FORCE

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FORCE
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Newtons Laws

• Three Laws of Motion

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Aristotles Motion

• Natural Motion is up or down
• Down for falling objects
• Up for smoke
• Circular for heavenly bodies since without end
• Violent Motion
• Due to imposed forces such as wind pushing a ship
  or someone pulling a cart
• Natural state of motion is rest
• A force is needed to keep something moving

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Aristotles Basic Error

• Friction not understood as a force

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Galileos Motion

• Force is a push or a pull
• Friction is a force that occurs when objects move
  past each other
• Friction due to tiny irregularities
• Only when friction is present is a force required
  to keep something moving

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Galileos Inclined Planes

• Ball rolling downhill speeds up
• Ball rolling uphill slows down
• He asked about ball on smooth level surface
• Concluded it would roll forever in absence of
  friction

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Inertia

• Resistance to change in state of motion
• Galileo concluded all objects have inertia
• Contradicted Aristotles theory of motion
• No force required to keep Earth in motion around
  sun because no friction

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Newton

• Born 1665
• Built on Galileos ideas
• Proposed three laws of motion at age of 23

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Newtons First Law
Ourtesy www.lakeheadu.ca/alumni/ hockey.gif

• Every object continues in its state of rest, or
  of motion in a straight line at constant speed,
  unless compelled to change that state by forces
  exerted on it.
• Also called Law of Inertia things move according
  to their own inertia
• Things keep on doing what they are doing
• Examples Hockey puck on ice, rolling ball, ball
  in space, person sitting on couch

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Mass

• Amount of inertia depends on amount of massor
  amount of material (number and kind of atoms)
• Measured in kilograms
• Question Which has more mass, a kilogram of
  lead or a kilogram of feathers?
• Mass vs. Volume volume is how much space
  something occupies

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Experiencing Inertia

• Inertia is resistance to shaking
• Which is easier to shake, a pen or a person?
• Why is it so hard to stop a heavy boat?

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Inertia in a Car

• Discuss three examples of inertia in a car

• Car hitting a wall
• Car hit from behind by a truck
• Car going around a corner

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Newtons Second Law

• Law of Acceleration
• The acceleration produced by a net force on an
  object is directly proportional to the magnitude
  of the net force, and is inversely proportional
  to the mass of the body.
• Acceleration net force mass
• F ma
• Acceleration is in direction of net force

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Units

• F ma
• Unit of force is the Newton (N)
• 1 N 1 kg m/s2

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Net Force

• Net Force means sum of all forces acting
• Sum is Vector sum

F2
F1
Resultant force
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Understanding the Second Law
Force

• The cause of acceleration is
• _________ resists acceleration
• The greater the force, the ________ the
• ______________
• The greater the mass, the _________ the
  acceleration.

Mass or inertia
greater
acceleration
less
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F ma is Three Equations

• F and a are vectors
• So F ma equation is really three
• SFx max SFy may SFz maz

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Examples

• What force is required to accelerate a 1000 kg
  car at 2.0 m/s2 ?
• Answer F ma 1000 kg x 2.0 m/s2 2000
  N.
• What is the acceleration of a 145 g baseball
  thrown with a force of 20.0 N?
• a F/m 20.0 N/0.145kg 138 m/s2

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F ma Example m unknown

• An astronaut puts a 500.0 N force on an object of
  unknown mass producing an accelerations of 0.462
  m/s2 . What was the mass?
• M F/a 500.0N/0.462 m/s2 1082 Kg 1.08 x
  103 Kg

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Net force example

• If four teams are playing tug of war (imagine a
  rope that looks like a cross, with the flag tied
  in the middle). Each team is 90 from each
  other. Team A pulls with an overall force of 350
  N to the North, Team B pulls with an overall
  force of 270 N to the South, Team C pulls with an
  overall force of 150 N to the East and Team D
  pulls with an overall force of 250 N to the West.
  If the flag in the middle has a mass of .25 kg,
  what is the magnitude and direction of its
  acceleration?

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Putting it all together.

• Calculate the change in force of a car that has a
  mass of 2500 kg if it goes from 45 m/s to rest in
  7 seconds at a stop sign, then accelerates up to
  65 m/s in 5 seconds.

