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If something is moving, then
something MUST be pushing
on it. Things don’t move all
by themselves!
Aristotle
Galileo
Oh, baloney! Once an object is
moving in a straight line, it’s
going to keep right on moving,
unless it runs into something.
That is, of course, as long as
there is NO friction! Friction is
what slows things down.
Galileo…
Born in Pisa 1564
Galileo found that, ignoring
the effect of the air, all
freely falling objects had
the SAME acceleration,
regardless of their mass or
the height from which they
were dropped.
The Law of Falling Bodies
Galileo described HOW things moved, but
not WHY they moved that way.
Galileo wrote, “the present does not seem to
be the proper time to investigate the cause of
the acceleration of natural motion….”
Galileo died in 1642.
When Isaac Newton, born Christmas day,
1642, began his studies of motion in the
second half of the seventeenth century, that
statement was no longer appropriate.
Because Galileo had been so effective in describing
motion, Newton could turn his attention to
dynamics.
Dynamics is the study of why an object
moves the way it doeswhy it starts to move instead of remaining at rest,
why it speeds up or moves on a curved path, and
why it comes to a stop.
Newton’s most famous book was “Principia”,
published in 1687. This book first listed what
came to be known as
Newton’s Three Laws of Motion
Forces
Force: a push or a pull
Forces are vectors. ( you push or pull in a
direction!)
There are Four Fundamental Forces in our
universe
1. Gravitational Force
2. Electromagnetic Force
3. Strong Nuclear Force
4. Weak Force
The strongest of these forces is….
The Strong Nuclear Force
(it holds the nucleus of all atoms
together)
The weakest of these forces is….
Gravity
The unit for Force is the Newton, N
If someone was pushing on you with one Newton
of Force, it wouldn’t hurt much.
One Newton of Force is about the same as the
weight of a quarter pound hamburger patty.
Inertia
Inertia: an object’s resistance to a change in its
motion
Mass: how you measure inertia unit: kg
Newton’s First Law of Motion:
“The Law of Inertia”
An object at rest
remains at rest unless
a net external force
acts on it.
An object in motion
continues that motion
unless a net external
force acts on it.
Second Law
If there is a net external force acting on an object, it
will accelerate.
Fnet
a
m
or
Fnet  ma or F  ma
(I call this “the granddaddy of all physics equations”!)
Same Force on different mass….
Third Law
For every force, there is an equal but opposite
force.
Action / Reaction forces
For every force, there is an equal but opposite
force.
Action / Reaction forces
For every force, there is an equal but opposite
force.
Action / Reaction forces
• The gun pushes on the bullet. The bullet
pushes back on the gun!
The Action / Reaction forces do NOT act on
the same object.
I kick the wall (Action)
The wall kicks me back (Reaction)
• While driving down the road, an
unfortunate bug strikes the
windshield of a bus.
• The bug hit the bus and the bus hit
the bug.
• Which of the two forces is greater:
the force on the bug or the force on
the bus?
For every force, there is an EQUAL by
opposite force!
A child pulls on a 5.0 kg wagon with a net
force of 20.0 N. What is the wagon’s
acceleration?
m = 5.0 kg
Fnet = 20.0 N
a = Fnet / m
a = 20.0 / 5.0 =
a = 4 m/s2
A dog pulling a man on a sled over ice can
accelerate the sled at 2 m/s2. If the sled
and man have a combined mass of 150.0
kg, what was the net force on the sled?
m = 150.0 kg
a = 2 m/s2
Fnet = ma
Fnet = 150.0 kg x 2 m/s2 = 300 N
When released, the lift provides a
net force of 6 N on a 2 kg balloon.
If it started at rest, how fast will it
be moving in 4.0 s?
Fnet = 6 N
m = 2 kg
vo = 0
t=4s
vf = ?
vf = vo + at, so we need “a”.
a = Fnet / m
a = 6 / 2= 3 m/s2
vf = 0 + 3 x 4
vf = 12 m/s
A 1500 kg. car starts from rest and is moving
at 10 m/s after 5.0 s. What was the net
force on the car?
vf = vo + at
m = 1500 kg
a = ( v f – v o) / t
Vo = 0
a = (10 – 0) / 5 = 2 m/s2
Vf = 10 m/s
Fnet = ma
t = 5.0 s
Fnet = 1500 kg x 2 m/s2
Fnet = ?
