General Physics 1500

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General Physics 1500
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• Dr S. Loch
• Office Allison Lab room 113
• Lectures MWF 8am
• Office hours Mon 330pm-5pm
• and Fri 9-11am.

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Important information for the class
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• Course textbook
• College Physics. Serway and Faughn. Vol I. 7th
  Ed.
• Labs meet on Wednesdays. The first lab meeting
  is Wed of this week (the 9th January).
• It will be to your advantage to read the
  Experiment and/or Lab Handout before attending
  the lab
• Recitations meet on Mondays. The first
  recitation is Monday 14th January.
• Room assignments and times for lab and recitation
  will be posted on the bulletin board outside PKH
  103.

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Grade assignment
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Homework problems
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• One homework assignments will be done per week,
  with 10 questions per assignment, covering one
  chapter each week.
• The homework will not be graded, instead
  solutions will be posted after the deadline for
  the homework assignment has passed.
• It is strongly in your interest to do the
  homework assignments. They will help you to
  develop the problem solving skills that will be
  tested in the class tests and recitation quizzes.
• Much of physics is problems solving, so you are
  expected to be able to use the skills you will
  learn to solve problems you have not seen before.

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Classroom response questions
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• I will be presenting certain questions in class,
  to test your understanding of some basic
  concepts.
• It will be expected that you will read the book
  before coming to class, so some of the questions
  will be based on material from the book.
• The questions will be answered via a handheld
  keypad, which you must purchase.
• They will be multiple choice questions.
• The answers will register your attendance at
  class.
• You must purchase your own electronic clicker.
  They are called iclickers. They can be
  purchased from the Auburn University Bookstore.
  You should be able to trade them back to the
  bookstore at the end of the semester.

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The aims of the class
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• On of the aims of this class is to teach you to
  think in a physics way.
• As you see each concept, try to get a mental
  picture of how it works.
• You will learn as much about how to solve
  problems as you do about the laws of physics
  themselves.
• So you will need to approach this class
  differently from many of the other classes you
  are taking. Simply memorizing solutions will not
  help.
• Doing lots of homework problems is the best way
  to do well in the class. As you do each problem,
  think of what strategy you are using to solve the
  problem.

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Syllabus Overview
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• Mechanics
• 1.1 Units, dimensional analysis and trigonometry
• 1.2 Motion in 1-D
• 1.3 Vectors and motion in 2-D
• 1.4 The laws of motion
• 1.5 Energy
• 1.6 Momentum and collisions
• 1.7 Rotational motion and the law of gravity
• 1.8 Rotational equilibrium and rotational
  dynamics
• 1.9 Solids and Fluids

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Syllabus Overview
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• Thermodynamics
• 2.1 Thermal physics
• 2.2 Energy in Thermal Processes
• 2.3 The Laws of thermodynamics
• Vibration and Waves
• 3.1 Vibration and Waves
• 3.2 Sound
• Note that the lecture notes can be downloaded
  from
• electro.physics.auburn.edu/loch

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1. Mechanics
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• 1.1 Units, dimensional analysis and trigonometry
• 1.1.1 Dimensional analysis
• Dimensional analysis is a way of making sure that
  an equation is correct, and that you have the
  right units in your answer.
• The dimensions in an equation are the units that
  we are working in (cm, s, kg etc).
• We will mostly work with SI units (kg, m, s),
  with some use being made of cgs (cm, g, s) and US
  customary units.
• If you write an answer with no units, or
  incorrect units, you will drop a point.

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Rules for dimensional analysis
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• Dimensions can be treated as physical quantities,
  and obey the normal rules of algebra.
• When an equation is written out, dimensions are
  held in square brackets , and manipulated as if
  they were numbers/variables.
• Only quantities of the same dimension can be
  added.
• Terms on either side of an equation must have the
  same dimension.