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a vf-vi/t or a F/m

• a1 0-45/7 -6.42 m/s2
• a2 65-0/5 13 m/s2
• The difference between them is 19.42 m/s2.
• F m x a 2500 kg x 19.42 m/s2
• 48550 N difference between the two
  accelerations

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Newtons Third Law

• Forces always come in pairs
• Two forces on different objects
• Every action has an equal and opposite reaction
• Whenever one object exerts a force on a second
  object, the second exerts an equal and opposite
  force on the first
• Example hammer hits nail

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Example pushing on wall

• What are the forces when you push on a wall?
• You exert force on wall
• You accelerate in the opposite direction
• Wall must have exerted a force on you in the
  direction you accelerated (by 2nd Law)

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Example person walking

• Foot exerts force backward on ground
• Ground exerts force forward on foot

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Example Throwing ball

• Pitcher exerts force on ball
• Ball exerts equal and opposite force on pitcher
• Why doesnt pitcher move?

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Example Rocket

• Rocket engine exerts rearward force on gas
  molecules
• Molecules exert forward force on rocket.

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Book on Table

• The mass of the book is one kg. What is the
  force (magnitude and direction) on the book?
• 9.8 N upward

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Really putting it all together

• Calculate the Force necessary to launch a
  cannonball with a mass of 15 kg if it is fired at
  an angle of 43 if it hits a target 210 m away in
  6.3 seconds?
• What can we solve in this problem?
• What equations do we need to solve this problem?
  

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What we need to solve the force

• Vx dx/t 210/6.3 33.3 m/s
• Vf2 Vi2 2 a(d) Vi 0 for this problem
• a Vf2/2d 33.32 / 2(210) 2.64 m/s2
• Force of the cannon F m(a)
• F 15 kg (2.64 m/s2) 39.6 N

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The Horse and the Cart Problem

• If there is always an equal an opposite reaction,
  how does anything move? For example, if you have
  a horse and a cart, how does the horse pull the
  cart?

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The Horse and Cart Problem.

• These appear to be the equalizing forces.

A - B B - C C -D ABCD no acc!
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The Horse and Cart Problem.
Because it is accelerating, the force the horse
exerts on the cart has increased. By Newton's
third law, the force of the cart on the horse has
increased by the same amount. But the horse is
also accelerating, so the friction of the ground
on its hooves must be larger than the force the
cart exerts on the horse. The friction between
hooves and ground is static (not sliding or
rolling) friction, and can increase as necessary
(up to a limit, when slipping might occur, as on
a slippery mud surface or loose gravel). So,
when accelerating, we still have B -C, by
Newton's third law, but DgtC and BgtA, so DgtA.
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More Examples

• Can you think of some more examples of Newtons
  Third Law in Action?
• Imagine an astronaut floating in deep space, with
  only his spacesuit. Is there any way for him to
  move himself back to earth?

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Mass vs. Weight

• Mass is intrinsic property of any object
• Weight measures gravitational force on an object,
  usually due to a planet
• Weight depends on location of object
• Question 1 How does mass of a rock compare when
  on Earth and on moon?
• Question 2 How does its weight compare?

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Review Mass vs. Weight

• What is mass?
• Answer quantity of matter in something or a
  measure of its inertia
• What is weight?
• Answer Force on a body due to gravity

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Weight of 1 Kilogram

• 9.8 Newtons
• About 2.2 pounds
• Compare the weight of 1 kg nails with 1 kg
  styrofoam
• Answer Same

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Weight Examples

• What does a 70 kg person weigh?
• Weight mass x g(acceleration due to gravity)
• W mg 70 kg x 9.80 N/m2 686 N
• An object weighs 9800 N on Earth. What is its
  mass?
• m W/g 9800 / 9.8 m/s2 1000 kg

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Atwoods Lab

• You have 25 washers on your lab setup, if you
  have a unbalanced force, you will have
  acceleration. You will be using the stopwatch
  function of your data collector.
• Make a chart to record mass, time, acceleration
  and force.
• Put all washers on one side, raise that side to
  the top, then release it timing how long it takes
  to reach the bottom. Record this time.
• The mass of one washer is 16 g. It is the
  difference in mass that causes the acceleration.
  Calculate the difference in mass and record in
  table. 1st mass is 25 x 16, 2nd mass is 23 x
  16, 3rd mass is 21 x 16 etc.
• Calculate the Acceleration 2d/t2 (d 1 m for
  the fall) so a 2/ t2
• Calculate the Net force of the fall and record.
  (F ma)
• Move one washer at a time over to the other side
  and repeat.
• Continue until the machine no longer turns (12 or
  13 trials)

