Motion

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Motion Force Dynamics

• Physics 11

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Galileos Inertia

• Galileo attempted to explain inertia based upon
  rolling a ball down a ramp
• Predict what would happen in each of the
  following situations

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Forces and Motion

• Predicting the motion of an object is known as
  kinematics and as we have seen in the previous
  section, result in the equations of motion
• Now, we will begin to consider the forces that
  act on an object to describe the why of motion
  this is known as dynamics

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Inertial Mass

• Inertia is often understood as the resistance of
  an object to a change in its motion
• Inertial mass is used to describe this property
  of an object
• Another type of mass, gravitational mass,
  describes the attraction between massive objects

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Fundamental Forces

• There are four forces that result in the
  behaviours we observe in the Universe
• Gravitation
• Electromagnetic
• Strong Nuclear
• Weak Nuclear

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Gravitation

• All massive objects attract other massive objects
• This means that the Earth exerts a force on you
  (toward the centre of the Earth) but at the same
  time, you exert an equal and opposite force on
  the Earth
• Because the mass of the Earth is significantly
  larger than your mass, your acceleration toward
  the Earth is much greater than the Earths
  acceleration toward you

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Weight vs. Mass

• Although mass and weight are used interchangeably
  in common vernacular, from the standpoint of
  scientific language, this is not correct
• Mass is the measure of the amount of matter in an
  object and does not change it is measured using
  a balance
• Weight is the measure of the gravitational
  attraction between objects and can change it is
  measured using a spring scale

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Weight vs. Mass

• Although they are different, weight and mass are
  related using the following equation

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Newtons 1st 2nd Laws of Motion

• Physics 11

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Newtons Laws

• There are three laws that Newton used in
  Principia in order to explain motion
• What are the three laws?

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Newtons Laws of Motion

1. An object at rest or in uniform motion will
   remain rest or in uniform motion unless acted on
   by an external force.
2. Acceleration is directly proportional to the
   force applied to an object and inversely
   proportional to its mass.
3. For every action, there is an equal and opposite
   reaction.

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Newtons Laws of Motion

1. An object at rest or in uniform motion will
   remain rest or in uniform motion unless acted on
   by an external force.
2. Acceleration is directly proportional to the
   force applied to an object and inversely
   proportional to its mass.
3. For every action, there is an equal and opposite
   reaction.

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Inertial and Non-Inertial Frames of Reference

• An inertial frame of reference is one in which
  Newtons Laws are valid
• An inertial frame is either at rest or in uniform
  motion but they are no accelerating
• A non-inertial frame of reference is one in which
  Newtons Laws are not valid
• Accelerating frames of reference are always
  non-inertial

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Newtons Second Law

• Acceleration is directly proportional to the
  force applied to an object and inversely
  proportional to its mass.

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Friction

• Physics 11

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Friction

• Friction is a contact force and occurs when one
  object moves or is attempted to be moved across
  another
• Based upon physical properties, it is possible to
  determine the maximum amount of frictional force
  that can be present but friction only acts to
  oppose motion

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Static vs. Kinetic

• Static frictional forces exist when there is no
  motion
• Kinetic frictional forces exist when one object
  slides across another
• Static frictional forces are greater than kinetic
  frictional forces

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Coefficient of Friction

• The maximum amount of frictional force that can
  exist between two surfaces is related to the
  weight of the object and the properties of the
  surfaces
• We use the coefficient of friction (µ) to
  describe interaction of the two surfaces
• Typically you will be given a static and kinetic
  coefficient depending on the situation

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Normal Force

• The normal force is the force that opposes the
  gravitational force (weight)
• Currently your weight is pushing down on the
  chair you are sitting on and the chair is pushing
  back with a force that is equal and opposite
• Similarly, you and the chair are applying a force
  on the floor and the floor is applying an equal
  and opposite force on you and the chair

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Normal Force

• In most situations, the normal force will simply
  be the opposite of the weight

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Direction and the Frictional Force

• The direction of the frictional force will not be
  determined from the equation
• Instead, you need to look at your diagram and
  apply the correct direction (positive or
  negative) to the force
• The direction will always be the opposite of the
  direction of motion

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Frictional Force

• The frictional force is the product of the normal
  force and the coefficient of friction
• Common coefficients of friction are available in
  Table 4-2, p. 97

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Uniform Motion

• Normally, when an object is in a state of uniform
  motion, the applied force is equal to the kinetic
  frictional force
• Additionally, when a force is applied to an
  object, the force that is applied just before it
  begins to move is assumed to be equal to the
  static frictional force

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Net Force

• Physics 11

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Putting it All Together

• Now that we have considered Newtons Second Law,
  you can use that to analyze kinematics problems
  with less information than we have used
  previously
• We can either use dynamics information to then
  apply to a kinematic situation or vice versa

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Free Body Diagrams

• A free body diagram will be used in most dynamics
  problems in order to simplify the situation
• In a FBD, the object is reduced to a point and
  forces are drawn starting from the point

FN
Fa
Ff
Fg
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The Net Force

• In most situations, there is more than one force
  acting on an object at any given time
• When we draw the FBD we should label all forces
  that are acting on an object and also determine
  which would cancel each other out
• Ones that do not completely cancel out will be
  used to determine the net force

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The Net Force

• The net force is a vector sum which means that
  both the magnitude and direction of the forces
  must be considered
• In most situations we consider if Physics 11, the
  forces we consider will be parallel or
  perpendicular

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An Example

• A 25kg crate is slid from rest across a floor
  with an applied force 72N applied force. If the
  coefficient of kinetic friction is .27,
  determine
• The acceleration of the crate?
• The time it would take to slide the crate 5.0m
  across the floor.

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FBD
FN250N
Fa72N
Ff?
Fg-250N
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Use the frictional force equation to determine
the magnitude of the frictional force
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The net force is the sum of the forces (acting
parallel or anti-parallel)
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Use Newtons Second Law to solve for the
acceleration
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Use kinematics to solve for the time taken to
cross the floor
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Springs and Hookes Law

• Physics 11

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Springs

• A mass-spring system is given below. As mass is
  added to the end of the spring, how would you
  expect distance the spring stretches to change?

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Springs
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Springs

• 2 times the mass results in a 2 times of the
  displacement from the equilibrium point
• 3 time the mass 3 times the displacement

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Hookes Law

• Fspring Applied force
• X displacement of the spring from the
  equilibrium position
• K the spring constant

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Hookes Law

• the restoring force is opposite the applied
  force. (negative sign)
• Gravity applied in the negative direction, the
  restoring force is in the positive direction