Forces by zhangyun

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									Forces and Newton’s
        Laws




 Remnants of supernova 1987A, a
    cosmic display of forces
• For millennia, thinkers around the
  world sought to incorporate the idea of
  forces into a complete physical
  description of motion:
          Historical
         Perspectives
• Circa 350 BCE: Aristotle proposes that
  the “natural” state of an object is
  stationary
• 1553: Galileo Galilei says that an
  objects retain their velocity unless
  acted upon by a force
• 1679: Isaac Newton incorporates
  Galileo’s ideas into his Laws of Motion
     Falling Apples or
       Pure Genius?
• Isaac Newton was probably one   of the 3
  smartest individuals in human   history
  (at least mathematically)
• When he encountered a problem   he
  couldn’t solve with current
  mathematical techniques, he’d   invent
  new branches of math
   Unification, Part 1
• Newton’s work was very significant, as
  it represented one of the first
  attempts to unify natural phenomena
• Falling apples, rocks, and even the
  motion of planets could all be
  explained with one simple idea
• In a sense, this demystified nature
  Interesting Tid-Bits
• Unfortunately, his social skills
  weren’t on par with his intellect…
• He was a deeply religious individual
• After publishing Principia and Opticks,
  he spent a large portion of life
  working on Alchemy
• His autopsy revealed large amounts of
  mercury in his body, which might
  explain his eccentricity
      Newton’s 1st Law
• An object moving at constant velocity
  will stay that way unless acted upon by
  an outside force
• Objects at rest will remain at rest
  unless acted upon by a force
• In other words, objects are lazy…
                 Examples?
•   Hoop/ring
•   Penny Drop
•   Egg/Beaker
•   F4 Videos
• Why did Aristotle get it backwards?

• It’s likely that he didn’t think to
  include how friction and air resistance
  affect motion

• We’ve seen the clarity of Newton’s 1st
  Law in the absence of air resistance
 How Lazy Are Objects?
• An objects resistance to a change in
  motion is called inertia
• We can also describe an object’s
  inertia as its laziness
• Mass is actually a measure of an
  object’s inertia
Rank the inertia of the following
in increasing order: a car, bug,
         you, and NCSSM
•   1.   NCSSM, car, you, bug
•   2.   car, NCSSM, you, bug
•   3.   bug, car, you, NCSSM
•   4.   you, NCSSM, bug, car
•   5.   bug, you, car, NCSSM
Imagine sitting in a car at rest. If
you throw a tennis ball in the air, it
  will land back in your hand. What
 will happen if you throw it up, then
             accelerate?
• 1. It will land in front of you

• 2. It will land back in your hand

• 3. It will hit you in the face
Which car accident would cause a
  person to get thrown through
       their windshield?
• 1. A car moving at high speeds hits
  something in front of it
• 2. A car at rest is rear ended by a
  fast moving car
• 3. A car moving at high speeds is hit
  by a car behind going a few miles/hour
  faster
• 4. A car loses control and spins out
  If the sun were to disappear,
   what would happen to Earth?

• 1. It would continue moving in its
  normal orbit
• 2. It would move off in a straight line
• 3. It would spiral in towards the sun’s
  previous location
• 4. It would stop
Reference Frames Are Key
• Your reference frame is essentially
  your point of view
• A reference frame is inertial if it
  does not accelerates
Which reference frame is
      not inertial
• 1. A car moving at constant velocity
• 2. A rock, sitting at the edge of a
  cliff
• 3. A car rounding a curve at constant
  speed
• 4. A rock rolling down a hill at
  constant velocity
         Why is this so
           Important?
• Imagine a baby, born on a bus with the
  windows blacked out
• The baby spends its first few years on
  the bus, learning about the world with
  no knowledge of life outside the bus
• How would their ideas of motion
  contrast with ours?
         Types of Forces
•   Gravity
•   Tension
•   Friction
•   The “Normal” Force
•   Electrical and Magnetic Forces
•   Nuclear Forces
         “Net” Forces
• What happens if more than one force
  acts upon an object?
• Forces are vector quantities, so they
  add like any other vectors
• The Net force is simply the vector sum
  of all forces acting upon an object
• An object with a net force of 0 is said
  to be in equilibrium
 Which object is in equilibrium?

