Transcript Newtonslawsforcesgravityx

Newton’s
Laws of
Motion
Isaac Newton! 1642 –1726/7
• Invented Calculus
• White Light = Rainbow
• Reflecting Telescope
• Laws of Motion
• Theory of Gravitation
Newton’s First Law of Motion
1st Law -- Law of Inertia
• An object at rest will stay
at rest unless an
unbalanced force acts
upon it.
• An object in motion will
stay in motion at
constant velocity, unless
acted upon by an
unbalanced force.
A Force is a Push or a Pull! (Phet)
Like a golf ball resting on a
tee, a giant block of poop on
a table will not move unless
an unbalanced force act on it.
Poop
Balanced Force
Suppose two greedy students are fighting over the poop and
they decide to settle the matter with a tug-of-war. If they pull
with equal force in opposite directions, does the poop move?
100 Newtons
100 Newtons
Poop
Unbalanced Force
If the student on the right is pulling with more force that student
wins the poop!
75 Newtons
150 Newtons
Poop
WINNER
!
Newton’s First Law of Motion
INERTIA: an object’s
ability to resist changes in
motion.
MASS: is the measure of
an object’s inertia.
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•
The greater an
object’s mass the
more inertia!
The more inertia the
harder it is to move or
stop.
Which box is harder to move?
Which box has greater inertia?
10kg
20kg
If Mr. Sapone throws two frozen balls of pureed cow intestines at you, one 5kg and one
50kg, which one will be harder to stop? Which one has more inertia?
5k
g
More mass means
more inertia and
greater resistance to
changes in motion.
50kg
Newton’s First Law of Motion
1st Law -- Law of Inertia
• An object at rest will stay
at rest unless an
unbalanced force acts
upon it.
• An object in motion will
stay in motion at
constant velocity, unless
acted upon by an
unbalanced force.
Why doesn’t a
rubber band
ball thrown
upwards travel
into space?
Force of Gravity
Why does a sliding box
eventually stop?
Force of Friction
Phet Physics: Friction
• If you push a box to the right,
which direction does friction
act in?
• If you push a box to the left,
which direction does friction
act in?
• Is there a maximum amount of
friction on the 50kg box?
• Which has more maximal
friction, the box or the
refrigerator?
• In order for the box to move
what can you say about the
force of friction versus the
force you are pushing with?
Friction Always Opposes Motion
Image via openstax collegephysics
Even though a surface may look smooth, if blown up and observed under a microscope
a smooth surface will have jagged edges as shown in the picture above. These edges
are what cause friction when an object slides across another object. As a simple
example of apparent smoothness, look at a computer screen with a magnifying glass.
Air also provides friction (think of sticking your arm out of a fast moving vehicle).
Newton’s 1st Law: Inertia
1.
Explain what happens in the image above in terms of inertia?
1.
Why is it easier to push a car versus a truck?
1.
How does inertia help explain the bed of nails demonstration?
1.
If you throw a baseball in space what happens to it?
1.
If you give a box a big push and it slides across the floor, why does it stop?
1.
Explain this and Mr. Sapone’s table cloth trick in terms of inertia.
1.
Explain the spinning eggs demonstration in terms of Newton’s first law.
2.
Why is it just as difficult to shake a stone in a weightless state in space as it is in its
weighted state on earth?
3.
You decide to attach your skateboard to a car and stand on it.
1.
If the car drives off slow and steadily, what happens?
2.
If the car guns it and accelerates very quickly what happens?
1.
Explain the hanging mass demonstration on the right.
1.
When pulled gently where does the string break?
2.
When pulled hard and fast where does the string break?
2.
If you stood on a carpet and Mr. Sapone yanked it from underneath you really
quickly, what would happen? Pulling the Carpet Out from Under you.
Activity: Spinning Eggs
Activity: Penny Pull
Activity: Hanging Mass Pull
Newton’s Second Law
• A Force acting on an object is
equal to the object’s mass
times its acceleration.
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F = force (N)
m = mass (kg)
a = acceleration (m/s2)
Object’s with more mass require
far more force to make them
accelerate (change their motion)
Handout
Phet Physics: Forces
• Go to the Phet Simulation
and click on the Net Force
tab. Make sure the boxes
that say “sum of forces” and
“values” are check-marked.
