Physic 110 Lecture 07 from Chapter 4'''Sections 1 to 4

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Physic 110 Lecture 07 from Chapter
4...Sections 1 to 4

• Laws of Motion

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Homework Assignment 07
Conceptual questions Chapter 4 2 and 8 on
page 108

• Problems
• Chapter 4, Problem 6 on page 109
• Chapter 4, Problem 11 on page 109

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Classical Mechanics

• Describes the relationship between the motion of
  objects in our everyday world and the forces
  acting on them
• Conditions when Classical Mechanics does not
  apply
• very tiny objects (lt atomic sizes)
• objects moving near the speed of light

4
Newtons Three Laws of Motion

• Newtons 1st Law A bodys natural state is
  either at rest or at uniform speed along a
  straight line unless acted on by an unbalanced
  force.
• Newtons 2nd Law The acceleration of an object
  is directly proportional to the net force acting
  on it, in the same direction as the force, and
  inversely proportional to the mass of the body.
  
• Newtons 3rd Law Whenever one object exerts a
  force on a second object, the second object
  exerts an equal and opposite force on the first.

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Terms used to explain the 3 Laws of Motion

• State of Rest a state where a body does not
  move.
• Uniform Motion motion when by a body has
  constant velocity.
• Acceleration rate of change of velocity with
  respect to time.
• Mass a measure of a bodys resistance to changes
  in motion.
• Force an interaction which pushes or pulls on a
  body.

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Force

• a push or a pull
• force is a vector quantity
• Two varieties of force
• Contact force a force resulting from physical
  contact between objects
• Field force a force acting between disconnected
  objects.

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Contact and Field Forces
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Its time for Physics Theater

• Please welcome the actors of the
• Newtonian Theater Performing Troupe.
• State of Rest
• State of Uniform Motion
• Unbalanced Force
• Acceleration
• A Body
• Another Body

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Act 1 Newtons 1st Law of Motion

• When our story opens.......
• we find A Body at a State of Rest.
• Suddenly from out of nowhere we notice Another
  Body with a State of Uniform Motion

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Newtons First Law

• Bodies have two natural states
• either
• at rest
• or
• at uniform speed along a straight line
• Only unbalanced forces can change a state of
  rest or a state of uniform motion.

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Plot of Act 1

• As long as A Body and Another Body do not
  interact or conflict with either each other or
  with Unbalanced Force, life is good, carefree,
  and pretty much the same all the time.
• Both Bodies stay in their natural states as we
  observe their motion (or lack of motion).
• End of Act 1

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Act 2 Newtons 2nd Law of Motion

• When Act 2 opens.......
• We find A Body at a State of Rest watching
  Another Body in a State of Uniform Motion.
• All during Act 1, A Body had been watching
  Another Body running around, flaunting his
  carefree natural state.
• Running here....
• Running there...
• Running along in a straight
  line.

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Act 2 continues

• As A Body watches him run, she yearns to feel the
  wind through her hair and wonders about the
  bliss, pleasure, and fame that comes from being
  in a State of Uniform Motion
• But she realizes, deep in her heart, that NO,
  the first Law says her natural state is to be
  happy and content and stationary with her State
  of Rest.

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Act 2....Still more action

• Suddenly we hear a knock on the door. Not
  waiting for someone to answer, the door is pushed
  in and swaggers an Unbalanced Force. From his
  appearance, he must be one of those dangerous
  contact forces.
• He sidles over to A Body and introduces himself.
• Then he tells her, that if she wants to move like
  Another Body, he can give her some action.

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Act 2....Still more action

• A Body looks him over and remembers how her
  mother always warned her about strange forces.
  But still, she wonders, maybe if I try just a
  little bit of Unbalanced Force it would still be
  safe. I mean, what could a tiny, little force
  hurt?
• So she tells Unbalanced Force that she accepts
  his offer, but just to make it a small one.
• With his offer accepted, Unbalanced Force, begins
  interacting and pushing on A Body.

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Act 2....Still more yet.

• Suddenly, in a flash, State of Rest transforms
  into Acceleration. A Body starts to move across
  the room going faster and faster in the same
  direction that Unbalanced Force is pushing her.
• At first it feels good, but then as the speed
  increases, she gets scared and yells to
  Unbalanced Force ...STOP, I want to Stop, Now.
• Unbalanced Force stops pushing, but when he
  does....
• .

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Act 2 Comes to a Close

• but when he does.....
• Acceleration changes into State of Uniform
  Motion. Meanwhile A Body continues moving at the
  speed she had attained when Unbalanced Force was
  removed.
• As Act 2 ends, we see A Body moving quickly at
  constant speed along a straight line in a State
  of Uniform Motion.
• End of Act 2
• .

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Newtons 2nd Law of Motion

• Newtons 2nd Law The acceleration of an object
  is directly proportional to the net force acting
  on it, in the same direction as the force, and
  inversely proportional to the mass of the body.
  
