Kinematics in one dimension

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Kinematics in one dimension

• What is your frame of reference?
• Motion is relative.
• Reference frame the background from which
  speed, velocity, location, and time, is
  measured.
• Also grades, and how well off you are, and does
  your family have a cool car.

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Speed distance / time How fast are they going?
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How fast

• How fast is the man going relative to the plane?

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Speed

• Speed is how fast something is going
• magnitude only.
• It is the distance traveled divided by the time
  interval during which the motion occurred
• SI units are meters and seconds or m/s
• Average speedd/t
• Meters / second

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To signify the change in something

• We use delta
• Change in velocity can be also written as
• Final initial

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How fast can you run

• Speed equals
• the change in distance over a given time

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Make a graph from the tableWhat does the slope
of the graph represent?
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Instantaneous speedAverage speed

• The speed at any instant
• In your car your speed is measured
  instantaneously by your odometer
• Average speed will be the final distance minus
  the initial distance divided by the time
  involved.

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• We signify average with a bar over the SI unit

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Remember the SI prefixes and base units

• 16 kilo 1,000 meters
• 100 Centimeters 1 meter
• 1,000millimeter 1 meter
• Speed will usually be measured in
• Meters per second or m/s

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Velocity

• Velocity is a quantity describing both speed
• and direction
• Frame of reference makes a big difference
• Compare speed and velocity.
• What is the difference???

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Constant velocity

• Must have not only constant speed
• Must also have same direction
• An object changing direction has a change in
  velocity

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Average velocity

• Average velocity is the change in distance over a
  set period of time.
• You give an example.
• The formula is written as shown

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Acceleration

• The rate at which the
• Velocity is changing
• Can be positive or negative
• Is it directional?

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Acceleration

• Acceleration is the change in velocity divided by
  the time interval in which the change occurred.

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Free Fall on earth

• All matter is attracted by all other matter
• Free fall means only gravity is affecting the
  object
• We are ignoring air resistance
• Elapsed time is ___________
• At the earths surface

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Change in velocity
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Acceleration in Meters per second square

• SI units are (meters per second squared)
• Acceleration due to gravity at the earths
  surface is 10 meters per second every second

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Rules

• If the acceleration is positive then the velocity
  is increasing. If acceleration is negative then
  the velocity is decreasing.
• A change in direction is a change in acceleration
  whether or not your speed changes

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More rules

• If velocity is constant, acceleration is 0
• A change in acceleration will cause the distance
  time graph to be curved.
• A constant acceleration will result in a linear
  increase in velocity.

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Free fall (no air resistance)

• Instantaneous velocity
• of an object falling from rest
• after an elapsed time t can be
• expressed in meters
• per second, where
• g 10m/s every second

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Graphing

• The slope of the distance /time graph is the
  velocity
• If the velocity is constant (not changing) the
  graph of the distance/ time will be a straight
  line
• If there is acceleration the distance/time graph
  will be curved

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Constant acceleration

• Using calculus Newton found that given constant
  acceleration (gravity)
• Distance equals ½ the acceleration times the time
  involved squared

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Constant velocity, no acceleration
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Constant Acceleration
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Constant accelerationSlope of the velocity /
time

• Increasing velocity
• Constant acceleration
• Distance will increase
• in a curved line

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Chapter 3 Projectile Motion

• Chapter 2 was Linear motion
• in one plane
• either constant velocity and no acceleration or
  accelerated motion
• Chapter 3 is Non linear motion in a curved path
• Two components
• Vertical or y axis
• Horizontal or x axis

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Scalar vs. vector quantities

• Scalar is magnitude only. Examples mass

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Soh Cah Toa

• Pythagoras Theorem - a2 b2 c2 Sine Rule -

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Resolving Vectors

• To add two vectors, it is necessary simply to put
  the one vector directly after the other. The
  third vector then completes a triangle, which is
  the resultant vector if the other two are added
  together. This can be found using Pythagoras'
  Theorem if the triangle is a right-angled
  triangle, or the sine and cosine rules if it is
  not.

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Projectile Motion

• Follow a curved path
• Look at horizontal path independently of vertical
  
• If no air resistance or other force is present
  horizontally the horizontal velocity remains
  constant
• Vertical velocity will be affected as in chapter
  2 by 10 m/s squared

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Projectile motion

• Consider the vertical component independent of
  the horizontal component
• To calculate the time in the air use formulas
  D1/2 gt squared
• and vgt
• Find the vertical hang time and the use this to
  calculate the horizontal distance

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Range x axis

• Horizontal ranges the same if the sum of the
  degrees is 90
• Example a projectile at 30 will have the same
  range as one that is at 60
• Do an example using 20 m/s

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Satellites

• Projectiles that are traveling fast enough to
  fall or circle around the earth are satellites
• Example is 8km/s at altitudes of 150 km
• Force of gravity at that altitude is almost the
  same as on earth
• No or little air

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Horizontal and vertical components

• Vertical component use
• sin function

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Momentum PMV

• It is a vector
• Direction counts
• Once you go
• the wrong way
• you will keep going
• the wrong way!

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Momentum

• Momentum a quantity defined as the product of an
  objects mass and its velocity.
• Momentum has direction like velocity.
• Momentum mass times velocity
• Momentum pmv

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Momentum out of control

• Going too fast
• Going in the
• wrong direction

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Conservation of ?

• Conservation of momentum The total amount of
  momentum in a system is conserved.
• Other conservations of ?

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Bouncing off?

• Items may bounce off each other but the total
  momentum is conserved.
• They may collide and have the same total momentum
  after the collision as before.

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Conservation of ?

• Conservation of momentum The total amount of
  momentum in a system is conserved.
• Other conservations of ?