• Set it up so that 150N of
force is pulling left and 50N
is pulling right. What is the
net force?
• Set it up so that there is
300N of force pulling to the
right and 150N of force
pulling to the left. What is
the net force?
• How is net force calculated?
These four cubes are resting on a frictionless surface. Each cube is pushed and
pulled by different forces. Rank each object from the highest to lowest net force
Force arrows show direction only, they are not drawn to scale.
70N
100N
50N
100N
35N
65N
80N
90N
10kg
10kg
10kg
10kg
(a)
(b)
(c)
(d)
[1]
Highest
[2]
[3]
[4]
Lowest
Explain:
These four cubes are resting on a frictionless surface. Each cube is pushed and
pulled by different forces. Rank each object from the highest to lowest net force
Force arrows show direction only, they are not drawn to scale.
40N
30N
10kg
10N
(a)
[1]
Highest
[2]
75N
65N
60N
10kg
10kg
(b)
(c)
[3]
[4]
Lowest
85N
10N
90N
10kg
(d)
Explain:
These four cubes are resting on a frictionless surface. The same force (50N) is
applied to each cube. Rank each object from the highest to lowest acceleration:
Force = 50N
Force = 50N
Force = 50N
Force = 50N
2kg
3kg
1kg
4kg
(a)
(b)
(c)
(d)
[1]
Highest
[2]
[3]
[4]
Lowest
Explain:
These four cubes are resting on a frictionless surface. Each cube is pushed and pulled by
different forces. Rank each object from the highest to lowest acceleration.
Force arrows show direction only, they are not drawn to scale.
40N
30N
5kg
10N
(a)
[1]
Highest
[2]
75N
65N
60N
10kg
15kg
(b)
(c)
[3]
[4]
Lowest
85N
10N
90N
20kg
(d)
Explain:
These four cubes are resting on a table. Each cube is made of a different material.
Rank these cubes in terms of mass, weight and volume from largest to smallest.
(a)
(b)
(c)
(d)
Mass Highest to
[1]
Lowest
[2]
[3]
[4]
or
Not enough
information
Weight Highest
[1]
to Lowest
[2]
[3]
[4]
or
Not enough
information
Volume Highest
[1]
to Lowest
[2]
[3]
[4]
or
Not enough
information
Mass: Measure of an objects
resistance to changes in motion or
the amount of matter in an object.
Mass is universal and does not
change.
Volume: The amount of physical
space an object takes up. How big
something is.
Weight: Measure of the force of
gravity acting on an object with
mass. Weight changes on different
planets.
Weight is a force!
Force: Newtons
Mass = kilograms
G = 9.8m/s (on earth)
Fw = mg
Gravity is stronger on earth than it is on the
moon so you weigh more on earth than on
the moon but your mass is the same on both.
What is the weight of an object on earth
that has a mass of 10kg?
[1] Your weight (lbs)_______
Excel File!
[2] Your mass (kg) ________ (divide your weight in lbs by 2.2)
[3] Calculate your weight in Newtons on each object (your mass in kg * g value).
[4] Convert your weight to pounds by multiplying your weight in Newtons by 0.2248
[5] Use this link to check your answers.
[6] Compare the gravity on other planets to earth.
[3]
Object
g value m/s2
Mercury
3.61
Venus
8.83
Earth
9.8
Moon
1.6
Mars
3.75
Jupiter
26
Saturn
11.2
Uranus
10.5
Neptune
13.3
Pluto
0.61
Sun
274
Weight (N)
[4]
Weight (lbs)
[6]
gobject/geart
h
1
[8]
Jump
Height
[7] Measure your vertical
jump height on earth in
meters ____.
[8] Calculate jump height
on other planets by
dividing jump height on
earth by the value
obtained in box [6] for
each location.
[9] On what planet is your
weight and jump height
very similar to that on
earth?
[10] Do you think
conditions on that planet
are similar to those on
earth?
Lunar Jump
Mass does not change. If you had a 10kg cube on earth
and transported it to Mars and Pluto its mass would
always be 10kg. Only its weight would change.
