Science 111

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Science 111

• Chapter 2
• Newtons Laws of Motion

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Isaac Newton

• Isaac Newton continued Galileos study of motion.
• Brilliant conclusions.
• Summarized in three laws of motion.

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Newtons First Law of Motion

• Every object continues in a state of rest, or in
  a state of uniform motion in a straight line at
  constant speed, unless it is compelled to change
  that state by forces exerted upon it.
• Newtons First Law is a summary of the results
  obtained by Galileo.

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Question A ball is being whirled around by a
string. If the string suddenly breaks (or is let
go), what direction will the ball travel A, B,
or C? (Neglect gravity)
A
B
C
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Answer Path B

• While attached to the string, the ball is forced
  to follow a curved path.
• But once the string is gone, no force is exerted
  and (law of inertia) it follows a straight-line
  path B.

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Question A ball at the end of a string swings
back and forth in pendulum motion. Right when it
reaches its lowest point, the string is cut.
Which path will the ball follow.
A
B
C
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Answer B

• When the string is cut, the ball is moving
  horizontally.
• After the string is cut, there are no forces
  horizontally so the ball continues horizontally
  at constant speed.
• But there is the force of gravity acting
  downwards, (continued next page)

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Answer continued

• The downward gravitational force causes the ball
  to accelerate downwards.
• The ball gains downward speed.
• The combination of constant horizontal speed and
  downward increasing speed produces a curved path
  (a parabola).
• This is most closely matched by path B.

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Chapter 2 Exercise 5

• Before the time of Galileo and Newton, it was
  thought by many learned scholars that a stone
  dropped from the top of a tall mast on a moving
  ship would fall vertically and hit the deck
  behind the mast by a distance equal to how far
  the ship had moved forward while the stone was
  falling. In light of your understanding of
  Newtons laws, what do you think about this idea?

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Related Question

• Question To hit a target, should a bomber
  airplane release its bomb before, when, or after
  it passes over the target?

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Answer to Ch.2 Ex. 5

• Neglecting air-resistance, the stone will fall
  down staying adjacent to the mast. It does not
  get left behind.
• What happens when you drop a penny while in an
  airplane going hundreds of miles per hour? Does
  it shoot backwards through the plane? No, it
  seems to fall normally.

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Ch. 2 Ex. 5 answer continued

• The dropped objects had a forward speed and keep
  that forward speed when released.
• They gain downward speed as they fall but
  maintain their horizontal speed, keeping up with
  the boat or plane.
• So, have you decided when the bomber should drop
  the bomb?

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Answer to bomber question

• The bomber should release the bomb before it
  passes over the target.
• The bomb and plane will both continue forward.
• The bomb will appear to be falling straight down
  beneath the plane to an observer in the plane.

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Demonstration??

• If Im running across the room towards a spot on
  the floor holding a penny and I want to release
  the penny so it hits that spot, I need to release
  before I reach the spot.
• If I release when Im at or beyond the spot, the
  penny will continue to move forward and land
  beyond the spot.

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Sec. 2.2 Newtons Second Law

• Newtons second law of motion is
• The acceleration produced by a net force on an
  object is directly proportional to the net force,
  is in the same direction as the net force, and is
  inversely proportional to the mass of the object.
• This is conveniently expressed as an equation
• Acceleration (net force) / mass or
• a F/m or F ma

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a F/m

• F represents the net (or total) force acting on
  the object ( ?F).
• m is the mass of the object.
• a is the acceleration.
• a is directly proportional to F and inversely
  proportional to m.
• a will have the same direction as F.

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F ma

• Forces cause accelerations, greater forces will
  cause greater accelerations.
• m is the mass or inertia, greater mass, for the
  same force, will mean less acceleration.

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Acceleration

• Acceleration is the change in motion.
• An object can be moving northward while feeling
  an eastward force and hence having an eastward
  acceleration.
• It will continue moving north but also gain some
  eastward velocity. It will curve and be heading
  northeast.

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Free Fall

• Free fall is when the only force acting on an
  object is gravity.
• Examples
• A falling skydiver (neglecting air resistance).
• An asteroid flying through the solar system.
• The space station orbiting the Earth.

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Free fall is rare

• None of my free fall examples have only gravity
  acting.
• Skydiver will feel air resistance forces.
• Asteroid will feel forces from solar wind,
  magnetic fields, and other things.
• Space station experiences some air resistance.

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Free fall acceleration

• Okay, free fall is an idealized situation, but
  still useful.
• Objects in free fall near the Earths surface all
  have a downward acceleration of g 10 m/s2.

