Chapter Two Notes: In-Class and From Text
Chapter Two Notes: In-Class and From Text Physics 125
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This 4 page Class Notes was uploaded by Nora Salmon on Thursday January 15, 2015. The Class Notes belongs to Physics 125 at University of Alabama - Tuscaloosa taught by Prof. Andreas Piepke in Fall2015. Since its upload, it has received 247 views. For similar materials see Physics 1 w/Calculus in Physics 2 at University of Alabama - Tuscaloosa.
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Date Created: 01/15/15
Chapter Two Motion in One Dimension Chapter Two Notes from Text 21 What is physics 0 Many principles many applications 0 In this chapter studying the motion of objects as they travel along a single axis onedimensional motion 22 Motion 0 The classification and comparison of motions is called kinematics Motion in one dimension is restricted in three ways It is along a straight line only whether the line is up down or diagonal does not matter but it must be straight Forces cause motion The moving object is either a particle a pointlike object such as an electron or an object that moves like a particle o This means that all the components of the object move the exact same direction and at the same rate ie a block of wood 23 Position and Displacement 0 An object s position is always described relative to a reference point Often this is the origin or zero point of an axis Two directions positive and negative 0 A change in an object s position is called displacement or Ax Ax xfmal ximtlal where final and initial refer to the object s final and initial positions Displacement is the shortest straightline distance between xinitial and Xfinal it is NOT a measurement of the actual distance covered by the object The absolute value of a displacement value is its magnitude 0 Displacement is a vector quantity which is a quantity that has both magnitude and direction 24 Average Velocity and Average Speed 0 A common way to describe an obj ect s position is with a positiontime graph Position is on the yaxis vertical and time is on the xaxis horizontal Plotting points on a positiontime graph creates a line the slope of that line is the average velocity of the particle or object It is a ratio of displacement that occurs during a certain time interval Ax xz xl 0 v 7 9 At tz t1 Chapter Two Motion in One Dimension 0 An obj ect s average speed savg is a different quantity than average velocity I While average velocity involves an object s displacement average speed involves the total distance an object covers independent of direction total distance I Savg At I Because average speed neglects direction it is NOT a vector quantity 25 Instantaneous Velocity and Speed 0 The phrase how fastquot most commonly refers to how fast at a given instantquot I This is called instantaneous velocity v Instantaneous velocity is the limit of a particle s average velocity as the time interval measured approaches zero Ax O U llmAt0 E o In other words the instantaneous velocity of a particle or object is the derivative of an object s change in position with respect to time I It is the rate at which an object s position is changing at any specified instant o Instantaneous speed is the magnitude of velocity it is a measurement of how fast something is travelling while neglecting in which direction the particle is travelling 26 Acceleration 0 A particle accelerates when its velocity changes I For 1dimensional motion a particle s average acceleration over time is given by the equation 122 121 Av tz vl A t The instantaneous acceleration of a particle is the derivative of its velocity with respect to time o This means that a particle s acceleration at any single instant is the rate at which its velocity is changing I Acceleration is a vector that has both magnitude and direction therefore an object can accelerate positively or negatively I Constant Velocity Scenario when an object s velocity is constant its acceleration is O I The acceleration of an object in free fall on earth due to gravity is 98 ms2 0 Acceleration velocity and speed I If the signs of a particle s acceleration and velocity are the same negative velocity and a negative acceleration for example the particle s speed increases aavg Chapter Two Motion in One Dimension I If the signs of a particle s acceleration and velocity are opposite the particle s speed decreases In this case the directions of the acceleration and velocity oppose one another decreasing the speed 27 Constant Acceleration 0 When a particle s acceleration is constant its average and instantaneous accelerations are equal I There is a special equation for this case 1Hquot which can be written as v 120 at I another equation utilizing constant acceleration and position is x xo v0t at2 I See pg 24 in the textbook for an example utilizing these equa ons 28 Mathematical derivation of the constant acceleration equation 29 FreeFall Acceleration 0 Objects in a vacuum accelerate at a constant rate which is called free fall acceleration I This is the same for ALL objects regardless of characteristics like mass shape and density I It has a negative value because it applies to objects falling or moving in the negative direction on the yaxis o Freefall motion I On its way up the object s velocity decreases until at the apex of its ight v0 ms I On its way down the object s velocity increases 0 Displacement if the object is thrown straight up the displacement at the end of its ight will be 0 it returns to where it started 210 Graphical integration motion analysis 0 You can integrate the acceleration graph to find velocity I Take the definite integral of a certain time period to find a specific velocity I Take the indefinite integral of the acceleration graph to find a governing equation for which you can plug in any time period to find the object s velocity I Sample problem on pg 28 0 You can integrate the velocity graph to find position Chapter Two Class Notes Time is what clocks measurequot Albert Einstein 0 To talk about motion we must define space and time I Space is 3D and boundless I Time is 1D I Space Time boundless 4D continuum Chapter Two Motion in One Dimension 0 In classical physics time is an invariant quantity that has absolute meaning Motion a change in position 0 Motion is described with kinematics I Objects in motion follow a trajectory or path in space This can be plotted on a Cartesian coordinate plane 0 The Galilean Principle of Relativity all observers must find the same law of classical physics mechanics no one system is better than another 0 Kinematics vs dynamics I Kinematics how objects move I Dynamics why objects move Describing motion 0 Displacement how far an object travelled from its starting point I This is not the same as distance travelled I Displacement is a vector quantity while distance travelled is scalar and ignores the direction of motion I Speed and velocity Avg speed distance travelledtime Avg velocity displacement time o Instantaneous velocity the derivative of a positiontime graph at any specific point I Derivative of position with respect to time o Acceleration rate of change of velocity I Vector quantity I Average acceleration change in velocityjtime I Instantaneous acceleration derivative of velocity with respect to time