Download I. Newton`s Laws of Motion

Motion & Forces
Newton’s Laws of Motion
“If I have seen far, it is because I have stood
on the shoulders of giants.”
- Sir Isaac Newton
(referring to Galileo)
A. 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.
B. 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
C. Newton’s Third Law
 Newton’s
Third Law of Motion
 When one object exerts a force
on a second object, the second
object exerts an equal but
opposite force on the first.
Motion & Forces
Describing Motion
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
force.
A. Motion
 Problem:
 Is your desk moving?
 We
need a reference point...
 nonmoving point from which
motion is measured
A. Motion
 Motion
 Change in position in relation to
a reference point.
Reference point
Motion
A. Motion
Problem:
 You are a passenger in a car
stopped at a stop sign. Out of the
corner of your eye, you notice a
tree on the side of the road begin
to move forward.
 You have mistakenly set yourself
as the reference point.
B. Speed & Velocity
 Speed
d
 rate of motion
v t
 distance traveled per unit time
distance
speed 
time
B. Speed & Velocity
 Instantaneous
Speed
 speed at a given instant
 Average
Speed
total distance
avg. speed 
total time
B. Speed & Velocity
 Problem:
 A storm is 10 km away and is
moving at a speed of 60 km/h.
Should you be worried?
 It depends
on the
storm’s
direction!
B. Speed & Velocity
 Velocity
 speed in a given direction
 can change even when the
speed is constant!
C. Acceleration
vf - vi
a t
 Acceleration
 the rate of change of velocity
 change in speed or direction
a
v f  vi
t
a:
vf:
vi:
t:
acceleration
final velocity
initial velocity
time
C. Acceleration
 Positive
acceleration
 “speeding up”
 Negative
acceleration
 “slowing down”
D. Calculations
Your neighbor skates at a speed of 4 m/s.
You can skate 100 m in 20 s. Who skates
faster?
GIVEN:
WORK:

d = 100 m
t = 20 s
v=?
d
v t
v=d÷t
v = (100 m) ÷ (20 s)
v = 5 m/s
You skate faster!
D. Calculations
A roller coaster starts down a hill at 10 m/s.
Three seconds later, its speed is 32 m/s.
What is the roller coaster’s acceleration?
GIVEN:
WORK:

vi = 10 m/s
t=3s
vf = 32 m/s
vf - vi
a=?
a t
a = (vf - vi) ÷ t
a = (32m/s - 10m/s) ÷ (3s)
a = 22 m/s ÷ 3 s
a = 7.3 m/s2
D. Calculations
Sound travels 330 m/s. If a lightning bolt
strikes the ground 1 km away from you,
how long will it take for you to hear it?
GIVEN:
WORK:

v = 330 m/s
t=d÷v
d = 1km = 1000m
t = (1000 m) ÷ (330 m/s)
t=?
t
=
3.03
s
d
v t
D. Calculations
How long will it take a car traveling 30 m/s
to come to a stop if its acceleration is
-3 m/s2?
GIVEN:
WORK:

t=?
vi = 30 m/s
vf = 0 m/s
a = -3 m/s2
t = (vf - vi) ÷ a
t = (0m/s-30m/s)÷(-3m/s2)
vf - vi
a t
t = -30 m/s ÷ -3m/s2
t = 10 s
E. Graphing Motion
Distance-Time Graph
A
B

slope = speed

steeper slope =
faster speed

straight line =
constant speed

flat line =
no motion
E. Graphing Motion
Distance-Time Graph
A



B

Who started out faster?
 A (steeper slope)
Who had a constant speed?
 A
Describe B from 10-20 min.
 B stopped moving
Find their average speeds.
 A = (2400m) ÷ (30min)
A = 80 m/min
 B = (1200m) ÷ (30min)
B = 40 m/min
E. Graphing Motion
Distance-Time Graph
400

Acceleration is
indicated by a
curve on a
Distance-Time
graph.