Fnet = 3000 N
Fnet = ma,
so we need to find the acceleration.
More than one force can act on an object at the same
time. For example, two people could push on a
book at the same time. One person could push
toward the left and the other could push toward the
right. In this case the two forces would act against
each other.
What is the NET force?
2 N towards the left
If the book had a mass of ½ kg, what would be its
acceleration?
a = Fnet / m
a = 2 / .5
a = 4 m/s2 (left)
What if the opposing
forces were equal?
What is the net Force?
What is the
acceleration?
What if the forces were
in the same direction?
What is the net force?
If the book had a mass
of 2 kg, what is its
acceleration?
a = Fnet / m
a = 14 / 2 = 7 m/s2
• What are the unknown forces for the given
net force?
Forces on an Airplane
When Lift is larger than Weight,
the plane will….
When Weight is larger than Lift,
the plane will…
When Thrust is larger than Drag,
the plan will….
When Drag is larger than Thrust,
the plane will….
When Thrust = Drag, the plane
will…
When Lift = Weight, the plane
will….
We usually label forces as
negative or positive.
Forces upward are positive.
Forces downward are
negative.
Forces to the right are
positive.
Forces to the left are
negative
+
+
-
What is the net Force?
- 6 N + 18 N = + 12 N
What is the acceleration?
a = Fnet / m
12 / 3 = 4 m/s2
6N
3 kg
18N
What is the net Force?
- 6 N – 15 N + 18 N = - 3 N
What is the acceleration?
a = Fnet / m
a = - 3 N / 3 kg = - 1 m/s2
6N
15N
3 kg
18N
Weight
Weight, Wt. is the gravitational force on an
object
Weight = mass x gravity
W = mg
Since weight is a force, it is measured in
Newtons, N
Remember, “g” on Earth is 9.8 m/s2(10 m/s2)
What is the weight of a 42 kg child on Earth?
W = mg
m = 42 kg
W = 42 kg x 10 m/s2
W = 420 N
What is the mass of a 15000 N car?
W = mg
m=W/g
m = 15000 N / 10 m/s2
m = 1500 kg
Remember, one Newton is not a
very big force (about the same
as a ¼ pound).
So, your weight in Newtons is
MUCH bigger than your weight
in pounds!
In fact, you would have to multiply
your weight in pounds by 4.45
to get your weight in Newtons.
How much do you weigh in
Newton’s?
Even if you weigh
550 Newtons,
You still wouldn’t
be much of a
Sumo Wrestler!
(that’s only around 120 lbs)
A car weighs 1680 N on Earth. What is its
mass?
W = mg
m=W/g
m = 1680 N / 10 m/s2
m = 16.80 kg
A parachute provides a lift force of 400 N on
a parachutist that weighs 500 N. What is
the net force on him?
-100 N
What is his acceleration?
a = Fnet / m
What is his mass?
a = -100 / 50
a = -2 m/s2
Tension
Tension, T, is the force
that cables, ropes,
and strings pull with.
A child pulls up on a string
that is holding 2 fish of total
mass 5 kg. If he is
providing a tension of 60 N,
what is the net force on the
fish?
Fnet = + T – W
Fnet = 60 N – 50 N
Fnet = 10 N
What is the acceleration of the
fish?
a = Fnet / m
a = 10 / 5
a = 2 m/s2
One child pulls up on a box with a force
of 19 N. Another child pulls down on
the box with a force of 5 N. What is
the net Force?
Hold on, there’s another force not
drawn!
The gravitational force of weight is
pulling down!
Wt = mg, (g = 10 m/s2)
Wt = 2 kg x 10 m/s2 = 20 N
Draw the weight vector also!
Now, what is the net Force?
Net force = +19 N – 5 N – 20 N =
Net Force = - 6 N
What is the acceleration?
a = Fnet / m =
a=-6/2
a = -3 m/s2 It will accelerate downward.