• Or in equation form

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Act 3 Newtons 3rd Law of Motion

• When Act 3 opens.......
• We find A Body in a State of Uniform Motion.
  Meanwhile Another Body is also in a State of
  Uniform Motion.
• Oh no! It appears that A Body and Another Body,
  both in States of Uniform Motion along a straight
  line are moving directly towards each other.

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Act 3 Continues

• They move toward each other....unable to stop or
  change their motion.
• As they collide, Unbalanced Force steps in
  between A Body and Another Body and pushes on
  each of the two bodies with equal but opposite
  force.
• As he does, State of Uniform Motion, first
  becomes Acceleration (but negative), and then
  quickly changes into his final form of State of
  Rest.

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Act 3 The grand finale

• His job done, Unbalanced Force for pulls out from
  between A Body and Another Body.
• A Body looks at Another Body.
• Another Body looks back at A Body.
• Unbalanced Force staggers toward the door
  exhausted from his encounter. Exiting he leaves
  the Bodies with these memorable words of advice.
• Remember...for every action, theres an equal
  but opposite reaction.
• And with that he was gone.
• As they move toward each other unable to stop.
  When Act 3 opens.......
• We find A Body in a State of Uniform Motion.
  Meanwhile Another Body is also in a State of
  Uniform Motion.
• Oh no! It appears that A Body and Another Body,
  both in States of Uniform Motion along a straight
  line are moving directly towards each other.

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The Conclusion

• The moral of this tale.
• Is if you dont want to undergo acceleration,
  dont fool around with unbalanced forces.
• The End

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Newtons Three Laws of Motion

• Newtons 1st Law A bodys natural state is
  either at rest or at uniform speed along a
  straight line unless acted on by an unbalanced
  force.
• Newtons 2nd Law The acceleration of an object
  is directly proportional to the net force acting
  on it, in the same direction as the force, and
  inversely proportional to the mass of the body.
  
• Newtons 3rd Law Whenever one object exerts a
  force on a second object, the second object
  exerts an equal and opposite force on the first.

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Mass

• A measure of the resistance of an object to
  changes in its motion due to a force
• Scalar quantity
• SI units are kg
• Inertia is another name for this resistance to a
  change in motion.
• Mass is a measure of inertia.

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Newtons Second Law

• The acceleration of an object is directly
  proportional to the net force acting on it and
  inversely proportional to its mass.
• F and a are both vectors

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Units of Force

• From this relationship we define the SI units of
  force a Newton (N)
• The US Customary unit of force is a pound (lbf)
• 1 N 0.225 lbf

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Weight

• Weight the gravitational force acting on a
  bodys mass.
• where g is the acceleration due to gravity
• Weight is a force.

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More about weight

• Weight is not an inherent property of an object
• mass is an inherent property
• Weight depends upon location

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Example Problem

• A 5.0 kg bucket of water is raised from a well by
  a rope. If the upward acceleration of the bucket
  is 3.0 m/s2, find the force exerted by the rope
  on the bucket.
• Principle
• Known m 5 kg a 3.0 m/s2

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Example 1 Solution

• Known m 5 kg a 3.0 m/s2

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Example 2

• Assume that the three blocks shown move on a
  frictionless surface and that a 42 N forces acts
  on the 3 kg block. Find
• a) the acceleration of this system.
• b) the tension in the cord connecting the 3.0 kg
  and 1.0 kg block
• c) the force exerted by the 1.0 kg block on the
  2.0 kg block.

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Example 2 continued

• a) acceleration of system
• where
• so

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Example 2 continued

• b) tension in cord
• since the force in the cord causes the 1.0 and
  2.0 blocks to accelerate at 7.0 m/s2, the size of
  this force must be

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Example 2 continued

• c) force exerted on the 2.0 block by the 1.0
  block.
• Again, the 2.0 kg block is still being
  accelerated at 7.0 m/s2, so

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Example 3

• What is the acceleration of a freely falling 60
  kg skydiver if air resistance exerts a force of
  250 N?
• Once his chute opens
• his air resistance will
• be proportional to his
• speed squared. If the air resistance
• Fdrag4.0m/s v2 what will be his
• terminal speed with a deployed chute?

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Example 3 continued

• Principle
• SF m a
• Fdrag-Wm a
• where W m g
• 60kg 9.81m/s2
• 589 N
• so

Fdrag 250N
Wmg
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Example 3 continued
Fdrag 4m/s v2

• At terminal velocity the
• acceleration has gone
• to 0, so the forces balance
• each other. With a0
• SF m a
• Fdrag-W0
• 4.0m/s v2 - 589 N 0
• Solving for v gives

Wmg
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Homework Assignment 07
Conceptual questions Chapter 4 2 and 8 on
page 108

• Problems
• Chapter 4, Problem 6 on page 109
• Chapter 4, Problem 11 on page 109

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State of Rest State of Uniform Motion Unbalanced
Force Acceleration A Body Another Body