Earth
10kg
Mass = 10kg
Weight = 98N
Weight = 4.5lbs
Mars
10kg
Mass = 10kg
Weight = 37.5N
Weight = 8.4lbs
Weight = mass x gravity.
Pluto
10kg
Mass = 10kg
Weight = 6.1N
Weight = 1.4lbs
Newton’s Third Law
• For every action in
nature there is an equal
and opposite reaction.
• If you push a wall, the
wall is pushing back on
you with an equal force
in the opposite
direction.
Newton’s 3rd Law
1. If you have a 10kg block resting on a table
it has a weight of 98 Newtons (10kg x 9.8m/s )
2. The weight of the block acts downward
pushing on the table.
3. Since the block is not moving the net
force acting on it must be zero.
4. The table is pushing back on the book
equally in the opposite direction.
5. We call this the normal force.
2
FN = 98N
10kg
FW = 98N
Other Examples of Newton’s 3rd Law
Walking: you push down and back on the ground and it
pushes back on you propelling you forward.
Riding a Skateboard: you push backwards on the ground
and it pushes you forward.
Rockets: fuel is combusted and exhaust gasses are pushed
out in the opposite direction of intended motion. The
gasses push back.
Releasing a balloon: the stretched rubber pushes on the
air forcing it out and the air pushes back on it.
Stubbing Your Toe: when you hit your foot on a rock it hits
you with an equal and opposite force.
Rowing a boat: you use the oars to push the water
backwards and it pushes back on the oars in the other
direction.
Swimming: pushing off the wall propels you forward
because the wall pushes back on you.
Propeller: pushes air down, the air pushes back on it.
Balloon Car Project
• You have one week to design
and create a balloon powered
car.
• It must have wheels but
cannot use actual wheels.
• The car needs to go a total
distance of 5 meters and it
cannot leave the ground.
• You may work in groups of
two.
• You will be graded on the
creativity of your design and
how far the car travels.
• You may work alone or with a
partner.
GRADING:
15pts/m up to 75pts
Proper Design 15pts
Visual Appeal 10pts
• Attractive force between
any two objects with
mass.
• Gravity keeps us in orbit
around the sun. It keeps
us from flying off into
space. In fact, it keeps the
earth together and our
atmosphere from rushing
into space.
Io is the most volcanically active body in the solar system. There is
less gravity on Io which means lava eruptions travel much higher,
sometimes up to 60miles.
Why do Objects with mass attract one another?
Imagine stretching a sheet really tight and
putting a bowling ball in the center.
• We don’t really know for
sure. We know they do
and can do all sorts of
calculations based upon
our discoveries.
• Einstein thought space
itself becomes warped by
massive bodies.
• Standard model physics
posits the existence of
gravitons…tiny particles
that transmit the
gravitational force.
Why don’t people in the southern hemisphere fall off the earth?
GRAVITY Acts Inwards
on Earth. When you or
anyone jumps, it pulls
you back to the ground.
There is no such
thing as up or
down in space.
Phet Physics: Gravity
• Increasing the mass does what
to the force of gravity?
• Decreasing the mass does
what to the force of gravity?
• Decreasing the distance
between two objects does
what to gravity?
• Increasing the distance
between two objects does
what to gravity?
• Set the blue ball to 100kg and
the red ball to 1kg. Which one
has more gravity?
• Does gravity obey Newton’s
third law? Explain.
Newton’s Law of Universal Gravitation
an inverse-square laq
In plane English:
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Every object with mass attracts every
other objects with mass gravitationally.
The more massive the objects the more
gravity.
The further away objects are the less
gravity.
Double distance force is 4x as weak
Triple distance force is 9x as weak
m1m2
Fg = G 2
r
• The force of gravity between any
two objects is proportional to the
product of their masses divided by
the distance between them
squared.
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G= 6.67×10−11 N·(m/kg)2
r = distance between objects
m1 = mass object 1 (kg)
m2 = mass object 2 (kg)
Inverse-Square Law
Light
Sound
Electricity
Magnetism
Gravity
Img Src
A word Problem
• There are two round
objects in space. One of
them has a mass of
100kg and the other
one has a mass of 2kg.