• 1. A car accelerates from rest
• 2. A sky diver falls at constant
  velocity
• 3. An object is pulled upon by +200N
  and -300N forces
• 4. An air puck slides across the air
  table with the air supply turned off
      Newton’s 2nd Law
• The Net Force Acting upon an object is
  proportional to the resulting acceleration


• Net Force = mass x acceleration
• Fnet = ma
    Mathematical Notation
•   Fnet = SF
•   a = SF/m
•   (Bold indicates a vector quantity)
•   This law holds for each direction
    (x,y,z)
           Units?
• kg m/s2
• We call these units Newton’s,
  in honor of the man himself
 A 10N forces pulls a 4kg box to the
left, while a 8N force pulls it to the
      right. What is the box’s
            acceleration?
    Free-Body Diagrams
• With all the forces around us,
  computing net force can get complicated
• We use the concept of free-body
  diagrams to deal with this complexity
• A Free Body Diagram, or Force Diagram,
  is simply a picture of object that
  displays all the forces acting upon it
       Rules of Force
          Diagrams
• Forces vectors are drawn from the
  application point of a force
• Most of our diagrams will involve point
  masses (draw your vectors pointing away
  from the COM)
• The length of a force vector indicates
  the magnitude of the force
        Rules, Part 2
• Include forces acting on an object
• Do not include forces produced by an
  object
• Ex: Two skaters initially at rest push
  off of one another. In the diagram for
  skater 1, you would only include the
  force from skater 2
 The Jumbo Jet Revisited
• Fully loaded, a 747 jumbo jet has a
  mass of 300,000kg. Assuming it needs
  1900m of runway to reach a takeoff
  speed of 100m/s, how much force does
  each of 4 engines provide?
• Each engines provides 197kN of force
  (thrust), for a total of 788kN
• Now, let’s think about the impact of
  air resistance
• Imagine that at takeoff (v = 100m/s),
  the plane encounters 450,000N of air
  resistance
• How long will it take the plane to
  reach its cruising speed of 250m/s?
• 133 seconds
A Falling Body (without
    Air Resistance)
       A Hanging Mass
• A rock hangs freely, held up by two
  ropes
  Which is the correct force
diagram for a mass hanging from
    the ceiling by a rope?
 Which is the correct diagram for a
block pushed along a rough surface at
         constant velocity?
Same situation as before, but now the
   object accelerates to the right
          Weighing In
• What causes weight?
• How can weight change while mass
  remains constant?
• It turns out that weight is simply a
  measure of the gravitational force
  acting upon an object


• Weight = mg
         Force Diagram
         Implications
• From now on, indicate an object’s
  weight with mg on your force diagram
       Falling Bodies
         Revisited
• A hammer and a feather both accelerate
  at little g
• Does that mean they experience the same
  gravitational force?
• Definitely not; Earth has to pull
  harder on the hammer to create the same
  acceleration
                 Lift
• The force that keeps a plane in the air
  is called lift. Imagine a plane,
  flying perfectly level at constant
  velocity. What is the magnitude of the
  lift necessary to keep a 300,000kg
  Boeing 747 in the air?

• Lift = 3,000,000 N (up)
         Back to the F4…
•   Useful information
•   Force of wall on the plane = 13.3 MN
•   Force of thrust on the plane = .30 MN
•   Plane mass = 27,000 kg

• Find the plane’s acceleration while in
  contact with the wall (express your
  answer in “g”s)
        Yoda’s Force?
• Yoda has an uncanny ability to make
  things happen, despite his size
• I seem to recall a scene in Star Wars
  where he accelerates a very massive
  object (m = 30,000kg) straight up at a
  rate of 5.0 m/s/s
    In a Galaxy Far, Far
           Away…
• Now, Star Wars does not occur on Earth,
  which means g is not necessarily 10
  m/s/s
• Let’s say Yoda is on a planet where g =
  15 m/s/s (although is sure looks like g
  = 10m/s/s when you watch Star Wars…)
• What force is necessary for Yoda to
  accelerate this massive object (30,000
  kg) upward at 5.0m/s/s?