Changing slope =
changing velocity
Distance (m)
300
200
100
0
0
5
10
Time (s)
15
20
E. Graphing Motion
Speed-Time Graph
3

slope = acceleration
 +ve = speeds up
 -ve = slows down

straight line =
constant accel.

flat line = no accel.
(constant velocity)
Speed (m/s)
2
1
0
0
2
4
6
Time (s)
8
10
E. Graphing Motion
Speed-Time Graph
Specify the time period
when the object was...
 slowing down
 5 to 10 seconds
 speeding up
 0 to 3 seconds
3
Speed (m/s)
2

1
0
0
2
4
6
Time (s)
8
10

moving at a constant
speed
 3 to 5 seconds
not moving
 0 & 10 seconds
Bell Ringer
 What
is Speed?
 What
is Acceleration?
Motion & Forces
Defining Force
A. Force

Force - a push or pull that one body
exerts on another
 What forces are being
exerted on the football?
Fkick
Fgrav
A. Force
 Has
the ability to change an
object's motion :
 Starting
 Stopping
 Speeding up
 Slowing down
 Changing direction
A. Force
 May
change an object's shape
 Forces give energy to an object
 All of the forces acting on an
object together are known as net
forces
A. Force
 Forces
can be represented with
arrows called vectors .
 Vectors show the direction
and magnitude of a force .
 Forces are measured in
Newtons ( N).
A. Force

Balanced Forces
 forces acting on
an object that
are opposite in
direction and
equal in size
 no change in
velocity
 Net force = 0
A. Force

Unbalanced Forces
 unbalanced forces that are not opposite
and equal
 velocity changes (object accelerates)change in movement
 Net force is greater than zero
Fnet
Ffriction
Fpull
N
W
N
Bell Ringer
 What
is a Force?
 What
unit is force measured in?
 What
is a vector?
B. 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.
B. Newton’s First Law

Newton’s First Law of Motion
 “Law of Inertia”

Inertia
 tendency of an object to resist any
change in its motion
 increases as mass increases
B. Newton’s First Law
 Objects do not change their motion unless a force acts on
them
An object will NOT start moving unless a force acts on it.
An object will NOT stop moving unless a force acts on it.
An object will NOT change speed unless a force acts on it
An object will NOT change direction unless a force acts
on it
• http://www.youtube.com/watch?v=8zsE3mpZ6
Hw
The more mass an object has, the more inertia it has.
This means that the more mass an object has, the
harder it is to move, stop, or change the speed or
direction of the object.
B. Newton’s First Law
 Don’t
let this be you. Wear seat belts!
 Because
of inertia, objects (including
you) resist changes in their motion.
When the car going 80 km/hour is
stopped by the brick wall, your body
keeps moving at 80 m/hour.
C. Friction

Friction - force that opposes motion
between 2 surfaces
 depends on the:
• types of surfaces
• force between the
surfaces
C. Friction

Friction is greater...
 between rough surfaces
 when there’s a greater
force between the
surfaces
(e.g. more weight)
C. Friction

Three kinds of friction:
 Static—frictions between two
surfaces that are NOT moving
past each other
 Sliding—the force that
opposes the motion of two
surfaces sliding past each
other.
 Rolling—the friction between
a rolling object and the surface
it rolls on is rolling friction.
Bell Ringer
 What
is friction?
 What
are the three types of
friction?
 What
two things affect friction?
Motion & Forces
Force & Acceleration
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
A. Newton’s Second Law
F
a
m
F = ma
F
m a
F: force (N)
m: mass (kg)
a: accel (m/s2)
1 N = 1 kg ·m/s2
B. Gravity

Gravity
 force of attraction between any two
objects in the universe
 increases as...
• mass increases
• distance decreases
B. Gravity
Who experiences more gravity - the
astronaut or the politician?
 Which exerts more gravity the Earth or the moon?