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• When working with the dimension of an equation,
  one can either
• write down the units, eg. kg, m (I recommend
  this option) or
• Use a new symbol for each of the dimension.
• New symbol Unit
• Distance L - m
• Time T - s
• Mass M - kg

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1.1.1 Dimensional analysis
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• e.g. A car covers 60 miles in 2 hours, what is
  its speed?
• Check the following equation, relating the
  distance (x) covered to the velocity (v0),
  acceleration (a) and time (t).

These have to have the same units to be added
together.
Both sides of the equation should have the same
units.
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1.1.2 Significant figures
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• A significant figure is a RELIABLY KNOWN DIGIT.
• 4.5 has two significant figures, with the last
  figure being the limit of our certainty.
• Thus, 4.5 means 4.5?0.1
• It is important to use scientific notation when
  writing the number.
• Examples
• 1.5x103 has two sig. figs (note the importance of
  expressing the number in scientific notation)
• 4.5631 has 5 sig. figs
• 0.00015 1.5x10-4 has two sig. figs

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1.1.3 Uncertainty
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• So how to we determine the uncertainty in a final
  quantity, e.g. Fma?
• Rule for multiplying or dividing
• The number of sig. figs in the final product is
  the same as the number of sig. figs in the least
  accurate of the quantities being multiplied.
• Rule for addition/subtraction
• The number of sig. figs in the result is the
  smallest number of decimal places of any term in
  the sum

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1.1.4 Conversion of units
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• You need to know how to convert one unit into
  another. For example, express 20.0 inches in cm.
• To convert from one unit to another
• Write out the quantity you are starting with.
• Multiply by the conversion factor to go to the
  new units.
• Cancel out any units to leave yourself with the
  final quantity.

We use the fact that
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1.1.5 Coordinates and trig rules
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(x,y)

• We will work with two coordinate systems
• Cartesian (x,y)
• Plane polar
• Note that the x,y and ? values can be negative as
  well as positive.

y
0
x
0
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Trigonometry rules
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• You will need to know the following trig rules
  for a right angled triangle

• Hyp2Opp2Adj2
• SOHCAHTOA
• Sin(?)Opp/Hyp
• Cos(?)Adj/Hyp
• Tan(?)Opp/Adj

Hyp
Opp
Adj
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Section 1.2 Motion in One Dimension 1.2.1
Displacement and Frame of Reference
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• In this section we are going to investigate
  motion in one dimension.
• When solving a problem we must always chose a
  Frame of Reference (i.e. a set of coordinate
  axes).
• Displacement the change in position of an
  object.
• ?x xf - xi

x
xf
Displacement
xi
0
t
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1.2.2 Average speed and average velocity
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• Recap
• Scalar quantity has magnitude but no direction
  (e.g. mass, temperature, speed)
• Vectory quantity has both magnitude and direction
  (e.g. velocity)
• Speed is a scalar, while velocity is a vector.
• Vector quantities will have an arrow above them.
  Thus, represents velocity.
• Displacement is also a vector.
• In this chapter we will drop the arrow notation
  because we are only considering 1-D motion, and
  the sign gives us all of the direction
  information.

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1.2.2 Average speed and average velocity
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• Average speed (a scalar) is given by
• Average velocity is the displacement divided by
  the time period during which the displacement
  occurred.
• (v bar)
• denotes the
• average.

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Average velocity
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• It is useful to picture 1-D motion on a x vs t
  graph.
• The average velocity is the slope of a straight
  line joining the initial and final points on a
  position vs time graph.

• Note that the average velocity is a vector and
  must have a direction (usually shown by the sign)
• The average speed is a scalar and is the total
  distance divided by the total time

x
xf
xi
0
t
tf
ti
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Average velocity
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• The average velocity can be a reasonable estimate
  of the velocity, however it can also be
  misleading.
• Consider the following example

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1.2.3 Instantaneous velocity
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• A better way to measure the velocity of an object
  is its instantaneous velocity.
• The instantaneous velocity is the limit of the
  average velocity as the time interval ?t goes to
  zero.
• Note that the instantaneous speed is the
  magnitude of the instantaneous velocity.

