Lesson 1: momentum
• LT 2.1: I can use p=m·v to
calculate momentum, mass
or velocity.
• LT 2.2: I can describe how
changing the mass or velocity
of an object affects
momentum.
1
Momentum
• Momentum
– quantity of motion
p = mv
p
m v
p:
m:
v:
momentum (kg ·m/s)
mass (kg)
2
velocity (m/s)
Momentum
• Find the momentum of a bumper car if it has a
total mass of 280 kg and a velocity of 3.2 m/s.
GIVEN:
WORK:
p=?
m = 280 kg
v = 3.2 m/s
p = mv
p = (280 kg)(3.2 m/s)
p
m v
p = 896 kg·m/s
3
Momentum
• The momentum of a second bumper car is 675
kg·m/s. What is its velocity if its total mass is
300 kg?
GIVEN:
WORK:
p = 675 kg·m/s
m = 300 kg
v=?
v=p÷m
p
m v
v = (675 kg·m/s)÷(300
kg)
v = 2.25 m/s
4
• The momentum of an object is in the same
direction as its velocity.
• The more momentum a moving object has, the
harder it is to stop.
• The mass of an object affects the amount of
momentum the object has.
• For example, you can catch a baseball moving
at 20 m/s, but you cannot stop a car moving at
the same speed.
• The car has more momentum because it has a
greater mass.
5
• The velocity of an object also affects the
amount of momentum an object has.
• For example, an arrow shot from a bow
has a large momentum because, although
it has a small mass, it travels at a high
velocity.
6
An object’s momentum depends on velocity and mass.
Problem Solving If both dogs have the same velocity,
which one has the greater momentum?
7
Momentum Daily Dose
8
9
10
DD Questions:
1. Write the law of conservation of
momentum.
2. Calculate the momentum of the truck that
the Agent Smith was driving.
1. Mass = 3,000 kg and a velocity of 20 m/s North
3. Calculate the momentum of the truck
driven by the other agent .
1. Mass = 2,500 kg and a velocity of 24 m/s South
4. What is the total momentum of both the
trucks ( P before )
11
Questions cont
5. What will be the velocity of each truck
after the collision? Why is this the case?
(think about the law of conservation of momentum)
12
Lesson 2: Defining Force
• LT 2.3: I can differentiate
balanced and unbalanced
forces.
• LT 2.4: I can differentiate
static friction and kinetic
friction.
• LT 2.5: I can calculate net
force with friction.
13
Force
• Force
– a push or pull that one body exerts on another
– What forces are being
exerted on the football?
Fkick
Fgrav
14
Force
• Balanced Forces
– forces acting on an
object that are opposite
in direction and equal
in size
– no change in velocity
15
Force
• Net Force
– unbalanced forces that are not opposite and equal
– velocity changes (object accelerates)
Fnet
Ffriction
Fpull
N
N
W
16
What is meant by unbalanced
force?
If the forces on an object are equal and opposite, they are said
to be balanced, and the object experiences no change in
motion. If they are not equal and opposite, then the forces are
unbalanced and the motion of the object changes.
17
ConcepTest 1
TRUE or FALSE?
The object shown in the diagram must be at rest
since there is no net force acting on it.
FALSE! A net force does not
cause motion. A net force causes
a change in motion, or
acceleration.
Taken from “The Physics Classroom” © Tom Henderson, 1996-2001.
18
Friction
• Friction
– force that opposes motion between 2 surfaces
– depends on the:
• types of surfaces
• force between the surfaces
19
Friction
• Friction is greater...
– between rough surfaces
– when there’s a greater force
between the surfaces
(e.g. more weight)
20
FRICTION
FRICTION
STATIC
FRICTION-
KINETIC
FRICITON
SLIDING
FRICTION
ROLLING
FRICTION
21
NET FORCE AND FRICTION
• ***REMEMBER: FRICTION OPPOSES
MOTION. IF FRICTION IS INCLUDED IN A
NET FORCE PROBLEM, IT SHOULD BE
SUBTRACTED!!
EXAMPLE:
• YOU ARE PUSHING A BOX ALONG THE
FLOOR. YOU ARE APPLYING
• 10-N OF FORCE. OPPOSING FRICTION IS 2N. WHAT IS THE NET FORCE MOVING THE
BOX?
• 10-2=
8-N
22
Lesson 3: F=ma
• LT 2.6: I can use F=ma to
calculate force, mass or
acceleration.
• LT 2.7 I can use graphical
analysis to solve for force,
mass or acceleration
23
Newton’s Second Law
F
a
m
F = ma
F
m a
F: force (N)
m: mass (kg)
a: accel (m/s2)
2
1 N = 1 kg ·m/s
24
• What force would be required to accelerate a 40
kg mass by 4 m/s2?
GIVEN:
WORK:
F=?
m = 40 kg
a = 4 m/s2
F = ma
F
m a
F = (40 kg)(4 m/s2)
F = 160 N
25
• A 4.0 kg shotput is thrown with 30 N of force.
What is its acceleration?
