Transcript Centripetal Force

Meters of Motion, a watercolor by Champaign-Urbana artist, Billy Morrow Jackson, is the basis for
the poster announcing the 20th International Congress of Theoretical and Applied Mechanics,
held in Chicago in August of 2000.
Forces
Chapter 3
Sections 1 - 3
Chp 3 - Forces
• Section 1 – Weathering slides 3 - 20
• Section 2 – Gravity slides 21-38
• Section 3 – The Third Law of Motion slides 3952
Section 1 - Weathering
•
•
•
•
What You’ll Learn:
How force, mass, & acceleration are related
The three different types of friction
How air resistance affects falling objects
Force, Mass, and Acceleration
• You read about Newton’s first law of motion
which says that the motion of an object changes
only if an unbalanced force acts on it.
• Newton’s second law of motion describes the
relationship between the acceleration of an
object, its mass, and the forces exerted on it.
How are force & acceleration
related?
How are throwing a
ball as hard as
you can &
tossing it gently
different?
How are force & acceleration
related?
How are throwing a
ball as hard as
you can &
tossing it gently
different?
The first requires
more force
creating a
greater velocity
in less time.
Tossing gently
takes less force
as well as less
velocity and
acceleration.
Are mass & acceleration related?
<http://www.essexfellsrec.com>
• If you throw a softball
and a baseball as hard
you can, will they have
the same speed?
• Because a softball has
more mass, it will have
less velocity even though
you applied the same
force. This means that
acceleration also depends
mass as well as force.
Newton’s Second Law
• Newton’s second law of motion states that
the net force acting on an object causes the
object to accelerate in the direction of the net
force.
• To find the acceleration, you must know the
mass and the net force.
• Acceleration (α)= net force (in N)/mass (kg) or
α= F/m
How can the second law help find
net force?
• If you know an object’s mass & acceleration,
you can use Newton’s second law to find the
force by using the equation F=ma.
• Suppose a tennis ball leaves a racket with a
speed of 100 km/h with an acceleration of
5,000 m/s2. The ball’s mass is 0.06 kg. F=ma
so: (0.06 kg)(5,000m/s2)= 300 kg m/s2 = 300 N
Friction
• Friction is the force that
opposes the sliding
motion of two surfaces
that are touching each
other. The amount of
friction between the two
depends on two things:
the kind of surfaces &
the amount of force
pressing them together.
<http://z.about.com/d/skateboard/1/5/i
/M/axlestall4.jpg>
What causes friction?
polymer fabric welded with ultrasound
• Microwelds occur where
two surfaces stick
together due to
roughness. Friction is
caused by the
microwelds that form
where the surfaces are in
contact.
<http://www.sra-developments.co.uk/img/micrograph_01.gif>
What makes things stick together?
• The stronger the force pushing two surfaces
together, the stronger the microwelds will be.
• To move one surface over another, a force must
be applied to break the microwelds.
What is static friction?
• Static friction is the
force that keeps two
surfaces at rest from
sliding across each other.
• The mechanic shown
here is attempting to
break a nut seize caused
by static friction.
<http://www.beisansystems.com/procedures/
e39_fan_procedure_files/image010.jpg>
What is sliding friction?
• Sliding friction is the
force that works against
the motion of two
surfaces that are sliding
across each other.
• Another example would
be wheels spinning in
snow or mud. Sand or
gravel will increase the
<http://www.superphysics.netfirms.com/fricti1.jpg> sliding friction so the
wheels can roll w/o
slipping.
What is rolling friction?
• Rolling friction is the
frictional force between a
rolling object and the
surface it rolls on.
• A wheel digs into the
surface it is rolling over
deforming both the
wheel and the surface.
<http://www.ofs.edu.sg/our-schools>
Air Resistance
• Air resistance is a force that opposes the movement
of objects through the air. Similar to friction, air
resistance acts in the direction opposite to the object’s
motion.
<http://www.bmw.ie/ie/en/insights/technology/efficient_dynamics/innovative_technolo
gies/_shared/img/air_vent_control.jpg>
Air Resistance
• Objects falling toward
Earth are being pulled
downward by the force
of gravity.
• Air resistance is a force
that opposes the
movement of objects
through the air.
• Air resistance is similar
to friction.
<http://www.nasa.gov/centers/mars
hall/images>
Air Resistance
• In the case of a falling
object, air resistance
pushes up as gravity pulls
down.
• If there were no air
resistance, only gravity
would affect falling
objects.
• All objects would fall at
the same rate.
<http://z.about.com/d/inventors/1/5/0
/2/1/parachute2.jpg>
Air Resistance
<http://www.bioinformaticszen.com/>
<http://up
load.wikim
edia.org/wi
kipedia/co
mmons/3/
3f/Paper_s
heet.jpg>
• Different objects fall
with different
accelerations and
different speed due to
their size and shape.
