Chapter 5. Force and Motion I

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Chapter 5. Force and Motion I

• 5.1. What is Physics?      
• 5.2. Newtonian Mechanics      
• 5.3. Newton's First Law      
• 5.4. Force      
• 5.5. Mass      
• 5.6. Newton's Second Law      
• 5.7. Some Particular Forces     
• 5.8. Newton's Third Law      
• 5.9. Applying Newton's Laws

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What Causes Acceleration?

• Dynamicsthe study of causes of motion. The
  central question in dynamics is What causes a
  body to change its velocity or accelerate as it
  moves?

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Newtonian Mechanics
Newtons laws fail in the following two
circumstances

• 1. When the speed of objects approaches (1 or
  more) the speed of light in vacuum (c 8108
  m/s). In this case we must use Einsteins
  special theory of relativity (1905) .
  
• 2. When the objects under study become very
  small (e.g., electrons, atoms, etc.). In this
  case we must use quantum mechanics (1926).

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Force

• A force is a push or a pull. Force is a vector.
  All forces result from interaction.
• Contact forces forces that arise from the
  physical contact between two objects.
• Noncontact forces forces the two objects exert
  on one another even though they are not touching.

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• External forces include only the forces that the
  environment exerts on the object of interest.
• Internal forces are forces that one part of an
  object exerts on another part of the object.

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Combining Forces
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Principle of superposition for forces

• When two or more forces act on a body, we can
  find their net force or resultant force by adding
  the individual forces as vectors taking direction
  into account.

Note The net force involves the sum of external
forces only (internal forces cancel each other).
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Exercise 1

• The figures that follow show overhead views of
  four situations in which two forces acting on the
  same cart along a frictionless track. Rank the
  situations according to the magnitudes of the net
  force on the cart, greatest first.

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Newtons FIRST LAW
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Newton's First law Consider a body on which no
net force acts. If the body is at rest, it will
remain at rest. If the body is moving, it will
continue to moving with a constant velocity.

• Net force is crucial. Often, several forces act
  simultaneously on a body, and the net force is
  the vector sum of all of them
• An inertial reference frame is the one has zero
  acceleration.
• All newtons laws are valid only in the inertia
  reference frames.

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Mass

• The larger the mass, the harder is to cause its
  motion
• Mass and weight are different concepts

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DEFINITION OF INERTIA AND MASS

• Inertia is the natural tendency of an object to
  remain at rest or in motion at a constant speed
  along a straight line.
• The mass of an object is a quantitative measure
  of inertia.
• SI Unit of Inertia and Mass kilogram (kg)

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NEWTONS SECOND LAW OF MOTION

• When a net external force acts on an
  object of mass m, the acceleration a that results
  is directly proportional to the net force and has
  a magnitude that is inversely proportional to the
  mass. The direction of the acceleration is the
  same as the direction of the net force.

SI Unit of Force kgm/s2 newton (N)
Only External forces are considered in the
Newtons second law.
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Example 1  Pushing a Stalled Car

• Two people are pushing a stalled car, as
  Figure 4.5a indicates. The mass of the car is
  1850 kg. One person applies a force of 275 N to
  the car, while the other applies a force of 395
  N. Both forces act in the same direction. A third
  force of 560 N also acts on the car, but in a
  direction opposite to that in which the people
  are pushing. This force arises because of
  friction and the extent to which the pavement
  opposes the motion of the tires. Find the
  acceleration of the car.

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Example 2  Hauling a Trailer

• A truck is hauling a trailer along a level
  road, as Figure 4.32a illustrates. The mass of
  the truck is m18500 kg and that of the trailer
  is m227 000 kg. The two move along the x axis
  with an acceleration of ax0.78 m/s2. Ignoring
  the retarding forces of friction and air
  resistance, determine (a) the tension T in the
  horizontal drawbar between the trailer and the
  truck and (b) the force D that propels the truck
  forward.

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Questions

• The net external force acting on an object is
  zero. Is it possible for the object to be
  traveling with a velocity that is not zero? If
  your answer is yes, state whether any conditions
  must be placed on the magnitude and direction of
  the velocity. If your answer is no, provide a
  reason for your answer.
• Is a net force being applied to an object when
  the object is moving downward (a) with a constant
  acceleration of 9.80 m/s2 and (b) with a constant
  velocity of 9.80 m/s? Explain.
•  Newtons second law indicates that when a net
  force acts on an object, it must accelerate. Does
  this mean that when two or more forces are
  applied to an object simultaneously, it must
  accelerate? Explain.

