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Science 111

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Title: Science 111


1
Science 111
  • Chapter 2
  • Newtons Laws of Motion

2
Isaac Newton
  • Isaac Newton continued Galileos study of motion.
  • Brilliant conclusions.
  • Summarized in three laws of motion.

3
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.

4
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
5
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.

6
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
7
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)

8
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.

9
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?

10
Related Question
  • Question To hit a target, should a bomber
    airplane release its bomb before, when, or after
    it passes over the target?

11
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.

12
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?

13
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.

14
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.

15
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

16
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.

17
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.

18
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.

19
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.

20
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.

21
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.

22
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?

23
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.

24
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?

25
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.

26
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.

27
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.

28
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.

29
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.

30
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.

31
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.

32
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.

33
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.

34
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

35
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.

36
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

37
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

38
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.

39
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.

40
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.

41
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.

42
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.

43
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?

44
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.

45
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.

46
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.

47
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.

48
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.

49
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.

50
  • 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!).

51
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.

52
Examples of Vectors
  • Forces are vectors.
  • Velocities are vectors.
  • Accelerations are vectors.
  • Directions on how to get somewhere are vectors.
  • Electric fields are vectors.

53
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.
54
Question
  • A heavy truck collides head-on with a car
    weighing only half as much.
  • Which vehicle feels the greater force? How much
    greater?

55
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.

56
Question
  • A cannon fires out a cannonball.
  • How does the recoil of the cannon compare to the
    speed of the cannonball?

57
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.)

58
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)

59
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?

60
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?
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