19 N
2 kg
5N
mg = 20 N
A child pulls a 5 kg bucket out of well with a
rope. If the bucket accelerates upward at
1.2 m/s2, what is the tension in the rope?
m = 5 kg
a = 1.2 m/s2
T
T=?
 F = ma
T – mg = ma
mg
T = ma + mg
T = 5 x 1.2 + 5 x 9.8
T = 55 N
Normal force, N
Weight = mg
If the box is not moving up or
down, then the Normal force
must by equal to the Weight
But… what if you were moving up or down?
The Normal force would NOT be equal to your
weight if you’re accelerating up or down. And…
your weight seems to change!
A 50 kg woman steps on a scale in an elevator
that accelerates upward at 1.5 m/s2.
What is her REAL weight?
N
mg = 500 N
What is her APPARENT weight?
F = ma
N – mg = ma
mg
Her APPARENT weight is what she feels like she
weighs, given by the Normal force, N.
N = ma + mg
N = 50 x 1.5 + 500
Apparent weight = 575 N
Apparent Weight
When you ride an elevator, you “feel”
heavier or lighter than you actually weigh
because of the acceleration of the
elevator.
Your “apparent weight” is found by taking
your REAL weight, mg, and adding the
term ma, where “a” is your acceleration
Apparent weight = mg + ma
Do falling objects REALLY
accelerate toward the Earth
at 9.8 m/s2?
No, because of air resistance.
Air resistance is a force that
pushes up on an object as it
falls.
The faster you fall…
The greater the air resistance.
Eventually, the air resistance
pushing up on you is just as
large as your weight that is
pulling down on you!!
The faster the man falls, the more air resistance
pushes up on him. Eventually, there will be just as
much air resistance pushing up on him as his weight
pulling him down. What will be the NET force acting
then?
What will be his acceleration?
Once the air resistance pushing up is as large as
the weight pushing down, the NET force acting on
you is ZERO!
If the net force is zero, what is your acceleration?
ZERO!
This doesn’t mean you stop in mid air. But it does
mean that you stop accelerating!
You still continue to fall towards the Earth, but you
don’t pick up any more velocity- you continue to
fall towards the Earth at the same velocity.
This speed is called your “terminal velocity”
You will reach your terminal velocity when
Air resistance = your weight
Which one will have a faster terminal velocity?
You don’t reach terminal velocity until the air
resistance grows to as large a force as your
weight.
The more massive skydiver will have a faster terminal
velocity and hit the ground at a faster speed
The “Normal” Force, N
When an object is pressed against a
surface, the surface pushes back. (That’s
Newton’s 3rd Law)
This “push back” from the surface is
called the Normal Force, N
The word “normal” in math terminology
means “perpendicular”
The surface pushes back in a direction that
is perpendicular to the surface.
Normal force, N
Weight = mg
If the box is not moving up or
down, then the Normal force
must by equal to the Weight
Friction, f
• A force that always opposes motion
• Depends on two things: the roughness of
the surfaces and how hard they are
pressed together.
f = mN
m , mu- the “coefficient of friction” tells how
rough the surfaces are.
N, the Normal force tells how hard the
surfaces are pressed together
Example: How large is the frictional
force between 2 surfaces if the
coefficient of friction is 0.2 and the
Normal force is 80 N?
f = mN
f = 0.2 x 80
f = 16 N
There are two kinds of friction:
“static friction” (not moving) must
be overcome to initiate motion.
“kinetic friction” must be
overcome while an object is
moving
Static friction > Kinetic friction
You pull on a box with an applied force of 30 N. The coefficient of friction is
0.4. If the mass of the box is 2 kg, what is its acceleration?
1. Draw the box and all FOUR forces acting on it.
2. Write what you know and don’t know.
3. Write the equations, Fnet = ma and f = mN
4. Calculate the Normal force and the friction force.
5. Calculate the value of the net Force and then the
Normal force, N
acceleration.
FA = 30 N
m = 2 kg f = mN
m = 0.4
a=?
Fnet = ma
f = mN
N = mg = 2 x 10 = 20N
f = mN = 0.4(20) = 8N
Horizon: Fnet = FA - f
30N – 8N = 22N
a = Fnet / m
a = 11 m/s2
FA= 30 N
Weight = mg