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FRICTION

• Sliding (motion) Static (stationary)

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Sliding Friction

• Often called kinetic friction
• A force opposite to direction of motion
• Due to bumps in surfaces and electric forces

Surface under microscope
Ff
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Kinetic Friction is

• Dependent on nature of the two surfaces
• Directly proportional to the normal force between
  the surfaces
• Normal Force is perpendicular to the surface. If
  it is on a flat surface, it is equal to the
  weight of the object.
• Independent of velocity

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Reducing Friction

• In order to reduce friction we can
• A. Reduce surface area
• B. Reduce weight of object
• C. Change type of friction
• - sliding(the greatest amount)
• - rolling (use wheels to ease friction)
• - fluid ( Eliminate contact by using liquids or
  gases)

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Coefficient of friction mk

• Generally between zero and one
• Based on comparing Friction Force to Normal Force
• Normal Force is always perpendicular to surface
• Calculate from Ff / FN µk
• Can be more than one for special rubber
• Very low for ice, Teflon, lubricated surfaces,
  ball bearings

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Friction Good or Bad

• Mostly undesirable since reduces useful force and
  wastes energy
• Friction produces heat
• Necessary for walking!
• Necessary for braking

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Static Friction

• Force to start something moving
• Usually larger than kinetic friction for same
  surfaces
• Requires force to be exerted
• Before sliding begins, is equal and opposite to
  applied force

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Where are all the forces?

• Block on an inclined plane

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Free Body Diagram Example 1
If the box below accelerates to the right at 1
m/s2 Solve all of the following
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Solution 1

• Fgrav m x g 5 x 9.8 49 N
• Using the angle and the F applied, we can
  calculate the X and Y component of that force.
• Fx 15 sin 45 Fy 15 cos 45
• Fx 10.6 N Fy 10.6 N
• If the force of gravity is 49 N down and the
  applied force is 10.6 N up, then the normal force
  applied is the difference between the two. F
  norm 49-10.6 38.4 N

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Solution 1 cont.

• If the object has an a of 1 m/s2 and a mass of 5
  kg, then it has a net force of 5 N in the X
  direction.
• If the applied force in the X is 10.6 and the net
  is 5, then the force of friction is the
  difference between the two.
• Ffric 10.6-5 5.6 N
• To solve the coefficient of friction we use this
  equation Ff mkFN
• mk Ff/FN 5.6/ 38.4 .145

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Flat pull

• If you pull a 2505 g box with a force of 15 N at
  an angle of 53 to the horizon and the box
  accelerates at 2.0 m/s2 to the right, calculate
  the following
• Fn, Fg, Ff, Fnet, Fapp, Fx, Fy and µ

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Friction Lab

• Put a ramp flat in your lab space. Place two
  photogates relatively close together.
• If the mass of the sled is .040 kg calculate the
  Fnormal (FnFg if on flat surface)
• Now, using your sled car (no wheels) launch the
  car with your rubber band. Make sure that it
  goes through both photo gates (you may have to
  adjust photo gates). Use our acceleration
  procedure from lab and calculate the rate of
  deceleration.
• Calculate Ffric mass of sled x deceleration
• Calculate µ Ff/Fn

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Free body diagram example 2

• Say a box is sitting on 30 slope and is
  frictionless, so the only forces are the normal
  force and gravity. What is the block's
  acceleration down the slope if the mass is 3.0
  kg? What is the normal force?

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Free Body Diagram example 3

• A box is sitting on a 35 inclined plane. It is
  being pulled up the ramp by you with an
  acceleration of 2.5 m/s2. If the box has a mass
  of 25 kg and the force of friction is 3.5 N,
  solve all of the following Fnet, Fnormal,
  Fgravity, Fapplied, and µ.

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• A 50-N applied force (30 degrees to the
  horizontal) accelerates a box across a horizontal
  sheet of ice (see diagram). Glen Brook, Olive N.
  Glenveau, and Warren Peace are discussing the
  problem. Glen suggests that the normal force is
  50 N Olive suggests that the normal force in the
  diagram is 75 N and Warren suggests that the
  normal force is 100 N. While all three answers
  may seem reasonable, only one is correct.
  Indicate which two answers are wrong and explain
  why they are wrong.