• Compare the forces on a
sheet of paper to those
on a crumpled sheet.
Which has the greater
net downward force?
Section 2 - Gravity
• What You’ll Learn:
• How gravity & weight are related
• The difference between mass & weight
What is gravity?
• Gravity is an attractive
force between two
objects.
• It increases as the mass
of either object
increases, or as the
objects move closer to
one another.
• You can’t feel
gravitational force
between you and the
table. Why?
<http://openlearn.open.ac.uk/file.php>
<http://hegel.lewiscenter.org/users/mhuffine
/subprojects/Department/images/psci2.jpg>
Law of Universal Gravitation
• This lets us find the force
of gravity between any two
objects if their masses &
the distance between them
are known.
• G=universal gravitational
constant (never changes)
• D=distance; m=mass
<http://www.williamsclass.com/EighthS
cienceWork/ImagesEighth/Gravitational
Force.jpg>
Why is gravity called a long-range
force?
• Gravitational force
between two masses
decreases as the distance
between them increases.
• No matter how far apart
two objects are, the
gravitational force
between them never
completely goes to zero.
• This is also called the
inverse square law.
<http://schoolnet.gov.mt/earth_universe/i
mages/10184_w.jpg>
How did gravity help astronomers
find other planets?
<http://www.redorbit.com/modules/refli
b/article_images/8_d7f84ec36dbfda23aff
1a01e00a4b5e6.jpg>
• The motion of every
planet is affected by the
gravitational forces of
the other planets.
• In 1840 the farthest
known planet was
Uranus, but its motion
could not be explained
by the attraction of the
other known planets.
• Neptune’s discovery
resulted from this.
Earth’s Gravitational Acceleration
• A falling object in free fall accelerates at about
9.8 m/s2 (acceleration of gravity or g).
• The force of Earth’s gravity on a falling object is
the object’s mass times g.
• Force of gravity (N)=mass (kg) X accel of g
(m/s2) or F=mg
• You can use this equation to find the
gravitational force on a sky diver with a 60 kg
mass.
Earth’s Gravitational Acceleration
• You can use this equation
to find the gravitational
force on a sky diver with a
60 kg mass.
• F=mg or
• F= (60 kg)(9.8 m/s2) =
588 Newtons.
• The gravitational force on
the sky diver is 588 N.
<http://verticalextremeskydiving.com/ESW
/Images/single.jpg>
How is weight calculated?
• The gravitational force
Earth exerts on an object
is its weight.
• Weight (N)=mass (kg) X
acceleration of gravity or
W=mg.
<http://www.global-b2bnetwork.com/direct/dbimage/50331349/Pers
onal_Training_Weight_Scale.jpg>
Is there a difference between weight
& mass?
• Weight is a force while mass is the measure of
the amount of matter in an object.
• Weight & mass are related, but they are not the
same.
• Mass stays the same but weight changes as the
location the object is in changes.
• You weigh more on Earth than on the moon
because the gravity decreases yet mass remains
the same.
Weightlessness & Free Fall
• What would happen if
you are standing on the
scale & the elevator
begins to fall rapidly?
• Astronauts in the space
shuttle experience
“weightlessness” because
they are farther from
Earth’s gravitational pull.
• The orbiting shuttle is in
free fall so everything
seems to float.
<http://www.batesville.k12.in.us/Physics/>
<http://www.nasa.gov/images/>
Projectile Motion
<http://www.mrfizix.com/home/projectil
emotion_files/image080.jpg>
• Thrown objects’ path
curves downward due to
gravity.
• Anything thrown or shot
is called a projectile.
• Throwing exerts a
forward force on the ball
propelling it horizontally.
• At the same time gravity
acts downward on the it.
What happens when an object has
both horizontal & vertical motion?
<http://www.mrfizix.com/home/projectile
motion_files/image080.jpg>
• The ball has a constant
horizontal velocity, but
increasing vertical
velocity.
• Gravity exerts an
unbalanced force on the
ball, changing the path
from only forward to
forward and downward
producing a curve.
Are horizontal & vertical distance
always the same?
• Which ball lands first?
• Which one travels the
farthest distance?
<http://www.mrfizix.com/home/proje
ctilemotion_files/image080.jpg>
Are horizontal & vertical distance
always the same?
• Which ball lands first?
Neither one; they land at
the same time.
• Which one travels the
farthest distance?
The ball that is thrown
travels farthest.
<http://www.mrfizix.com/home/proje
ctilemotion_files/image080.jpg>
Centripetal Force
• Acceleration toward the
center of a curved path
is called centripetal
acceleration.
• According to Newton’s
second law of motion,
the direction of the net
force on the ball must be
toward the center of the
curved path.
<http://content.answers.com/main>
Centripetal Force
• A ball inside a coiled
tube experiences
centripetal force which
forces it to move in a
circle.