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Instantaneous velocity
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• Consider the x vs t graph again.
• As the point tf moves closer to ti we get a
  better estimate of the instantaneous velocity.

x

• The instantaneous velocity at a given time is the
  slope of the position vs time graph at that time.

xi
0
t
ti
tf
tf
tf
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1.2.4 Average acceleration
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• The acceleration of an object is a measure of how
  much its velocity is changing over time.
• The average acceleration during a time interval
  is defined as the change in velocity divided by
  the time interval during which the change occurred

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Instantaneous acceleration
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• The instantaneous acceleration is the limit of
  the average acceleration as the time interval ?t
  goes to zero

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Instantaneous acceleration
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• The instantaneous acceleration at a given time is
  the slope of the velocity vs time graph at that
  time

v
vi
0
t
ti
tf
tf
tf
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Graphs of x vs t, v vs t and a vs t.
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• It can be shown that
• the area under a v vs t graph is equal to the
  distance covered.
• The difficulty picturing how an object is moving,
  from the graphs, is in how to relate x, v and a
  together (e.g. negative acceleration means that
  the objects velocity is decreasing, not that it
  is moving in a negative direction.)
• So when you see the x vs t graph, think of how
  the objects velocity is changing.
• When you see the v vs t graph, think of how the
  objects acceleration is changing.

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x
0
v
a
Constant displacement
t
t
t
x
a
v
Constant ve velocity
t
t
t
v
x
a
Constant ve acceleration
t
t
t
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1.2.5 One dimensional motion with constant
acceleration
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• Motion in 1-D with constant acceleration is a
  common occurrence, so we shall consider it in
  more detail.
• We shall derive a set of equations that can be
  used for constant acceleration.
• The four equations that we will derive will allow
  us to solve all 1-D constant acceleration
  problems.

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0
1.2.5 One dimensional motion with constant
acceleration

• We already know that
• Assuming ti0, tft, viv0 and vfv we would get

Equation 1
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1.2.5 One dimensional motion with constant
acceleration
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• We can also derive the following equations

Equation 2
Equation 3
Equation 4
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1.2.6 Free falling objects
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• A free falling object is any object moving under
  the influence of gravity only, regardless of its
  initial motion.
• Thus, objects thrown upwards/downwards and those
  dropped from rest are all free falling objects
  once they are released.
• Any free falling object experiences a constant
  acceleration directed downwards, denoted by g.
  On earth g9.8ms-2, regardless of its motion at
  any instant
• Thus we can use equations 1, 2, 3 and 4 for
  objects which are free falling, as long as we set
  a-g -9.8ms-2

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Method for answering physics problems
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• Get a mental picture of the problem.
• Write down what you know, and what you need to
  know.
• Plan out how you are going to tackle the problem.
• What equations will you use.
• If a 0 use average velocity equation
• If a ? 0 use the 4 kinematic equations
• Have a rough picture of the route you will take
  to get to the solution.

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1.3 Vectors and 2-D motion1.3.1 Properties of
vectors and scalars
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• In order to understand motion in more than one
  dimension, we will have consider vectors in more
  detail.
• Vectors have both a size and a direction.
• When drawing a vector, the size of the vector
  represents its magnitude.
• Two vectors are equal if they have both the same
  magnitude and direction (e.g. CD).

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Rules for adding two vectors
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• Only vectors with the same units can be added.
• You can add two vectors together graphically, by
  using the triangle method of addition
• Draw each vector to scale.
• Add the vectors nose-to-tail.
• The vector rules can be found in your book
  (p54-55).

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Rules for multiplying a vector by a scalar
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• Multiplication of a vector by a scalar gives a
  vector with the same direction, but with
  magnitude increased by the factor of the scalar.
• This means that the negative of a vector has the
  same size, but opposite direction.

