The Laws of Motion

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The Laws of Motion
or, Newtonian mechanics
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Newtons Laws of Motion

• The law of inertia. An object in motion remains
  in motion with constant velocity if the net force
  on the object is 0.
• Force and acceleration. If the net force acting
  on an object of mass m is F, then the
  acceleration of the object is a F/m. Or, F
  ma.
• Action and reaction. For every action there is an
  equal but opposite reaction.

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Newtons second law
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Newtons second law of motion
F m a

• F force acting on the moving object, a
  vector
• m mass of the moving object
• a acceleration of the moving object, a vector

What is force?
What is mass?
If the force is known, Newtons second law states
how the object (on which the force is acting)
accelerates
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Force and acceleration are vectors.
A vector has both magnitude and direction.
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Three kinds of acceleration
m speeds up
m slows down
m changes direction
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UNIFORM CIRCULAR MOTION
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Example
Centripetal acceleration (Christian Huygens
,1673)
Therefore, the force on m is
The string tension is the strength of the force
exerted by the string at either end.
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Analyze free fall including air friction
The aerodynamic drag force (C) depends on the
size, shape and surface roughness it is about
the same for both balls.

• The gravitational acceleration (g) is
  independent of mass.
• Effect of air is inversely proportional to mass
• heavy --- small effect of air
• light --- large effect of air

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Newtons third law
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Which vehicle exerts a greater force ? the tow
truck or the car?
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Newtons laws of motion

• The law of inertia. An object in motion remains
  in motion with constant velocity if the net force
  on the object is 0.
• Force and acceleration. If the net force acting
  on an object of mass m is F, then the
  acceleration of the object is a F/m. Or, F
  ma.
• Action and reaction. For every action there is an
  equal but opposite reaction.

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For every action there is an equal but opposite
reaction.
Newtons third law
Whenever one object exerts a force on another
object, the second object exerts an equal but
opposite force on the first object.
Forces always occur like this, in pairs.
We will see than this is very hard to accept! It
is just not common sense. That is why it took a
great genius like Newton to figure it out.
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Example A collision
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Universal Gravitation --- an example of
Newtons third law
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The Earth pulls the apple down (action).
The apple pulls the Earth up (reaction).
The two forces are equal (but opposite).
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When does a scientific theory become an accepted
fact?
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A puzzle
The truck pulls to the right. According to
Newtons third law, the car pulls to the left
with an equal force. So how can they start
moving, or accelerate?
Resolution Consider each part separately, and
dont forget that other forces are also acting.
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Harold Edgertons high speed photograph of Wes
Kessler kicking a football.
The force exerted by the ball on the toe
(reaction) is equal to the force exerted by the
toe on the ball.
Really hard to accept!
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Momentum, p mv
Total momentum is conserved
Proof
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The four fundamental forces

• Gravity
• Electromagnetic
• Strong nuclear force
• Weak nuclear force

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FIN
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Newtons second law and calculus
Isaac Newton invented calculus to solve the
equation of motion to calculate motion for the
force that is acting. Generally, calculus is the
mathematics that describes continuous change.