less
distance
more
mass
B. Gravity

Weight
 the force of gravity on an object
W = mg
W: weight (N)
m: mass (kg)
g: acceleration due
to gravity (m/s2)
MASS
WEIGHT
always the same
(kg)
depends on gravity
(N)
B. Gravity

Would you weigh more on Earth
or Jupiter?
 Jupiter because...
greater mass
greater gravity
greater weight
Bell Ringer
 What
is the formula for Weight?
 What is gravity?
 What is the formula for Newton’s
2nd Law of motion?
 What unit of measurement is
force measured in?
 What are the units for: velocity,
acceleration, distance, mass?
B. 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.”
C. 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
C. Air Resistance

Terminal Velocity
 maximum velocity reached
by a falling object
F
 reached when…
air
Fgrav = Fair
 no net force
 no acceleration
 constant velocity
Fgrav
C. Air Resistance

Terminal Velocity
 increasing speed  increasing air
resistance until…
Fair = Fgrav
Animation from “Multimedia Physics Studios.”
C. Air Resistance

Falling with air resistance
 heavier objects fall faster
because they accelerate
to higher speeds before
reaching terminal
velocity F
=F
grav
air
 larger Fgrav
 need larger Fair
 need higher speed
Animation from “Multimedia Physics Studios.”
D. Calculations

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
D. Calculations

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
D. Calculations

Mrs. J. weighs 557 N. What is her
mass?
GIVEN:
WORK:
F(W) = 557 N
m=?
a(g) = 9.8 m/s2
m=F÷a
F
m a
m = (557 N) ÷ (9.8 m/s2)
m = 56.8 kg
Bell Ringer
 What
force would be required to
accelerate a 40 kg mass by 4 m/s2?
 A 4.0 kg shot-put is thrown with 30
N of force. What is its
acceleration?
 Sound travels 330 m/s. If a
lightning bolt strikes the ground 1
km away from you, how long will it
take for you to hear it?
Motion & Forces
Nonlinear Motion
A. Projectile Motion

Projectile
 any object thrown
in the air
 acted upon only
by gravity
 follows a
parabolic path
called a trajectory
 has horizontal and vertical velocities
PROJECTILE MINI-LAB
A. Projectile Motion

Projectile Velocities

Horizontal and vertical velocities are
independent of each other!
A. Projectile Motion

Horizontal Velocity
 depends on inertia
 remains constant

Vertical Velocity
 depends on gravity
 accelerates
downward at
9.8 m/s2
B. Circular Motion

Centripetal Acceleration
 acceleration toward the center of a
circular path
 caused by centripetal force
 The word centripetal means “to move
toward the center”.
What
would
happen if
the string
broke?
B. Circular Motion

On the ground...
 friction provides centripetal force
B. Circular Motion

In orbit...
 gravity provides centripetal force
ROUND LAB
B. Circular Motion

In orbit...
 Which satellites travel faster?
Near-Earth Satellites
Geostationary Satellites
C. Free-Fall

Free-Fall
 when an object is influenced only
by the force of gravity

Weightlessness
 sensation produced when an object
and its surroundings are in free-fall
 object is not weightless!
C. Free-Fall

Weightlessness
 surroundings are falling at the same
rate so they don’t exert a force on
the object
Go to Space Settlement Video Library.
C. Free-Fall
Space Shuttle Missions
Go to CNN.com.
Go to NASA.
NASA’s KC-135 - “The Vomit Comet”
Motion & Forces
Action and Reaction
A. Newton’s Third Law
 Newton’s
Third Law of Motion
 When one object exerts a force
on a second object, the second
object exerts an equal but
opposite force on the first.
A. Newton’s Third Law

Problem:
 How can a horse
pull a cart if the cart
is pulling back on
the horse with an equal but
opposite force?
 Aren’t these “balanced forces”
resulting in no acceleration?
NO!!!
A. Newton’s Third Law

Explanation:
 forces are equal and opposite but
act on different objects
 they are not “balanced forces”
 the movement of the horse
depends on the forces acting on
the horse
A. Newton’s Third Law

Action-Reaction Pairs

The hammer exerts
a force on the nail
to the right.