-B
A-B
A-BA(-B)
A
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Working out the components of a vector
0
y

• All vectors can be split into horizontal (Ax) and
  vertical (Ay) components
• Thus,

0
x
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Adding vectors using their components
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• To add two vectors algebraically
• First find the components of the two vectors.
• The new vector evaluated as follows
• Total x-component sum of x-components
• Total y-component sum on y-components
• Use Pythagoras theorem to work out the magnitude
  of the resultant vector
• Use one of the trig rules to work out the angle

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Consider the following addition AB
0
y
y
y
Ay
AB
AB
B
By
By
B
Ax
x
Ax
Bx
x
x
Ay
A
A
Bx
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1.3.2 Displacement, velocity and acceleration in
two-dimensions
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• We can now generalize our 1-D expressions of
  motion, so that they work in 2-D.
• The displacement is defined as the change in the
  position vector

y
x
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Velocity and acceleration in 2-D
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• The average velocity is the displacement divided
  by the time interval
• The instantaneous velocity is the limit of the
  average velocity as the time interval goes to
  zero
• There are similar definitions for the average and
  instantaneous acceleration

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1.3.3 Projectile motion
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• Consider a projectile fired into the air, e.g. an
  American football.
• Such 2-D motion problems can be split into two
  1-D motion problems.
• In the y-direction
• ay g.
• In the x-direction
• ax0 ms-2
• Thus, we can use the equations from the last
  section.

vy
y
vx
?
vx
?
vy0
vy
?0
0
x
vx0
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The x-component of projectile motion
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• There is zero acceleration (neglecting air
  resistance) acting in the x-direction, so
• The velocity component in the x-direction remains
  constant
• Thus the displacement is

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The y-component of projectile motion
0

• Let vy0 denote the initial y-velocity, and g the
  free-fall acceleration. Thus, we can use the
  equations of a free-falling body to give

where
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The resultant speed and angle of projectile motion
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• To work out the resultant speed of the object at
  any time, use pythagoras theorem.
• To work out the angle of the velocity vector, use

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1.3.4 Relative velocity
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• A frame of reference is our coordinate system
  which we will use to describe the motion of the
  objects we are studying. We can have a
• Stationary or
• Moving frame of reference
• A measured velocity can be different in different
  frames of reference
• Thus all velocities must be measured relative to
  a frame of reference. We denote the velocity of
  object a, relative to the frame e as vae

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Relative velocities
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• Consider a boat trying to cross a river
• If the velocity of the boat relative to the river
  is vbr
• And the velocity of the river relative to the
  earth is vre.
• The vbe, the velocity of the boat relative to the
  earth is given by the sum of the vectors

River
vre
vbr
vbe
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Section 1.4 The Laws of motion1.4.1 The
concept of Force
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• We are used to the idea of a force being caused
  by a physical interaction with an object. These
  forces are called contact forces
• e.g. collisions, a person pushing or pulling on
  an object
• A field force is another source of forces. In
  this case a field is created by one object, which
  then causes a force on another
• e.g. Gravity the force caused by the
  gravitational field of the earth acts of the
  objects with mass in that field.
• There are other field forces, such as an electric
  field, a magnetic field.
• These fields act without the two objects
  necessarily coming into contact

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1.4.1 The concept of force
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• Force is a vector quantity, thus has both
  magnitude and direction.
• Thus we need to use vector addition to work out
  the total force on an object
• Force is measured in units of Newtons (N)

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1.4.2 Newtons first law
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• An object moves with a velocity that is constant
  in magnitude and direction, unless acted upon by
  a nonzero net force.
• That is, if ?F0, an object at rest remains at
  rest and an object moving with some velocity
  continues with that same velocity.
• By net force, this means the vector sum of all of
  the forces on an object.
• The tendency of an object to maintain its
  original state of motion is called INERTIA.
• MASS is the physical quantity that measures the
  resistance of an object to changes in its
  velocity due to a force.