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Newton's Third Law
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Newton's Third Law

• If one object is exerting a force on a second
  object, then the second object is also exerting a
  force back on the first object. The two forces
  have exactly the same magnitude but act in
  opposite directions.

• Forces always exist in pairs.
• It is very important that we realize we are
  talking about two different forces acting on two
  different objects.

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Question

• A father and his seven-year-old daughter are
  facing each other on ice skates. With their
  hands, they push off against one another.
• Compare the magnitudes of the pushing forces that
  they experience.
• Which one, if either, experiences the larger
  acceleration? Account for your answers.

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EXAMPLE 3 Pushing Two Blocks

• In Fig. 3-29a, a constant horizontal force of
  magnitude 20 N is applied to block A of mass 4.0
  kg, which pushes against block B of mass 6.0 kg.
  The blocks slide over a frictionless surface,
  along an x axis.
• What is the acceleration of the blocks?
• What is the force acting on block B from block A

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Example 4  The Accelerations Produced by Action
and Reaction Forces

• Suppose that the mass of the spacecraft in
  Figure 4.7 is mS11 000 kg and that the mass of
  the astronaut is mA92 kg. In addition, assume
  that the astronaut exerts a force of P36 N on
  the spacecraft. Find the accelerations of the
  spacecraft and the astronaut.

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NEWTONS LAW OF UNIVERSAL GRAVITATION
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NEWTONS LAW OF UNIVERSAL GRAVITATION

• Every particle in the universe exerts an
  attractive force on every other particle. For two
  particles that have masses m1 and m2 and are
  separated by a distance r, the force that each
  exerts on the other is directed along the line
  joining the particles and has a magnitude given
  by

The symbol G denotes the universal gravitational
constant, whose value is found experimentally to
be
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DEFINITION OF WEIGHT

• The weight of an object on or above the earth
  is the gravitational force that the earth exerts
  on the object. The weight always acts downward,
  toward the center of the earth. On or above
  another astronomical body, the weight is the
  gravitational force exerted on the object by that
  body.
• SI Unit of Weight newton (N)

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• When the height of object H above the Earth is
  small

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The Gravitational Acceleration Constant
When air resistance can be ignored and
any object under only gravitational force will
free fall with a constant acceleration
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RELATION BETWEEN MASS AND WEIGHT

• Mass is an intrinsic property of matter and does
  not change as an object is moved from one
  location to another.
• Weight, in contrast, is the gravitational force
  acting on the object and can vary, depending on
  how far the object is above the earths surface
  or whether it is located near another body such
  as the moon.

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Questions

• When a body is moved from sea level to the top
  of a mountain, what changesthe bodys mass, its
  weight, or both? Explain.

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Questions

• The force of air resistance acts to oppose the
  motion of an object moving through the air. A
  ball is thrown upward and eventually returns to
  the ground.
• (a) As the ball moves upward, is the net force
  that acts on the ball greater than, less than, or
  equal to its weight? Justify your answer.
• (b) Repeat part (a) for the downward motion of
  the ball.

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The Normal Force

• The normal force FN is one component of the
  force that a surface exerts on an object with
  which it is in contactnamely, the component that
  is perpendicular to the surface.

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APPARENT WEIGHT
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The Friction Force
When the object moves or attempts to move along a
surface, there is a component of the force that
is parallel to the surface. This parallel force
component is called the frictional force, or
simply friction. It is always against the
relative motion or the attempts of the motion
between object and surface.
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Tension
Tension is the force exerted by a rope or a cable
attached to an object

1. Tension in a Nonaccelerating rope the magnitude
   of tention is the same everywhere in the rope.
2. An Accelerating rope the magnitude of tension is
   not the same everywhere in the rope that has a
   mass however, the magnitude of tension is the
   same everywhere in the rope that is massless.