The nail exerts an
equal but opposite
force on the
hammer to the left.
A. 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
A. Newton’s Third Law

Action-Reaction Pairs

Both objects accelerate.

The amount of acceleration
depends on the mass of the object.
F
a 
m

Small mass  more acceleration

Large mass  less acceleration
Examples:
 As a man exits a canoe, the canoe
moves in the opposite direction. The
canoe has an equal and opposite
reaction to the man’s action.
 A gun exerts a force on a bullet and
the bullet exerts the
SAME force on the gun.
 As the paddle is pushed backward in
the water the canoe moves forward.
 A swimmer pushes water back with
his arms, but his body
moves forward.
B. Momentum

Momentum
 quantity of motion
p = mv
p
m v
p:
m:
v:
momentum (kg ·m/s)
mass (kg)
velocity (m/s)
B. 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=?
p = mv
m = 280 kg
p = (280 kg)(3.2 m/s)
v = 3.2 m/s
p = 896 kg·m/s
p

m v
B. 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
v=p÷m
m = 300 kg
v = (675 kg·m/s)÷(300 kg)
v=?
v = 2.25 m/s
p

m v
C. 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
C. Conservation of Momentum

Elastic Collision
 KE is conserved

Inelastic Collision
 KE is not conserved
C. Conservation of Momentum

A 5-kg cart traveling at 1.2 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
v=?
p
m v
v=p÷m
v = (21 kg·m/s) ÷ (7 kg)
v = 3 m/s
pafter = 21 kg·m/s
C. 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
C. 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 kg)
v=?
v = - 4 m/s
p
(4 m/s backwards)
m v
Motion & Forces
Forces in Fluids
A. Archimedes’ Principle

Fluid
 matter that flows
 liquids and gases

Buoyancy
 the ability of a fluid to exert an
upward force on an object
immersed in it
A. Archimedes’ Principle

Bouyant Force
 upward force exerted by a fluid on an
immersed object
 bouyant force > weight
balloon rises
 bouyant force < weight
balloon sinks
 bouyant force = weight
balloon floats
A. Archimedes’ Principle

Archimedes’ Principle
 the bouyant force on an object in a
fluid is equal to the weight of fluid
displaced by the object
Not
More
water
needs
water
is
to displaced
betodisplaced
in order
in order
cancel
to to
Veryenough
little
water
needs
be displaced
intoorder
cancel weight
weight
 ball sinks.
 ball floats lower
in the water.
on surface.
View Buoyancy JAVA Applet.
View animations produced by students at Poly Prep Country Day School in Brooklyn, New York.
B. Pascal’s Principle

Pascal’s Principle
 pressure applied to a fluid is
transmitted unchanged throughout
the fluid
View hydraulics explanation.
F1
P
A1
F2
A
A2
B. Pascal’s Principle

A car weighing 1000 N sits on a 250 m2 platform.
What force is needed on the 10 m2 plunger to
keep the car from sinking?
GIVEN:
WORK:
Platform:
F = 1000 N
A = 250 m2
Plunger:
F=?
A = 10 m2
1000 N =
250 m2
F2
F1 F2

A1 A2
10 m2
(1000 N)(10 m2)=(250 m2)F2
F2 = 40 N
C. Bernoulli’s Principle

Bernoulli’s Principle
 as the velocity of a fluid increases,
the pressure exerted by the fluid
decreases
 EX:airplane lift, curve balls
C. Bernoulli’s Principle
Airplane lift
View airplane wings explanation.
Curve Ball
C. Bernoulli’s Principle
Funnel Demos
View funnel explanation.
View inverted funnel explanation.
C. Bernoulli’s Principle

Venturi Effect
 fluids flow faster through narrow
spaces causing reduced pressure
 EX: garden sprayer, atomizer,
carburetor
C. Bernoulli’s Principle
Venturi Effect - Atomizers