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Newtons Laws

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Title: Newtons Laws


1
Newtons Laws
  • The Study of Dynamics

2
Isaac Newton
  • Arguably the greatest scientific genius ever.
  • Came up with 3 Laws of Motion to explain the
    observations and analyses of Galileo and Johannes
    Kepler.
  • Discovered that white light was composed of many
    colors all mixed together.
  • Invented new mathematical techniques such as
    calculus and binomial expansion theorem in his
    study of physics.
  • Published his Laws in 1687 in the book
    Mathematical Principles of Natural Philosophy.

3
What is Force?
  • A force is a push or pull on an object.
  • Forces cause an object to accelerate
  • To speed up
  • To slow down
  • To change direction

4
Newtons First Law
  • A body in motion stays in motion at constant
    velocity and a body at rest stays at rest unless
    acted upon by a net external force.
  • This law is commonly referred to as the Law of
    Inertia.

5
The First Law is Counterintuitive
Aristotle firmly believed this. But Physics B
students know better!
6
Implications of Newtons 1st Law
  • If there is zero net force on a body, it cannot
    accelerate, and therefore must move at constant
    velocity, which means
  • it cannot turn,
  • it cannot speed up,
  • it cannot slow down.

7
What is Zero Net Force?
Physics
A book rests on a table.
Even though there are forces on the book, they
are balanced. Therefore, there is no net force on
the book. SF 0
8
Diagrams
  • Draw a force diagram and a free body diagram for
    a book sitting on a table.

9
Sample Problem
  • A monkey hangs by its tail from a tree branch.
    Draw a force diagram representing all forces on
    the monkey

10
Sample Problem
  • Now the monkey hangs by both hands from two
    vines. Each of the monkeys arms are at a 45o
    from the vertical. Draw a force diagram
    representing all forces on the monkey.

11
Mass and Inertia
  • Chemists like to define mass as the amount of
    stuff or matter a substance has.
  • Physicists define mass as inertia, which is the
    ability of a body to resist acceleration by a net
    force.
  • Dr Julius Sumner Miller

12
Sample Problem
  • A heavy block hangs from a string attached to a
    rod. An identical string hangs down from the
    bottom of the block. Which string breaks
  • when the lower string is pulled with a slowly
    increasing force?
  • when the lower string is pulled with a quick jerk?

Top string breaks due to its greater force.
Bottom string breaks because block has lots of
inertia and resists acceleration. Pulling force
doesnt reach top string.
13
Helicopters, Cafeterias, Airplanes and Busses
  • Can a helicopter simply take off and let the
    earth bring its destination to it?
  • Can you jump in the hall and let the cafeteria
    come to you?
  • If luggage falls out of the overhead on the
    airplane wont it kill you?
  • If you toss a ball up in the bus, will it hit the
    people in the back?
  • Does a fly on the bus crash into the back when
    the bus takes off?

14
Newtons Second Law
  • A body accelerates when acted upon by a net
    external force.
  • The acceleration is proportional to the net force
    and is in the direction which the net force acts.

15
Newtons Second Law
  • ?F ma
  • where ?F is the net force measured in Newtons (N)
  • m is mass (kg)
  • a is acceleration (m/s2)

16
Units of force
  • Newton (SI system)
  • 1 N 1 kg m /s2
  • 1 N is the force required to accelerate a 1 kg
    mass at a rate of 1 m/s2
  • Pound (British system)
  • 1 lb 1 slug ft /s2

17
Working 2nd Law Problems
  • Draw a force or free body diagram.
  • Set up 2nd Law equations in each dimension.
  • SFx max and/or SFy may
  • Identify numerical data.
  • x-problem and/or y-problem
  • Substitute numbers into equations.
  • plug-n-chug
  • Solve the equations.

18
Sample Problem
  • In a grocery store, you push a 14.5-kg cart with
    a force of 12.0 N. If the cart starts at rest,
    how far does it move in 3.00 seconds?

19
Sample Problem
  • A catcher stops a 92 mph pitch in his glove,
    bringing it to rest in 0.15 m. If the force
    exerted by the catcher is 803 N, what is the mass
    of the ball?

20
Sample Problem
  • A 747 jetliner lands and begins to slow to a stop
    as it moves along the runway. If its mass is 3.50
    x 105 kg, its speed is 27.0 m/s, and the net
    braking force is 4.30 x 105 N
  • a) what is its speed 7.50 s later?
  • b) How far has it traveled in this time?

21
Newtons Third Law
  • For every action there exists an equal and
    opposite reaction.
  • If A exerts a force F on B, then B exerts a force
    of -F on A.

22
Examples of Newtons 3rd Law
23
Sample Problem
  • You rest an empty glass on a table.
  • a) How many forces act upon the glass?
  • b) Identify these forces with a free body
    diagram.
  • c) Are these forces equal and opposite?
  • d) Are these forces an action-reaction pair?