• The centripetal force is
the force toward the
center exerted by the
walls of the tube on the
ball.
<http://content.answers.com/main>
How does centripetal force depend
on traction?
• When a car rounds a
curve, a centripetal force
must be acting on the car
to keep it moving in a
curved path; otherwise it
will slide off the road.
• The centripetal force is
traction. Rain or ice can
reduce traction causing
the car to slide in a
straight line off the road.
<http://webassign.net/serpop/5-13.gif>
Can gravity be a centripetal force?
• Imagine swinging a yo-yo on a string above your
head.
• The string places centripetal force on the yo-yo
much like the Earth’s gravitational pull places
centripetal force on the Moon o keep it moving
in a nearly circular orbit.
<http://www.aerospaceweb.org/question/astronomy/moon/orbit.jpg>
Section 3 – The Third Law of
Motion
• What You’ll Learn:
• Newton’s law of motion
• How to find momentum
<http://www.president.vt.edu/presreports/pres0102/balls.jpg>
Newton’s Third Law
• If you push against the
wall while wearing skates,
you’ll roll backwards.
• This example of
Newton’s third law of
motion describes action
& reaction.
• “To every action force
there is an equal &
opposite reaction force.”
<http://www.sciencetoymaker.org/balloon
/images/newton.gif>
How do action & reaction happen?
<http://pro.corbis.com/images/4215995438.jpg?size=572&uid=%7B7D48F44BCF66-4720-BED9-7A89BD975B3B%7D>
• When a force is applied
in nature, a reaction
force occurs at the same
time.
• When you jump on a
trampoline you exert a
downward force at the
same time as the
trampoline exerts an
upward force on you.
How do action & reaction make you
move?
• Even though the forces are equal when you are
walking, they are acting on objects that have
different masses.
• Earth has more mass than you do; thus, their net
force is not equal.
• Unequal net forces determine the direction you
move.
<http://www.qca.org.uk/libraryAss
ets/images/walking(1).jpg>
What is rocket propulsion?
• In a rocket engine, burning
fuel produces hot gases.
• The rocket engine applies
a force on the gases &
causes them to escape out
of the back of the rocket.
• By Newton’s third law, the
gases apply a reaction force
on the rocket & push it in
the opposite direction.
<http://exploration.grc.nasa.gov/educati
on/rocket/Images/newton3r.gif>
• How many different
action/reaction pairs
can you identify
from this NASA
poster?
• List them.
<http://swift.sonoma.edu/education/
newton/newton_3/newpost3.jpg>
Momentum
• A moving object has a property called
momentum which is related to how much force
is needed to change an object’s motion.
• The momentum of an object is the product of
its mass & its velocity. p represents momentum
• Momentum (kg∙m/s)=mass (kg) X velocity(m/s)
or p=mv.
• Two cars can have the same velocity but the one
with greater mass has a larger momentum.
Momentum
• P=mv
• What is the momentum
of a bicycle with a mass
of 18 kg traveling at 20
m/s?
<http://www.skiepic.com/amsterdam_bicycles/ps0b_amsterda
m_bicycle_cell.jpg>
Momentum
<http://www.skiepic.com/amsterdam_bicycles/ps0b_amsterda
m_bicycle_cell.jpg>
• P=mv
• What is the momentum
of a bicycle with a mass
of 18 kg traveling at 20
m/s?
• p=(18 kg) X (20 m/s)
• p=360 kg∙m/s
• The bicycle’s momentum
is 360 kg∙m/s.
How are force & momentum related?
• Recall that acceleration is the difference between
final & initial velocity, divided by the time.
• Also, net force on an object is its mass times its
acceleration.
• Combining these two relationships gives the
following equation: F=(mvf – mvi)/ t or
Force = change in momentum/ time
How are force & momentum related?
• When you catch a ball,
your hand applies a force
on the ball that stops it.
• The force your hand
exerts on the ball & the
force the ball exerts on
your hand are equal.
• The force depends on
the mass & initial
velocity of the ball &
how long it takes to stop.
• Final velocity = zero.
<http://pro.corbis.com/images/4216083561.jpg>
What is the law of conservation of
momentum?
• Momentum can be
passed from one object
to another.
• When a cue ball hits a
group of balls that are
motionless, the cue ball
slows down and the
other balls move.
• The momentum lost
equals the momentum
gained.
<http://farm1.static.flickr.com/>
What happens when objects collide?
• In a game of pool, suppose one ball is moving
in one direction & another ball moving the same
direction strikes it from behind.
• The ball that is struck will continue to move in
the same direction, but more quickly.
• The striking ball has given it more momentum
in the same direction.
Meters of Motion, a watercolor by Champaign-Urbana artist, Billy Morrow Jackson, is the basis for
the poster announcing the 20th International Congress of Theoretical and Applied Mechanics,
held in Chicago in August of 2000.