0
Final speed = v=at
Average speed vavg= (Final speed – Initial speed)/2
Vavg = ½ at
Now we can calculate the distance traveled as
d= vavg t = (½ at) t = ½ at2
Note: This is only true for constant acceleration.
Free Fall


Suppose you fall off a 100 m high cliff .
How long does it take to hit the ground and how
fast are you moving when you hit?
1 2
d  at
2
2d
t 
a
2
2d
(2)(100m)
2
t


20
.
4
s
 4.52 s
2
a
9.8m / s

Now that we know the time to reach the
bottom, we can solve for the speed at the
bottom
v  at
v  (9.8m / s )( 4.52 s )  44.3m / s
2

We can also use these equations to find
the height of a cliff by dropping something
off and finding how log it takes to get to
the ground (t) and then solving for the
height (d).
While traveling in Scotland I came across Stirling
Bridge. To find out how deep it was I dropped
rocks off of the bridge and found that it took them
about 3 seconds to hit the bottom. What was the
approximate depth of the gorge?
25%
1.
2.
3.
4.
25%
25%
2
3
25%
15m
30m
45m
90m
1
4