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Review Newtons Laws of Motion

• Newtons First Law
• Every object continues in its state of
  rest, or of motion in a straight line at constant
  speed, unless compelled to change that state by
  forces exerted on it.
• Newtons Second Law
• The acceleration produced by a net force
  on an object is directly proportional to the
  magnitude of the net force, and is inversely
  proportional to the mass of the body.
• Newtons Third Law
• Whenever one object exerts a force on a
  second object, the second exerts an equal
  opposite force on the first

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Action- Reaction Lab

• Adjust the smart track (or lab table) to be as
  level as possible(may have to put lab book under)
  put rubber band around one car.
• Squeeze two cars together and attach with the car
  link.
• Position car in middle of track, making sure all
  wheels are on track.
• With a quick upward motion, pull the link
  straight up and out from the cars.
• Describe how the cars move in a data table.
• Start adding marbles to cars and repeat
  procedures above
• Make all these combinations of marbles in cars
• 0,0 0,1 0,2 0,3 1,1 1,2 1,3 2,2 2,3
  3,3
• Sum up the action reaction effect on cars and
  marbles.

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Draw the free body diagram
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Draw the free body diagram, if a .1 m/s2 and
the force you push on the lawnmower is 25 N,
solve for every force you know.


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• Say a box is sitting on 40 slope ramp. If the
  mass is 3.0 kg? What are all the forces acting on
  the box and what is µ?

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• Renee is on Spring Break and pulling her 21-kg
  suitcase through the airport at a constant speed
  of 0.47 m/s. She pulls on the strap with 120 N of
  force at an angle of 38 above the horizontal.
  Determine the normal force and the total
  resistance force (friction and air resistance)
  experienced by the suitcase.

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• For each collection of listed forces, determine
  the vector sum or the net force.
• Set A58 N, right42 N, left98 N, up98 N, down

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• Hector is walking his dog (Fido) around the
  neighborhood. Upon arriving at Fidella's house (a
  friend of Fido's), Fido turns part mule and
  refuses to continue on the walk. Hector yanks on
  the chain with a 67.0 N force at an angle of
  30.0 above the horizontal. Determine the
  horizontal and vertical components of the tension
  force.

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• Helen is parasailing. She sits in a seat harness
  which is attached by a tow rope to a speedboat.
  The rope makes an angle of 51 with the
  horizontal and has a tension of 350 N. Determine
  the horizontal and vertical components of the
  tension force.

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• Jerome and Michael, linebackers for Souths
  varsity football team, delivered a big hit to the
  halfback in last weekends game. Striking the
  halfback simultaneously from different directions
  with the following forces
• FJerome 1230 N at 53FMichael 1450 at 107
• Determine the resultant force applied by Jerome
  and Michael to the halfback. (The directions of
  the two forces are stated as counter-clockwise
  angles of rotation with East.)

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• 2. A box is pulled at a constant speed of 0.40
  m/s across a frictional surface. Perform an
  extensive analysis of the diagram below to
  determine the values for the blanks.

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• Use your understanding of force relationships and
  vector components to fill in the blanks in the
  following diagram and to determine the net force
  and acceleration of the object. (Fnet ma
  Ffrict µFnorm Fgrav mg)

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Friday Problem 1
The 5-kg mass below is moving with a constant
speed of 4 m/s to the right. Use your
understanding of force relationships and vector
components to fill in the blanks in the following
diagram and to determine the net force and
acceleration of the object. (Fnet ma Ffrict
µFnorm Fgrav mg)  

• A 5-kg mass below is moving with a an
  acceleration of 4 m/s2 to the right. The
  coefficient of friction for this surface is .2.
  Use your understanding of force relationships and
  vector components to determine all your forces.
•  

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Friday Problem 2

• You are pushing a 200 kg block up a 20 hill
  with a force of 200 N. If the box moves up the
  hill with a constant speed of 2 m/s, calculate
  all the forces involved and calculate µ.

