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Newton’s 2nd Law
Force and Acceleration
Galileo Conceptualized
Acceleration

G – Money defined the rate of change
of velocity as acceleration


Acceleration = change of velocity divided
by time
Any change!



Slowing down
Speeding up
Changing direction
Galileo Conceptualized
Acceleration

Acceleration is a vector quantity

It is a change in:


Speed, Direction or Both
So, a change in velocity is a change in
acceleration
Galileo Conceptualized
Acceleration

Unless I miss my
guess, this skier is
accelerating all
over the place…
Galileo Conceptualized
Acceleration

Suppose you are flying




In 1 second your speed steadily
increases from 30 km/hr to 35
km/hr
The next second you speed
increases from 35 km/hr to 40
km/hr and so on
Your velocity changes by 5
km/hr each second
Acceleration = Change of
velocity/time

5km/hr ÷ 1s = 5km/hr per s
Galileo Conceptualized
Acceleration

Free Fall


When air resistance
does not affect the
falling motion of an
object
Free fall acceleration is nearly
identical for everything

Acceleration = Change of
velocity/time

For free fall: 10m/s2
…And I’m free. Free fallin’
~T. Petty
Galileo Conceptualized
Acceleration

How much speed does an object thrown
straight up lose per second?


Since it fights against gravity, 10m/s
Once it starts down it moves just as if it
were dropped from rest at that height

Thus, accelerates back down at 10m/s2
Force Causes Acceleration

Since acceleration is a change in
velocity:

Newton’s first law applies


An object stays in constant velocity unless a
net force acts upon it
This net force (push or pull) causes the change
in acceleration
Force Causes Acceleration

Acceleration is directly proportional to
the net force on an object


Twice the net force = twice the
acceleration
10 times the net force = 10 times the
acceleration
Force Causes Acceleration

Acceleration is directly proportional
to the net force on an object


The same net force on twice the mass
= half the acceleration
The twice the net force on twice the
mass = the same acceleration as before
Mass Is a Measure of Inertia

The more massive a
thing is, the more
inertia it has



The more it wants to
stay at rest
The more it wants to
stay in motion
“Get in my belly!”
If a bear is chasing
you, run zigzag
Tastes like chicken…
Mass Is a Measure of Inertia

Mass is NOT Weight!



Mass is the measure of how much stuff is
in an object
More massive objects have more stuff
packed in them
Less massive objects have less stuff
packed in them

Ping pong ball vs. bowling ball
Mass Is a Measure of Inertia

Mass is NOT Weight


Mass depends on how much stuff is packed
in an object
Weight depends on gravity


One changes and the other doesn’t
Which does what?
Mass Is a Measure of Inertia

Mass is NOT Weight

You can be weight-less not
mass-less

The amount of stuff packed
into you does not change
Mass Is a Measure of Inertia

Mass and weight are not
the same but they are
proportional to each
other


An object with a large
mass has a large weight
In the same location,
twice as much mass
weighs twice as much
Mass Is a Measure of Inertia

Mass is NOT Volume


Mass is a measure of how much stuff is
packed into an object
Volume is a measure of how much space
that object take up
Mass Is a Measure of Inertia

Mass is NOT Volume

If an object has a large mass, it might
have a large volume

Not always:




Ping pong ball vs. golf ball
Bag of rice vs. bag of feathers
Bag of rocks vs. bag of cotton balls
Mass is measured in kilograms
Mass Is a Measure of Inertia

What does mass weigh?



One kilogram weighs 9.81 Newtons
One kg = 2.2 lbs
So 1 pound must =4.45 Newtons
Mass (Inertia) Resists
Acceleration

More massive objects
resist a change in their
“natural” state


Natural state = equilibrium
Massive, heavier objects
require more force to
move/slow or change
direction
Mass (Inertia) Resists
Acceleration

For the same force, twice as much
mass gives ½ as much acceleration


Three times as much mass = 1/3
Four times as much mass = 1/4
Mass (Inertia) Resists
Acceleration

Acceleration ~ 1/mass

Inversely proportional


One goes up, the other goes down
The bigger the mass (the denominator)
the smaller the acceleration
Linking Force, Acceleration
and Mass


Isaac Newton was the first to connect
force and mass with acceleration
Newton’s 2nd Law of Motion