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1.4.3 Newtons second law
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• The acceleration of an object is directly
  proportional to the net force acting on it, and
  inversely proportional to its mass.
• This means that the unit of force (N) is
  equivalent to 1 kg m/s2
• 1N?1kg m/s2

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1.4.3 Newtons 2nd law and the gravitational force
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• The force between two objects of mass m1 and m2,
  a distance r apart is given by
• Where G is the universal gravitational constant
• G6.67x10-11 Nm2/kg2

54
Summary of Newtons Second Law and the
Gravitational Force equation
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• Newtons Second Law
• The Equation for the gravitational force between
  two objects

Fg
Fg
m1
m2
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1.4.4 Weight and Mass
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• Let us put the constants for the earths mass and
  radius into the equation for the gravitational
  force
• We see that the quantity g, the acceleration
  due to gravity comes out of the equation
• On a planet with different m2 or r, the
  acceleration due to gravity would be different

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1.4.4 Weight and mass
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• We call the force acting on an object of mass
  m, the WEIGHT of the object.
• Thus the weight of an object is
• and this is a FORCE, with units Newtons (N).
• Note that this is different from the normal use
  of the word weight.
• An objects MASS (m) never changes, and is
  measured in kg. The objects WEIGHT (w) can
  change, if it is taken to a different planet, or
  to a different altitude on the earth.

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1.4.5 Newtons Third law
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• Forces in nature always exist in pairs.
• If two objects interact, the force F12 exerted by
  object 1 on object 2 is equal in magnitude and
  opposite in direction to the force F21 exerted by
  object 2 on object 1
• This is the same as saying that the action force
  is equal and opposite to the reaction force.
  Note that they act on different objects.
• F12 -F21

F12
F12
Object 2 (nail)
Object 1 (hammer)
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The normal force
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• Consider the forces on an object which rests on
  the ground.
• The object is pushing down on the earth with a
  force mg.
• The ground must be exerting a reaction force on
  the object, which is equal and opposite to the
  force of the object pushing on the earth.
• This reaction force is called the normal force.

n
Fmg
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1.4.6 Applications of Newtons laws
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• We will use many examples, where a rope or string
  joins two objects (in which we neglect the mass
  of the rope)
• The magnitude of the force exerted along the rope
  is called the tension, and is the same at all
  points in the rope

T
T
Rope
TT
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Free-body diagrams
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• These are diagrams where we draw only the objects
  of interest, and the forces acting upon them.
• One can then split the forces up into their
  components, and solve for the directions which
  are in equilibrium and those which are
  accelerating

n
CAR
Fg
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Solving Newtons Law problems
0
y
n

• Draw a Fee-body diagram
• Chose a set of coordinate axes
• Split the forces up into their x and y-components
• Work out which directions are in equilibrium, and
  which are accelerating.
• For equilibrium ?F0
• For non-equilibrium ?Fma

CAR
x
Fg
n
Fgx
x
Fgy
Fg
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1.4.7 Forces of friction
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• Imagine trying to drag an object across a rough
  surface.
• The force opposing your force is called the
  friction force.
• If you start by applying zero force to an object,
  and slowly increase the force, here is what will
  happen
• To begin with the object will not move, thus the
  friction force is equal to your applied force.
• At some critical force, the object will start to
  move.
• The object will then accelerate in the direction
  of the applied force.

Normal force n
Friction force f
Applied force F
Weight mg
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Forces of friction
0
Kinetic region
Static region
Friction force fk
Friction force fs
Applied force F
Applied force F
fsF
0
Static region
Kinetic region
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Forces of Friction
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• The force of static friction can take any values
• where ?s is the coefficient of static friction,
  and n is the normal force
• The force of kinetic friction takes the value
• where ?k is the coefficient of static friction.
• The values of ?k and ?s depend upon the surfaces
  which are in contact.
• In general, ?k is less than ?s .