GIVEN:
WORK:
m = 4.0 kg
F = 30 N
a=?
a=F÷m
F
m a
a = (30 N) ÷ (4.0 kg)
a = 7.5 m/s2
26
What is the mass of each object?
27
Slope=a/f=m
• Object 1: 6 ÷ 2.3 = 2.6 m/s/s
• Object 2: 5.5 ÷ 5.5 = 1 m/s/s
• Object 3: 2.5 ÷ 6.3 = 0.4 m/s/s
28
What is the acceleration of the
object?
1450 ÷ 0.150 = 9700
kg
29
Lesson 4: Gravity and W=mg
• LT 2.8: I can use W=mg to
calculate weight.
• LT 2.9: I can differentiate
between mass and weight.
• LT: 2.10: I can explain the
relationship between gravity,
air resistance and terminal
velocity.
30
Gravity
• Weight
– the force of gravity on an object
W = mg
W=Fg: weight (N)
m: mass (kg)
g: acceleration due
to gravity (m/s2)
MASS
WEIGHT
always the same
(kg)
depends on gravity
(N)
31
• IF Mrs. T weighs 557 N. What is her mass?
GIVEN:
WORK:
F(W) = 557 N
m=?
a(g) = 9.8 m/s2
m = W÷ g
W
m g
m = (557 N) ÷ (9.8 m/s2)
m = 56.8 kg
32
ConcepTest
• Is the following statement true or false?
– An astronaut has less mass on the moon since the moon exerts
a weaker gravitational force.
– False! Mass does not depend on gravity, weight does. The
astronaut has less weight on the moon.
33
Gravity
• Gravity
– force of attraction between any two objects in the
universe
– increases as...
• mass increases
• distance decreases
34
Gravity
• Who experiences more gravity - the astronaut or
the politician?
• Which exerts more gravity the
Earth or the moon?
less
distance
more
mass
35
Gravity
• Would you weigh more on Earth or
Jupiter?
– Jupiter because...
greater mass
greater gravity
greater weight
36
Gravity
• Accel. due to gravity (g)
– In the absence of air resistance, all falling
objects have the same acceleration!
– On Earth: g = 9.8 m/s2
W
g
m
elephant
g
W
m
feather
Animation from “Multimedia Physics Studios.”
37
Air Resistance
• Air Resistance
– a.k.a. “fluid friction” or “drag”
– force that air exerts on a moving object to oppose its
motion
– depends on:
•
•
•
•
speed
surface area
shape
density of fluid
38
Air Resistance
• Terminal Velocity
– maximum velocity reached by a falling
object
– reached when…
Fair
Fgrav = Fair
– no net force
 no acceleration
 constant velocity
Fgrav
39
Air Resistance
• Terminal Velocity
– increasing speed  increasing air resistance until…
Fair = Fgrav(WEIGHT)
40
Animation from “Multimedia Physics Studios.”
Air Resistance
• Falling with air resistance
– heavier objects fall faster because
they accelerate to higher speeds
before reaching terminal velocity
Fgrav = Fair
– larger Fgrav (WEIGHT)
 need larger Fair
 need higher speed
41
Animation from “Multimedia Physics Studios.”
Newton figured out
what the force of
gravity depends
on...
...but he had no clue
what caused gravity.
"Uncle
Fuzzy"
(Einstein) later figured
out WHY gravity
exists!
42
"Hey Marge. Look, Einstein was
right!" - Homer Simpson
43
Lesson 5: Newton’s Three Laws of Motion
• LT 2.11: I can use Newton’s
three Laws of Motion to
explain the interaction of
forces between objects.
• LT 2.12: I can construct a
vehicle that demonstrates
Newton’s three laws.
44
• Sir Isaac Newton (1643-1727) an English
scientist and mathematician famous for his
discovery of the law of gravity also
discovered the three laws of motion. He
published them in his book Philosophiae
Naturalis Principia Mathematica
(mathematic principles of natural
philosophy) in 1687. Today these laws are
known as Newton’s Laws of Motion and
describe the motion of all objects on the
scale we experience in our everyday lives.
45
“If I have ever made
any valuable
discoveries, it has
been owing more to
patient attention,
than to any other
talent.”
Sir Isaac Newton
46
Inertia
An object at rest tends
to stay at rest and
an object in motion
tends to stay in
motion unless acted
upon by an
unbalanced force.
47
Newton’s First Law
• Newton’s First Law of Motion
– An object at rest will remain at rest and
an object in motion will continue moving
at a constant velocity unless acted upon
by a net force.
48
What does this mean?
Basically, an object will “keep doing what it
was doing” unless acted on by an
unbalanced force.
If the object was sitting still, it will remain
stationary. If it was moving at a constant
velocity, it will keep moving.
It takes force to change the motion of an
object.
49
Examples from Real Life
A powerful locomotive begins to pull a
long line of boxcars that were sitting at
rest. Since the boxcars are so massive,
they have a great deal of inertia and it
takes a large force to change their
motion. Once they are moving, it takes
a large force to stop them.