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Acceleration due to Gravity

• Why do all objects (near the Earths surface in
  free fall) feel this same acceleration?
• Galileo first discovered this is true, but why is
  it true?

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Why always g 10 m/s2?

• Objects with greater mass feel a greater force
  but also have more inertia.
• More force and more mass result in the same
  acceleration.

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Question

• A 1-kg rock is thrown at 10 m/s straight upward.
  Neglecting air resistance, what is the net force
  that acts on it when it is half way to the top of
  its path?

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Answer

• Because we neglect air resistance, the only force
  exerted on the 1-kg rock is simply the force of
  gravity mg.
• Thats mg (1 kg)(9.8 m/s2) 9.8 newtons.
• Its the same answer no matter where the rock is
  along the trajectory and no matter what speed
  its moving.
• Recall, a 1-kg object always weighs 9.8N.

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Additional Comments

• The velocity vector changes during the motion,
  first upward then downward. With decreasing
  speeds than increasing.
• The net force is always 9.8 newtons downward
  during this motion.
• The acceleration is always 9.8 m/s2 downward
  during this motion.

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Still more comments

• If the rock had had a mass of 2 kg, the force
  throughout the trajectory would have been 19.6
  newtons, the acceleration would still have been
  9.8 m/s2.
• Even when the rock is momentarily still at the
  top of the trajectory, the gravitational force is
  still acting and it is still accelerating.

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Air-resistance

• Falling objects that feel an air-resistance force
  will not be in free fall.
• The strength of the air-resistance force acting
  on a moving object depends on
• The shape of the object.
• The speed at which the object is moving through
  the air.

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Falling with Air Resistance

• Imagine an object falling from a great height.
• It accelerates downwards due to the weight force
  acting on it.
• Faster and faster it falls.
• Air-resistance will act upward on it.
• Net force will still be downward but less.

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Terminal Speed

• Still accelerating downward.
• Air-resistance force grows larger as speed
  increases.
• Eventually, weight down air-resistance up, zero
  net force.
• Will then fall at constant speed.
• Called terminal speed.

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Terminal speeds vary

• The air-resistance (or drag) force increases
  with speed.
• The greater the weight of the object, the faster
  it has to move for air-resistance to balance the
  weight.
• A ping-pong ball has a much lower terminal speed
  than a golf ball.

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Heavy and light parachutists

• The heavy gal will have the greater terminal
  speed.
• They both have net force zero acting - but that
  only means they move with constant speed, not
  that they have the same speed.

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Weight and Shape

• A piece of paper will have a lower terminal speed
  than the same paper crumpled into a tight ball.
• The air-resistance force at terminal speed
  depends on both weight and shape.
• Objects with large surface areas will have more
  air resistance and lower terminal speeds.

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Question

• A woman jumps out of a plane.
• She falls faster and faster through the air, her
  acceleration
• (a) increases
• (b) decreases
• (c) remains the same

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Answer (b) decreases

• Decreases? But her speed is getting faster and
  faster!
• Yes, she is still accelerating downwards, but she
  is not gaining speed as quickly as before, the
  acceleration is less.
• The air-resistance increases as she speeds up,
  less net force, less acceleration.

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Skydiver, sample numbers

• Time Falling Speed
• T 0 s v 0 m/s
• T 1 s v 10 m/s
• T 2 s v 19 m/s
• T 3 s v 26 m/s
• T 4 s v 30 m/s
• T 5 s v 31 m/s
• Speed increases

• Acceleration
• a 10 m/s/s
• a 9 m/s/s
• a 7 m/s/s
• a 4 m/s/s
• a 1 m/s/s
• Acceleration decreases

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Comments

• If there had been no air-resistance, the fall
  would have been at the constant acceleration of g
  9.8 m/s2, even after she opens her parachute!
• With air, the mathematics of the fall can be
  written out using Newtons 2nd law

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Math Comments

• Falling with air resistance mathematically
• a Fnet/m (mg - R)/m g - R/m
• R is the air-resistance force
• Downward is the positive direction.
• If R0, then ag.
• As R increases, a decreases.
• When Rmg, a0, terminal speed.

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Opening the Chute

• When a skydiver opens their chute, the R jumps to
  a much higher value.
• The net force will briefly be upward, upward
  acceleration.
• She will still be falling downward but with
  decreasing speed.
• Speed slows until new terminal speed reached.