The distance between
them is 3 meters.
Calculate the force of
gravity.
m1m2
Fg  G 2
r
m1m2
Fg  G 2
r
m1
G= 6.67×10−11 N·(m/kg)2
m2
Mass = 100kg
2kg
r = 3 meters
Fg  (
)
(
)(
(
)
)
2
m1m2
Fg  G 2
r
m1
G= 6.67×10−11 N·(m/kg)2
m2
Mass = 100kg
2kg
r = 3 meters
Fg  (
(100kg)( 2kg )
)
2
( 3m )
6.67×10−11 N·(m/kg)2
Force of the Sun’s Gravity
• The sun has a mass of
1.9891 × 1030kg and the
earth has a mass of
5.97219 × 1024kg. The
average distance
between the earth and
sun is 1.496 × 1011m.
Calculate the force of
gravity.
G= 6.67×10−11 N·(m/kg)2
m1m2
Fg  G 2
r
Fg  (
( )( )
)
2
( )
Which Object will hit the ground first?
All Objects fall at the same rate! Why?
Newton’s Law of Gravity
m1m2
Fg  G 2
r
Equate them
Mass cancels
m1m2
G 2  ma
r
Newton’s Second Law
F  ma
mearth
aG 2
r earth
The Acceleration due to gravity on the surface of a massive body is proportional
to the mass of the object and your distance from the center of the object.
m planet
a=G 2
r planet
Mass earth: 5.97219 × 1024kg
Radius of Earth: 6,378,100m
G constant: 6.67x10-11 N·(m/kg)2
Mass mars: 6.4185×1023 kg
Radius of mars: 3,389,500m
G constant: 6.67x10-11 N·(m/kg)2
Calculate the acceleration due
to gravity on mars and earth.
Period of a Pendulum
L
T  2
g
Purpose: to determine the value of g using
a simple pendulum.
L = length of string
g = 9.8m/s2
T= period of pendulum
(time to swing back and forth once)
Rearranging
4p L
g=
2
T
2
Heavy Bob
_____Length of String
_____Period of 10 revolutions
_____Period of 1 revolution
Light Bob
_____Length of String
_____Period of 10 revolutions
_____Period of 1 revolution
Does the mass of
the bob have any
impact on period?
Don’t forget to
do your
homework!
Mr. Sapone tells you that you have a lot
of potential. Then he pushes you off a
tall building. It takes four seconds before
your face makes smoochies with the
ground. How tall is the building?
You can calculate the distance an object falls using
the following formula:
y=
2
½at
y = distance
a = g = 9.8m/s2
t=time
S.H.H.S.
YOU
MASS = 50KG
ROFL
Thot
Before cheating on you with your best
friend, a woman rips out your heart
and while it is still beating she drops it
off of a building. It takes 3 seconds
before your heart hits the ground. How
tall is the building?
You can calculate the distance an object falls using
the following formula:
y = ½at2
Y = distance
A = g = 9.8m/s2
T=time
S.H.H.S.
STRIKE!!!
Mr. Sapone sees you at the bottom of a
20m tall building and since he didn’t have
access to a piano at the time, he drops a
bowling bowl on you. How long do you
have left to live
y = ½at2
You need to solve for t this time
S.H.H.S.
YOU
MASS = 50KG
y=
TERMINAL VELOCITY
½at2
Air Resistance
1ct
A dropped object will not speed up forever.
At some point air resistance will counteract
its acceleration and it will reach a maximum
fall speed or terminal velocity.
Imagine sticking your arm out of a window
of a moving car. What do you feel?
If the car keeps going faster and faster, what
happens to your arm?
A falling object feels air resistance and the
faster it falls the more air resistance it feels.
Weight
S.H.H.S.
Eventually the weight pulling an object
down balances with the air resistance
pushing up and there is no more
acceleration. The object continues
downward with a constant speed.
Projectile Motion:
• If I were to drop a bullet
and shoot a bullet
horizontally at the same
time, which one hits the
ground first?