• Just for comparison, how does this
  force compare to Yoda’s body weight (m
  = 15 kg)?
       The Rising Box…
• Imagine a person with mass 65kg,
  standing on a box
• If the box accelerates upwards at a
  rate of 3 m/s/s, what is the normal
  force of the box acting upon the
  person?
• What would it feel like if you were
  standing on the box?
• What would a scale read?
       Apparent Weight
• Think of a situation in which you feel
  heavier or lighter than normal
• Why do you feel this way?
• In such a situation, your apparent
  weight is more or less than your actual
  weight
• Why?
       Feeling Weight
• The sensation of weight comes from
  normal forces acting upon us
• Don’t believe me? Try standing in an
  elevator in free fall
• At the bottom of a roller coaster loop,
  the rider’s (mass 80kg) seat pushes him
  up with a force of 900N. What is the
  magnitude of the rider’s acceleration?
• a = 1.45 m/s/s (points up)
      Newton’s 3rd Law
• This is likely the most familiar law
• For every action, there exists an equal
  and opposite reaction
• In other words, nature always fights
  back
• Forces always come in pairs
             Examples
• Rockets
• Two Ice Skaters Push One Another
• Rifle Recoil
• 1) In a horse drawn carriage, the horse
  pulls the cart forward. According to
  Newton’s 3rd Law, the car pulls back
  with an equal force. If that’s the
  case, how does the horse or cart move?

• 2) A mack truck and bicycle collide.
  Which experiences the greater force?

• 3) What happens if you use a fire
  extinguisher in space?

• 4) What force actually moves a car
  forward?
       Forces in Space
• An astronaut (m = 120kg with gear)
  working on the ISS needs to push a
  massive object (m = 1500kg) forward
• If he pushes on it with 500N of force,
  what happens
• How can he safely push it forward?
         3 Block Problem
• Imagine three blocks of   different masses on a
  table
• Find the force of block   one on block two
• Find the force of block   two on block one
• Find the force of block   two on block three
• Examine the Atwood’s machine below,
  with m1 = 10kg and m2 = 30kg. If m2
  rests upon a block, what is the normal
  force acting upon it?

• Normal Force = 196N (up)
• Let’s return to the block/pulley
  situation. If block one lies on a
  frictionless surface, what is its
  acceleration? (m1 = 5kg, m2 = 10kg)
• a = 6.5m/s/s (to the right)
• On the diagram below, two blocks are
  connected by a rope. Block 1 has a
  mass of 5kg, while block 2 has a mass
  of 10kg. If block 1 is at rest, sitting
  on a rough surface, what is the
  magnitude of the frictional force
  acting upon block one?
• Friction = 98N, pointing to the left
• A person’s weight is 600N, when
  standing on a normal bathroom scale.
  What would the scale read if this
  person were in the Bryan elevator,
  arriving at the 4th floor (a =
  0.8m/s/s)?

• Normal Force/Apparent Weight   =
  552N(up)
    Tension: The Force
      That Binds Us
• Tension is a very important force
• The magnitude of the tension force in
  the same rope is always equal
• Why?
• Newton’s 3rd…
Pulley Problems
           Variations
• We can ask a variety of questions about
  the previous situation
• If the blocks are stationary or move at
  constant velocity, what is the
  frictional force?
• By how much do they accelerate?
• How much tension exists in the rope?
        Tension in 2D
• Think about the situation below
•   Draw force diagrams for the block
•   Write net force equations
•   Find the tension in rope 1
•   Find the tension in rope 2
• T1 = 173N

• T2 = 87N
    2D Tension, Part 2
• Now imagine a different block,
  suspended from the ceiling by two ropes
• Find the mass of the hanging object

• m = 3.5kg
• Imagine a different box, suspended by
  two different ropes




• Find the magnitude of the tension in
  the second rope, and the angle the rope
  makes w/ the horizontal
• Theta = 21.5 degrees
• T2 = 14.7N

								
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