The acceleration is proportional to the net
force applied
The acceleration goes in the same direction
as the net force
Acceleration is inversely proportional to the
mass
Linking Force, Acceleration
and Mass

Newton built on G-Money’s ideas and unified
the three variables:




Force
Mass
Acceleration
Acceleration = net force/mass



A = F/M
F=MxA
M = A/F
Friction Affects Motion

Friction occurs
when objects come
into contact


Solids, liquids and
gases
Always acts to
oppose motion
Objects in Free Fall Have
Equal Acceleration

G-Money Proved:




Free-fall Acceleration does not depend on
mass
Different Mass objects accelerate equally
Different mass objects will fall at the same
rate and hit the ground at practically the
same time
BUT, smart as he was, G-Money could
not explain why
Newton’s 2nd Law Explains
Why

N-Dawg put it all together and came up
with;
 f/m = F/M


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Big, bold F = large force, big, bold M = large
mass
Small m = small mass, small f = small force
It is an equal ratio!
All free fall objects have the SAME force to
mass ratio!
Newton’s 2nd Law Explains
Why


In free fall, there is no
air drag
The ONLY force acting
on the elephant and
feather is gravity

Gravity pulls the same
on everything
Newton’s 2nd Law Explains
Why

Try the ratio with:

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A 1kg rock
A 10kg boulder
Run the numbers and see for
yourself


I am not making this stuff up
Even Buckaroo Banzai agrees…
Newton’s 2nd Law Explains
Why

A 10kg bag of sheep eyes has a weight
of 100N. When dropped, what is its
acceleration?
Tastes like chicken…
Newton’s 2nd Law Explains
Why

A 5kg bag of calf brains has a weight of
50N. When dropped, what is its
acceleration?
Panko breaded calf brain with
oil, lemon and garlic dressing
Newton’s 2nd Law Explains
Why

Calculate the free fall acceleration of a
20kg bag of giraffe tongues.
Giraffe tongue braised in garlic
beef stock with lemon dressing
Acceleration is Less With Air
Drag

This is NOT free fall situation

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Falling through air

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Net force = weight
Net force = weight – air drag
Air Drag depends on two things:


Speed
Surface area
Acceleration is Less With Air
Drag

Air Drag: Speed


As an object falls,
acceleration occurs
and air resistance is
built up
The greater the
speed, the greater
the air drag
Acceleration is Less With Air
Drag
Acceleration is Less With Air
Drag


The greater the
speed, the greater the
air drag
You know this! Even
your dog know this…

Stick you head out the
window of a car
moving 10 mph and
one moving 55 mph!
Acceleration is Less With Air
Drag

Air Drag: Speed (cont)

As the object accelerates, air drag builds
(directly proportional)
Acceleration is Less With Air
Drag

Soon enough air drag is
built up (support force) to
cancel the acceleration due
to gravity

Support force = Gravity

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Gravity force
(weight)
(∑F = 0, yes, again…)
No acceleration = constant
speed = terminal speed
Dynamic equilibrium
Support force
(air drag)
Acceleration is Less With Air
Drag

Air Drag: Surface Area

The greater the surface area the greater
the air drag

The greater the surface area of the “down”
facing part, the greater the air drag
Acceleration is Less With Air
Drag

Weight and air drag

A heavier object falls
faster through air


The heavier weight
“plows” through the air
more effectively
Encounters more air
resistance but simply
pushes through it
Acceleration is Less With Air
Drag

A feather falls slower
(reaches terminal speed
faster) than an elephant
for this reason
Remember Your Targets!

Learning Target 1: Use Newton’s 2nd Law to describe and
predict motion

Explain, draw and interpret free body / force vector diagrams

Create “rate vs. time” graphs


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Interpret motion graphs to determine the motion of the object that
produced the graph
Predict the direction and magnitude of motion using a free body/force
vector diagram
Explain how friction affects motion
Remember Your Targets!

Learning Target 2: Use Newton’s 2nd Law to describe and
predict motion


Predict the direction and magnitude of motion using a free body/force
vector diagram
Calculate acceleration of an object (A = F/M, ∆v/∆t)
Remember Your Targets!

Learning Target 3: The Only Reason to Learn Algebra is to
do Physics

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
Calculate distance, speed and time (D = RT)
Calculate the net force acting on an object
Calculate acceleration of an object (A = F/M, ∆v/∆t)
Interpret motion graphs