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Sec. 2.3,2.4 Newtons Third Law

• Newtons Third Law of Motion
• Whenever one object exerts a force on a second
  object, the second object exerts an equal and
  opposite force on the first.
• Or, in its more infamous form,
• For every action there is an equal but opposite
  reaction.

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Infamous?

• The action-reaction statement is very often
  misused.
• People treat it like it means retaliation.
• If you do that action, you are going to provoke
  the inevitable reaction.
• Thats not how the law is meant at all.

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The Real Meaning

• Forces always affect two objects.
• Both feel the force.
• The same amount of force, at the exact same time,
  but in opposite directions.

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Newtons Third Law

• If I push on the wall, the wall pushes on me!
• Yes, I can push on the wall, but does it really
  push on me?

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Jeff vs. the Wall

• Floating in outer space, my push on the wall
  would cause the wall to fly away.
• Its push would cause me to fly the opposite
  direction.
• The force affects us both.

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Still dont believe it?

• What if Im just leaning on the wall, not
  actively pushing?
• Okay, I am still exerting a force on the wall, if
  it was on wheels or something my leaning could
  push it away from me.
• The third law claims that the wall must also be
  exerting a force on me.

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Lean on me

• The wall is exerting a force.
• Imagine I was leaning against you instead of the
  wall, you would have to exert a force to hold me
  up, the wall must also have been exerting a force.

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Every force affects two objects

• Another way of stating Newtons second law is
  that every force affects two objects.
• They both feel that force, the same magnitude of
  force, but in opposite directions.

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One force, two objects

• So, instead of thinking of it as two forces that
  happen to be equal and opposite
• think of it as a single force affecting two
  objects.
• All forces involve two bodies, they are both
  affected by the force at the same time, with the
  same strength, but in opposite directions.

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What is the reaction force?

• Bat hitting a ball.
• Ball hitting a window.
• Friction with ground slowing a sliding crate.
• Rocket motor pushing exhaust downwards.
• Balloon pushing air out of stem.

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• Bat hitting a ball. Ball hitting bat.
• Ball hitting a window. Window hitting (and
  slowing) the ball.
• Friction with ground slowing a sliding crate.
  Friction with crate pushing the ground (imagine
  sliding on a rug with the rug getting bunched
  up).
• Rocket motor pushing exhaust downwards. Exhaust
  pushing the rocket upwards.
• Balloon pushing air out of stem. Air pushing
  balloon forward (its a rocket!).

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Section 2.5 Vectors

• A vector is something with both a magnitude and a
  direction.
• Anything that, to be fully specified, requires
  giving both an amount and a direction, is a
  vector quantity.
• Things requiring only a single value are called
  scalars.
• See chapter 1 lecture notes.

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Examples of Vectors

• Forces are vectors.
• Velocities are vectors.
• Accelerations are vectors.
• Directions on how to get somewhere are vectors.
• Electric fields are vectors.

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Examples of non-vectors scalars

• Temperature
• Mass
• Height
• Volume
• Speed
• Age

These are all things that can be described using
a single number (scalar), usually with some units.
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Question

• A heavy truck collides head-on with a car
  weighing only half as much.
• Which vehicle feels the greater force? How much
  greater?

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Answer

• Newtons Third Law!
• They feel the same force.
• It doesnt matter if one is bigger.
• It doesnt matter whether the collision was
  head-on.

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Question

• A cannon fires out a cannonball.
• How does the recoil of the cannon compare to the
  speed of the cannonball?

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Answer

• This was a trick question.
• First, the force acting on the cannonball due to
  the cannon was equal (but opposite) to the force
  acting of the ball on the cannon.
• There were also forces of the cannon on
  gases/smoke/debris, and equal reactions of them
  on the cannon. (For simplicity, well generally
  ignore these extra interactions.)

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Cannonball Answer (cont.)

• The forces are the same magnitude, but the
  accelerations and velocities they cause will be
  different.
• Because the cannon is so much more massive, its
  recoil speed will be much less than the speed of
  the fired cannonball.
• (Newtons second law)

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Classic Puzzle

• If the horse pulls on the carriage with exactly
  the same force that the carriage pulls on the
  horse, how can horse and carriage move?

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Same Force, Different Object

• Yes, the horse is pulling on the carriage.
• Thats why the carriage moves forward!
• Yes, the carriage is pulling back on the horse.
• But the horse is inducing a forward push from the
  ground by pushing on it.
• The forward force from the ground is more than
  the backward force from the carriage and the net
  forward force explains the horses movement.
• End chapter 2. Questions about the exam?