On your way to school, a bug
flies into your windshield. Since
the bug is so small, it has very
little inertia and exerts a very
small force on your car (so small
that you don’t even feel it).
50
If objects in motion tend to stay in motion,
why don’t moving objects keep moving
forever?
Things don’t keep moving forever because
there’s almost always an unbalanced force
acting upon it.
A book sliding across a table slows
down and stops because of the force
of friction.
If you throw a ball upwards it will
eventually slow down and fall
because of the force of gravity.
51
In outer space, away from gravity and any
sources of friction, a rocket ship launched
with a certain speed and direction would
keep going in that same direction and at that
same speed forever.
52
Force
Force equals mass times acceleration.
F = ma
Acceleration: a measurement of how quickly an
object is changing speed.
53
A. Newton’s Second Law
• Newton’s Second Law of Motion
– The acceleration of an object is directly proportional
to the net force acting on it and inversely
proportional to its mass.
F = ma
54
What does F = ma say?
F = ma basically means that the force of an object
comes from its mass and its acceleration.
Something very massive (high mass)
that’s changing speed very slowly
(low acceleration), like a glacier, can
still have great force.
Something very small (low mass) that’s
changing speed very quickly (high
acceleration), like a bullet, can still
have a great force. Something very
small changing speed very slowly will
have a very weak force.
55
More about F = ma
If you double the mass, you double the force. If
you double the acceleration, you double the
force.
What if you double the mass and the
acceleration?
(2m)(2a) = 4F
Doubling the mass and the acceleration
quadruples the force.
So . . . what if you decrease the mass by half? 56
How much force would the object have now?
Action-Reaction
For every action there is an equal and
opposite reaction.
57
What does this mean?
For every force acting on an object, there is
an equal force acting in the opposite
direction. Right now, gravity is pulling you
down in your seat, but Newton’s Third Law
says your seat is pushing up against you
with equal force. This is why you are not
moving. There is a balanced force acting on
you– gravity pulling down, your seat pushing
up.
58
Newton’s Third Law
• Action-Reaction Pairs
• The rocket exerts a
downward force on the
exhaust gases.
• The gases exert an equal
but opposite upward force
on the rocket.
FG
FR
59
Review
Newton’s First Law:
Objects in motion tend to stay in motion
and objects at rest tend to stay at rest
unless acted upon by an unbalanced force.
Newton’s Second Law:
Force equals mass times acceleration
(F = ma).
Newton’s Third
Law:
For every action there is an equal and
opposite reaction.
60
JET CAR CHALLENGE
CHALLENGE:
Construct a car that will travel as far as possible
(at least 3 meters) using only the following
materials.
•
•
•
•
scissors
tape
4 plastic lids
2 skewers
• 2 straws
• 1 balloon
• 1 tray
How do each of Newton’s Laws apply?
61
HP target!
HP LT 2.17: I can use
Newton’s laws create a
visual project with an
explanation of each law
62
Guidelines for Newton’s Laws
Visual
1. Illustrate an example of each of the three laws of motion.
2. Use one poster board or large piece of paper – 3
illustrations on one board or sheet of paper.
3. You may draw or use images from magazines or the
Internet.
4. Include an explanation of how the illustration
demonstrates or describes the law of motion. Put the
explanation next to the illustration. Do not use a
separate sheet of paper for the explanation.
5. Make sure your illustrations are colorful and neat.
63
HP target!
HP LT 2.18: I can use
pbefore=pafter to prove the law
of conservation of
momentum.
64
Conservation of Momentum
• Law of Conservation of Momentum
– The total momentum in a group of objects doesn’t
change unless outside forces act on the objects.
pbefore = pafter
65
Conservation of Momentum
• A 5-kg cart traveling at 4.2 m/s strikes a
stationary 2-kg cart and they connect. Find their
speed after the collision.
BEFORE
Cart 1:
p = 21 kg·m/s
m = 5 kg
v = 4.2 m/s
Cart 2 :
m = 2 kg
v = 0 m/s
p=0
pbefore = 21 kg·m/s
AFTER
Cart 1 + 2:
m = 7 kg
p
v=?
p= 21 kg·m/s m
v=p÷m
v = (21 kg·m/s) ÷ (7 kg)
v = 3 m/s
pafter = 21 kg·m/s 66
v
Conservation of Momentum
• A 50-kg clown is shot out of a 250-kg cannon at a
speed of 20 m/s. What is the recoil speed of the
cannon?
BEFORE
AFTER
Clown:
m = 50 kg
v = 0 m/s
p=0
Clown:
p = 1000 kg·m/s
m = 50 kg
v = 20 m/s
Cannon:
m = 250 kg
v = 0 m/s
p=0
Cannon: p = -1000 kg·m/s
m = 250 kg
v = ? m/s
pbefore = 0
pafter = 0
67
Conservation of Momentum
• So…now we can solve for velocity.
GIVEN:
WORK:
p = -1000 kg·m/s v = p ÷ m
m = 250 kg
v = (-1000 kg·m/s)÷(250
v=?
kg)
p
m v
v = - 4 m/s
(4 m/s backwards) 68