Physics 2211 Mechanics Lecture 6 Knight: 4'7 to 5'3 Using Newtons 2nd Law

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Physics 2211 - MechanicsLecture 6 (Knight 4.7
to 5.3)Using Newtons 2nd Law

• Dr. John Evans

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Misconceptions

• Is there a force of motion that keeps a
  moving object moving?
• No.
• Can a normal force act sideways?
• No.
• Remember that
• Every force must have an agent that produces it
• Every contact force must act only at the point of
  contact
• The normal force acts only perpendicular to the
  surface in contact
• The friction force acts only parallel to the
  surface in contact
• The tension force from a string acts only along
  the line of the string.

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Free-Body Diagrams
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Drawing a Free-Body Diagram

• Identify all forces acting on the object. This
  step was described in Tactics Box 4.2.
• Draw a coordinate system. Use the axes defined
  in your pictorial representation. If those axes
  are tilted, for motion along an incline, then the
  axes of the free-body diagram should be similarly
  tilted.
• Represent the object as a dot at the origin of
  the coordinate axes. This is the particle model.
• Draw vectors representing each of the
  identified forces. This was described in Tactics
  Box 4.1. Be sure to label each force vector.
• Draw and label the net force vector . Draw
  this vector beside the diagram, not on the
  particle. Or, if appropriate, write .
• Then check that points in the same
  direction as the acceleration vector on your
  motion diagram.

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Example An elevator accelerates upward
Need a vertical coordinate axis. Need Tgtw so
that the motion is upward.
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Example An ice blockshoots across a frozen lake
Need vertical and horizontal coordinate
axes.Make thrust in the x direction weight and
normal force equal and opposite along y.
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ExampleA skier is pulled uphill
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Clicker Question 1
An elevator suspended by a cable is moving
upward and slowing to a stop. Which free-body
diagram below describes its motion?
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Chapter 4 Summary (1)
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Chapter 4 Summary (2)
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Equilibrium
An object on which the net force is zero is
said to be in equilibrium. The object might be
at rest in static equilibrium, or might be moving
in a straight line with constant velocity in
dynamic equilibrium. Both of these conditions
are identical from a Newtonian perspective
because Fnet 0 and a 0.
Since Newtons 2nd Law is represented by
vector equations, equilibrium implies the
following simultaneous equaitons
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Static Equilibrium ExampleA 3-way Tug-of-war (1)
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Static Equilibrium ExampleA 3-way Tug-of-war (2)
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Example Towing a car uphill (1)
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Example Towing a car uphill (2)
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2nd Law ExampleSpeed of a towed car (1)
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2nd Law ExampleSpeed of a towed car (2)
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2nd Law ExampleAltitude of a rocket (1)
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2nd Law ExampleAltitude of a rocket (2)
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Clicker Question 2
A Martian Lander is approaching the surface of
Mars. It is slowing its descent by firing its
rocket motor. Which of the free-body diagrams on
the right correctly describes the system?
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Mass and Weight
Mass and weight are not the same thing, but
they are related. Consider thr falling body
represented by the free-body diagram to the
right. The only force acting on it is its
weight, the downward pull of gravity, so Fnet
w. From Newtons 2nd Law, Fnet w ma
Galilelo discovered that any
object,regardless of its mass, has the same
acceleration afree-fall (9.80
m/s2, downward) (g, downward) Therefore,
w (mg, downward). The magnitude of the weight
force, in other words, the weight, is directly
proportional to the mass m, where g is the
constant of proportionality, so that w mg.Note
that m is invariant (unchanging), while g and w
depend on location.
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Mass Measurements
Beam BalanceMass measurement
Spring ScalesWeight measurements
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Apparent Weight
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Weightlessness
If an object falls so as to freely respond to the
force of gravity, its acceleration in the
vertical y direction will be ay -g. Therefore,
the apparent weight of the object is
wapp w(1 ay/g) w(1 - g/g) 0 In this
situation, the apparent weight of the object
vanishes and it is weightless.

Does weightlessness mean that the object has
no weight, i.e. that no gravitational force is
acting on it? NO. The force of gravity is still
present, but since the object and its
surroundings are freely responding to it, the
apparent acceleratrion and force are
zero. Example A man is on a spring scale
in an elevator. The cable breaks, and the
elevator falls without friction(ay-g). On the
way down, what will he see as his weight, as
indicated by the scale? Zero.
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End of Lecture 6

• Before next Monday, read Knight, Chapters 5.4
  through 5.6. On Wednesday we have a Review.