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Calculate mass

• Conversion of lbs. to kg
• One pound .45 kilograms
• One kilogram 2.2 pounds
• Good site http//www.easysurf.cc/cnvert.htm
• One foot .3 meters
• One meter 3.28 feet

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Calculate momentum
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Why does the earth still spin
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Momentum is of two kinds, angular and linear. 
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Angular momentum

• Angular momentum is the tendency of a rotating
  object to keep rotating at the same speed about
  the same axis of rotation. 
• angular velocity (symbol w), measured in radians
  per second (a radian is about 1/6 of a full
  circle -- there are 2p radians in a full
  circle). 

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• the magnitude of the angular momentum in this
  case is L mvr, where L is the angular momentum,
  m is the mass of the small object, v is the
  magnitude of its velocity, and r is the
  separation between the objects

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Angular momentum (spin)

• Angular momentum is conserved
• Why do you go faster when you pull in arms?

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Calculate angular momentum
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Formulas you must know.

• Distance equals average velocity times time
• Distance equal
• One half acceleration
• Times time squared

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• Momentum equals mass times velocity
• One hour 3,600 seconds
• 1km 1,000 m

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Balanced forces? Acceleration?
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Acceleration
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Graphs of acceleration, distance and velocity
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Force

• Force The cause of acceleration, or change in
  an objects velocity

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Newtons
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Forces balance
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Net force

• Usually there are many forces acting on an object
  at the same time.
• What are some of those forces on you?
• Net force the combination of all of the forces
  acting on an object. Direction is important.
• An object accelerates in the direction of the net
  force, and the acceleration will be the force
  divided by the mass.

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Unbalanced forces

• the net force will cause the object to move.
• If forces are balanced there is no acceleration

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Draw in the other forces to balance this car

• Gravity
• Forces on the
• Wheels
• To make the car
• accelerate

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Unbalanced forces and momentum

• http//www.regentsprep.org/Regents/physics/phys01/
  accident/default.htm
• Car crashes forces and momentum

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Friction

• Friction is a force that is created whenever two
  surfaces move or try to move across each other.
  It opposes the motion of either object
• Friction is dependant on the texture of both
  surfaces.
• Friction is also dependant on the amount of
  contact force pushing the two surfaces together
  (normal force).

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Friction slows us down
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Incline plane and gravity
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Friction
For Objects in Motion Kinetic Friction f mkn

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Some values for the coefficient of friction

• avg. tire-on-dry pavement 0.9
• smooth tire-on-wet pavement 0.5
• glass-on-glass 0.9
• metal-on-metal (dry) 0.6
• metal-on-metal (lubricated) 0.1
• steel-on-Teflon 0.05

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Air resistance

• Air resistance is a form of friction.
• Surface area shape, speed, and turbulence cause
  increases in air resistance

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Gravity
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Newton's Law of Gravity

• Each object in the universe attracts each other
  body. If object A has mass Ma and object B has
  mass Mb,then the force F on object A is directed
  toward object Band has magnitude
• F G Ma Mb / r2

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Gravity

• The force of attraction between two particles of
  matter due to their masses.
• The law of universal gravitation acts upon all
  the objects in the universe.

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• Where G is the gravitational universal constant
  and m represents the mass of the two objects
  being attracted and d is the distance that they
  are apart.

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• Acceleration of gravity at the surface of the
  earth is - 9.81 m/sec. sec.
• Free Fall The motion of a body when only the
  force of gravity is acting on it.

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We are all attractive
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Weight versus mass

• Weight mass times free fall acceleration.
• On land weight influences shape of the organism.
  Why not in water.
• Weight in space is ?

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Terminal velocity

• Terminal velocity when the
• Air resistance
• Force of gravity
• Balanced forces
• No acceleration

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• Terminal Velocity the maximum velocity reached
  by a falling object that occurs when the
  resistance of the medium is equal to the force
  due to gravity.
• Velocity will be constant once the force are in
  balance and terminal velocity is reached.

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Jumping out of a plane

• First out of plane accelerate
• Terminal velocity

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De acceleration when the chute opens
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• Archimedes principle The buoyant force on an
  object is equal to the weight of the fluid
  displaced by the object.
• Why do steel boats float?

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Newtons three laws

• Newton First Law of Motion An object at rest
  remains at rest and an object in motion maintains
  its velocity unless it experiences an unbalanced
  force.

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Inertia

• Inertia the tendency of an object to remain at
  rest or in motion with a constant velocity.

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Newtons Second Law

• Newtons Second Law The unbalanced force acting
  on an object equals the objects mass times its
  acceleration.

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Newtons third law

• Newtons third law For every action force, there
  is an equal and opposite reaction force.

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Newtons second law
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Newton's the measurement of force

• Units are Newton's which equal kilograms meters
  per second squared.
• One Newton equals .225 pounds.

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Why hydraulics work

• Pascals principle When force is applied to a
  confined fluid, an increase in pressure is
  transmitted equally to all parts of the fluid.
• The pressures must be the same
• Pressure Force / Area
• Force Pressure times Area

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How to lift a massive item

• The small
• Cylinder will move
• Further than the
• Large cylinder

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Why a planes wings work

• Bernoullis principle the pressure exerted by a
  moving fluid is less than the pressure of the
  surrounding fluid.
• A faster moving fluid (air) has less pressure.
• Air must move faster (go further) on the top
  surface of the wing, therefore the pressure is
  less.

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Bernoulli's law and airplane wings
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Net force of the wing is up
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Must know

• Velocity versus speed, motion
• Distance, velocity and acceleration
• Momentum
• Friction
• Gravity
• Terminal velocity
• All of Newtons laws
• PASCAL's laws and Bernoullis