24
Sample Problem (similar to 17)
  • A force of magnitude 7.50 N pushes three boxes
    with masses m1 1.30 kg, m2 3.20 kg, and m3
    4.90 kg as shown. Find the contact force between
    (a) boxes 1 and 2 and (b) between boxes 2 and 3.

25
Newtons 2nd Law in 2-D
  • The situation is more complicated when forces act
    in more than one dimension.
  • You must still identify all forces and draw your
    force diagram.
  • You then resolve your problem into an x-problem
    and a y-problem (remember projectile motion????).

26
Forces in 2-D
27
Forces in 2-D
28
Forces in 2-D
29
Forces in 2-D
30
Forces in 2-D
31
Sample Problem
  • A surfer hangs ten, and accelerates down the
    sloping face of a wave. If the surfers
    acceleration is 3.50 m/s2 and friction can be
    ignored, what is the angle at which the face of
    the wave is inclined above the horizontal?

32
Sample Problem
  • How long will it take a 1.0 kg block initially at
    rest to slide down a frictionless 20.0 m long
    ramp that is at a 15o angle with the horizontal?

33
Sample Problem
  • An object acted on by three forces moves with
    constant velocity. One force acting on the object
    is in the positive x direction and has a
    magnitude of 6.5 N a second force has a
    magnitude of 4.4 N and points in the negative y
    direction. Find the direction and magnitude of
    the third force acting on the object.

34
Mass and Weight
  • Many people think mass and weight are the same
    thing. They are not.
  • Mass is inertia, or resistance to acceleration.
  • Weight can be defined as the force due to
    gravitation attraction.
  • W mg

35
Sample Problem
  • A man weighs 150 pounds on earth at sea level.
    Calculate his
  • a) mass in kg.
  • b) weight in Newtons.

36
Apparent weight
  • If an object subject to gravity is not in free
    fall, then there must be a reaction force to act
    in opposition to gravity.
  • We sometimes refer to this reaction force as
    apparent weight.

37
Elevator rides
  • When you are in an elevator, your actual weight
    (mg) never changes.
  • You feel lighter or heavier during the ride
    because your apparent weight increases when you
    are accelerating up, decreases when you are
    accelerating down, and is equal to your weight
    when you are not accelerating at all.

38
Going Up?
39
Going Down?
40
Sample Problem
  • An 85-kg person is standing on a bathroom scale
    in an elevator. What is the persons apparent
    weight
  • a) when the elevator accelerates upward at 2.0
    m/s2?
  • b) when the elevator is moving at constant
    velocity between floors?
  • c) when the elevator begins to slow at the top
    floor at 2.0 m/s2?

41
Sample Problem
  • A 5-kg salmon is hanging from a fish scale in an
    elevator. What is the salmons apparent weight
    when the elevator is
  • a) at rest?
  • b) moving upward and slowing at 3.2 m/s2?
  • c) moving downward and speeding up at 3.2 m/s2?
  • d) moving upward and speeding up at 3.2 m/s2?

42
Announcements 12/7/2009
43
Normal force
  • The normal force is a force that keeps one object
    from penetrating into another object.
  • The normal force is always perpendicular a
    surface.
  • The normal exactly cancels out the components of
    all applied forces that are perpendicular to a
    surface.

44
Normal force on flat surface
  • The normal force is equal to the weight of an
    object for objects resting on horizontal
    surfaces.
  • N W mg

45
Normal force on ramp
  • The normal force is perpendicular to angled ramps
    as well. Its always equal to the component of
    weight perpendicular to the surface.

N mgcos?
46
Normal force not associated with weight.
  • A normal force can exist that is totally
    unrelated to the weight of an object.

N applied force
47
The normal force most often equals the weight of
an object
48
but this is by no means always the case!
49
Draw a free body diagram for the skier.
50
Normal force is perpendicular to the surface.
51
Gravitational force is straight down toward the
center of the earth.
W
52
Free body diagram contains only two forces.
N
W
53
Sample problem
  • A 5.0-kg bag of potatoes sits on the bottom of a
    stationary shopping cart. Sketch a free-body
    diagram for the bag of potatoes. Now suppose the
    cart moves with a constant velocity. How does
    this affect the free-body diagram?

54
Sample problem
  • Find the normal force exerted on a 2.5-kg book
    resting on a surface inclined at 28o above the
    horizontal.
  • If the angle of the incline is reduced, do you
    expect the normal force to increase, decrease, or
    stay the same?

55
Sample problem
  • A gardener mows a lawn with an old-fashioned push
    mower. The handle of the mower makes an angle of
    320 with the surface of the lawn. If a 249 N
    force is applied along the handle of the 21-kg
    mower, what is the normal force exerted by the
    lawn on the mower?

56
Sample problem
  • Larry pushes a 200 kg block on a frictionless
    floor at a 45o angle below the horizontal with a
    force of 150 N while Moe pulls the same block
    horizontally with a force of 120 N.
  • a) Draw a free body diagram.
  • b) What is the acceleration of the block?
  • c) What is the normal force exerted on the block?
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