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Tuesday Problem 1

• 5. The following object is being pulled at a
  constant speed of 2.5 m/s. Use your understanding
  of force relationships and vector components to
  fill in the blanks in the following diagram and
  to determine the net force and acceleration of
  the object. (Fnet ma Ffrict µFnorm Fgrav
  mg)

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• At one moment during a walk around the block,
  there are four forces exerted upon Fido - a 10.0
  kg dog. The forces are
• Fapp 67.0 N at 30.0 above the horizontal
  (rightward and upward)Fnorm 64.5 N, upFfrict
  27.6 N, leftFgrav 98 N, down
• Resolve the applied force (Fapp) into horizontal
  and vertical components, then add the forces up
  as vectors to determine the net force and
  calculate the acceleration.

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• A box is sliding down a ramp at an angle of 47
  to the horizontal. If it is accelerating at 2.5
  m/s2 and has a mass of 150 kg, what is the
  Fnormal, Fnet, Fgravity, Ffric and µ?

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Ramp Problem 1

• Say a box is sitting on 30 slope and is
  frictionless, so the only forces are the normal
  force and gravity. What is the block's
  acceleration down the slope if the mass is 3.0
  kg? What is the normal force?

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Rotation Centripetal Force
Coutesy Space.com

• How to Keep it Straight Without Getting Dizzy

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Rotation

• In addition to side to side (linear) motion,
  rotation plays an important role in physics,
  engineering, and life.
• Name some common phenomena or devices that show
  rotation

Tops, planets, bicycle, car wheels, gears,
pulleys, fans etc
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Speed on a Wheel

• Which horses on a carousel move the fastest,
  inner or outer?

Outer v radius x angular speed v rw
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Mass at the End of a String

• What force must the
• string exert on the mass?
• What is the direction of
• this force?

A force toward the center of the circle
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Centripetal Force

• Any force directed toward the center of a circle
  is called centripetal.
• Centripetal forces have clear causes such as
  tension in a string, gravity, friction etc.
• Some people call centripetal force a
  pseudoforce. (not real)
• They say a real force such as friction provides
  centripetal force.

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How Big is Centripetal Force?

• Fc mv2/r
• The faster the speed the more the force
• The tighter (smaller) the radius the more the
  force
• v2/r is called centripetal acceleration

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Is a mass moving at steady speed in a circle
accelerating?

• Yes. The direction is changing
• What is the direction of this acceleration?

Toward the center of the circle
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Car on a Curve

• When auto rounds corner, sideways acting friction
  between tires and road provides centripetal force
  that holds car on road

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Dont Confuse Inertia With Force

• Tubs inner wall exerts centripetal force on
  clothes, forcing them into circular path
• Water escapes through
• holes because it tends to move by inertia in
  a straight line path

Clothes Washer Photo courtesy HowStuffWorks.com
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How Can Water Stay In The Bucket?

• Bucket swung in a
• vertical circle
• What force pushes on the
• water?

Weight and normal force down
You have to swing the bucket fast enough for the
bucket to fall as fast as the water
There must be a normal force exerted by the
bottom of the bucket on the water, in addition to
gravity
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Centrifugal Force

• The force ON THE PAIL is inward (centripetal)
• The force ON THE STRING is outward (centrifugal)
• If the string broke, which way would the can go?

Tangent to the circle
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Change Your Point of View

• In rest frame of the can there appears to be a
  centrifugal force. This pseudoforce(or
  fictitious force) is a result of rotation

Unlike real forces, centrifugal force is not part
of an interaction
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Book on a Car Seat

• When a car goes around a curve to the left, a
  book slides
• Which way does it slide?
• Why doesnt it keep moving with the car?

There is not enough static friction force to keep
it going in a circle. This friction must provide
the necessary centripetal force.
The explanation in the rotating rest frame is
different. How?
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Roller Coaster Lab- Centripetal Force

• You are dropping the ball from 45, practice
  dropping the steel ball and the plastic ball to
  observe when it gets around the track.
• Attach the photogate and calculate the speed and
  centripetal force of the marble at the top of the
  loop from various distances for both marbles.
  Width of ball .019 m
• Complete the table for both marbles. (as many
  trials as necessary)
• steel .028 kg plastic .004 kg Fc mv2/r
  radius of loop .05 m
• Draw a free body force diagram when the ball is
  at the top of the loop, label all forces. Do the
  following lab to solve for the minimum force
  needed to keep the ball (steel and plastic) on
  the loop.

Mass(kg) Weight(N) Photogate Time (sec) Speed (m/s) Centripetal Force (N) Did the marble stay on track?