• Ruler Demo
• 2nd Law Apparatus
• Ballistics Cart
Thrown Sideways
• Regardless of whether thrown
vertically or dropped, objects fall at
exactly the same rate: 9.8m/s2.
t = 0s
t = 1s
They hit the
ground at the
same time!
t = 2s
Dropped Vertically
t =3s
Orbits: Falling Forever
A thrown object follows a
curved path as it falls to the
ground.
What happens if its thrown
at just the right speed?
It will fall forever!
1.
2.
3.
4.
The Sun Orbits around the earth.
The Earth Orbits around the sun.
The Earth Orbits around the moon.
The moon Orbits around the earth.
Two bodies with the same
mass orbiting a common
barycenter similar to some
asteroids (Antipoe 90)
Two bodies with a difference
in mass orbiting a common
barycenter similar to plutocharon system
Two bodies with a major
difference in mass orbiting a
common barycenter internal
to one body (similar to the
Earth–Moon system)
Two bodies with an extreme
difference in mass orbiting a
common barycenter internal
to one body (similar to the
Sun–Earth system)
Two bodies with the same mass orbiting
a common barycenter, external to both
bodies, with eccentric elliptic orbits (a
common situation for binary stars)
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Light is the fastest thing in the known
universe.
It can travel around the entire earth almost
8 times in a single second.
Light is pretty much instantaneous on earth.
Sound is much slower than light.
Sound travels at about 340m/s (1100ft/s)
When lightning strikes, you see the bolt
instantaneously.
It takes time for the thunder to reach your
ears.
Hence, there is a delay between seeing
lightning and hearing thunder even though
they occur together.
The less delay between thunder and
lightning, the closer you are to a strike.
In general, a 5 second delay between seeing
a lightning bolt and hearing the thunder
corresponds to a distance of about 1 mile.
Hearing thunder and seeing lightning
occurring together might mean you are
dead.
It take time for the thunder
to reach your ears
See lightning instantly
Speed Limit
C
186,000mi/s
It takes light from the sun 8
minutes to reach us!
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Light is fast on earth but space is really big.
The sun is about 93,000,000 miles away from us.
Even at the speed of light (186,000mi/s) it takes time for light to reach us from the sun.
In fact, light from the sun is about 8 minutes old.
So if the sun were to blow up right now, we wouldn’t know about it for 8 minutes.
The sun is relatively close to us compared to other stars which means the light we see from
stars in the nighttime sky may be millions or billions of years old.
The light from some stars we see with our naked eyes is thousands of years old.
Some galaxies and quasars visible with telescopes may be thousands or millions of years old.
1.
Will dropping a penny off the empire state building onto someone’s head kill
them? (Mythbusters did this!)
2. What is terminal velocity and what causes it?
3. You are hiking along the top of a very tall cliff. Suppose you want to know how far
down the ground is and you only have a stop watch and a rock. How can you
determine the height of the cliff?
4. You are watching the city’s fireworks go off on the fourth of July when you notice
that there is a delay between when you see the fireworks and when you hear
them. Explain why?
5. Mr. Sapone is fishing at a very legal reservoir that he has special permission to
fish in. He notices kids jumping off a tower into the water at the other end of the
lake. After the kids hit the water he hears the sound from their impact 1.3
seconds later. Assuming sound travels at 340m/s, how far away from the tower is
Mr. Sapone?
6. Explain the orbital dynamics of the earth-moon system.
7. You are hanging from a tree branch and Mr. Sapone is standing on the top of a
hill the so that he is at the same height as you. He shoots an arrow directly at
your thick skull and at the same exact time you let go of the tree. If the tree is
40m away from the base of the tree, will the arrow hit you?
8. An NFL player punts the football to the opposing team. It has a hang time of 4.3s.
How high did the football travel?
9. For a while some scientists speculated that traveling in space would be
impossible since it is empty (a vacuum) and there is nothing to push off of. How
can a spaceship change direction in space?
10. If you want to throw a ball a really far horizontal distance, is throwing it straight a
good idea?
11. When you look up at the sky you are looking at history. Explain?
ACTIVITY: How high
can you throw a
tennis ball?
y = ½at2
Hang Time __ __ __
Average time___
Cut in Half____ Why?
Height____