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For a massless string

• It is always directed along the rope.
• It is always pulling the object.
• 3. It has the same value along the rope

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Applying Newton's Laws

• Newton's Second Law

It can be written as two (or three) component
equations
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Equilibrium Applications of Newton's Laws of
Motion

• DEFINITION OF EQUILIBRIUM An object is in
  equilibrium when it has zero acceleration.

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EXAMPLE 5 Three Cords

• In Fig. 6-25a, a block B of mass M  15 kg
  hangs by a cord from a knot K of mass mK, which
  hangs from a ceiling by means of two other cords.
  The cords have negligible mass, and the magnitude
  of the gravitational force on the knot is
  negligible compared to the gravitational force on
  the block. What are the tensions in the three
  cords?

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Free-Body Diagrams

• Identify the object for which the motion is to be
  analyzed and represent it as a point.
• (2) Identify all the forces acting on the object
  and represent each force vector with an arrow.
  The tail of each force vector should be on the
  point. Draw the arrow in the direction of the
  force. Represent the relative magnitudes of the
  forces through the relative lengths of the
  arrows.
• (3) Label each force vector so that it is clear
  which force it represents.

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Example 6  Replacing an Engine

• An automobile engine has a weight W, whose
  magnitude is W3150 N. This engine is being
  positioned above an engine compartment, as Figure
  4.29a illustrates. To position the engine, a
  worker is using a rope. Find the tension T1 in
  the supporting cable and the tension T2 in the
  positioning rope.

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Example 7  Equilibrium at Constant Velocity

• A jet plane is flying with a constant speed
  along a straight line, at an angle of 30.0 above
  the horizontal, as Figure indicates. The plane
  has a weight W whose magnitude is W86 500 N, and
  its engines provide a forward thrust T of
  magnitude T103 000 N. In addition, the lift
  force L (directed perpendicular to the wings) and
  the force R of air resistance (directed opposite
  to the motion) act on the plane. Find L and R.

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Non-quilibrium Applications of Newton's Laws of
Motion

• DEFINITION OF NONEQUILIBRIUM
• An object is in nonequilibrium when it has
  non-zero acceleration.

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Example 8  Applying Newtons Second Law Using
Components

• A man is stranded on a raft (mass of man and
  raft1300 kg), as shown in Figure a. By paddling,
  he causes an average force P of 17 N to be
  applied to the raft in a direction due east (the
  x direction). The wind also exerts a force A on
  the raft. This force has a magnitude of 15 N and
  points 67 north of east. Ignoring any resistance
  from the water, find the x and y components of
  the rafts acceleration.

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Example 9 Towing a Supertanker

• A supertanker of mass m1.50108 kg is being
  towed by two tugboats, as in Figure. The tensions
  in the towing cables apply the forces T1 and T2
  at equal angles of 30.0 with respect to the
  tankers axis. In addition, the tankers engines
  produce a forward drive force D, whose magnitude
  is D75.0103 N. Moreover, the water applies an
  opposing force R, whose magnitude is R40.0103
  N. The tanker moves forward with an acceleration
  that points along the tankers axis and has a
  magnitude of 2.00103 m/s2. Find the magnitudes
  of the tensions T1 and T2.

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Conceptual Questions

• According to Newtons third law, when you push on
  an object, the object pushes back on you with an
  oppositely directed force of equal magnitude. If
  the object is a massive crate resting on the
  floor, it will probably not move. Some people
  think that the reason the crate does not move is
  that the two oppositely directed pushing forces
  cancel. Explain why this logic is faulty and why
  the crate does not move.
• A stone is thrown from the top of a cliff. As the
  stone falls, is it in equilibrium? Explain,
  ignoring air resistance.
• Can an object ever be in equilibrium if the
  object is acted on by only (a) a single nonzero
  force, (b) two forces that point in mutually
  perpendicular directions, and (c) two forces that
  point in directions that are not perpendicular?
  Account for your answers.

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• A circus performer hangs stationary from a rope.
  She then begins to climb upward by pulling
  herself up, hand over hand. When she starts
  climbing, is the tension in the rope less than,
  equal to, or greater than it is when she hangs
  stationary? Explain.
• A weight hangs from a ring at the middle of a
  rope, as the drawing illustrates. Can the person
  who is pulling on the right end of the rope ever
  make the rope perfectly horizontal? Explain your
  answer in terms of the forces that act on the
  ring.