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# 339 Class Note for PHYS 250 at PSU

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This 26 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at Pennsylvania State University taught by a professor in Fall. Since its upload, it has received 27 views.

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Date Created: 02/06/15

Chapter 2 Describing Motion Kinematics in One Dimension Equations of Constant Acceleration T equations we need to solve constant acceleration problems V0 v0 at Xe x0Vo Hid KinematicsDescription of Motion Reference Frames and Displacement Average Velocity lnstantaneous Velocity Acceleration Motion at Constant Acceleration Solving Problems Falling Objects Graphical Analysis of Linear Motion Galileo s discoveries of Jupiter s moons 1600 s with telescope showed that Earth was not the center of all orbits strongly supported a heliocentric model moons move back and forth across Jupiter He concludes they must be orbiting Jupiter Galileo 15641642 Demonstrated that Freely falling bodies move with constant acceleration Acceleration independent of mass Theory based on experimental observation Dynamics The Major Player Isaac NeWton 16421727 Develops Calculus to explain the theory of Mechanics and Gravitation Fzm From his general statements on motion he develops calculus and shows that 1 Planets follow elliptical motion 2 They sweep out equal areas in equal time conservation of angular momentum 3 From universal gravity he derives Kepler s 3lrd law Reference Frames and Displacement Any measurement of position distance or speed must be made with respect to a reference frame If you are sitting on a train and someone walks down the aisle their speed with respect to the train is a few miles per hour at most Their speed with respect to the ground is much higher Reference Frames and Displacement Distinction btwn distance and displacement Displacement blue line is how far the object is from its starting point regardless of how it got there Distance traveled dashed line is measured along the actual path Reference Frames and Displacement The displacement is written Left Displacement is positive 3 x1 x2 0 10 20 30 4 Distance m Copyrlghl 2005 Pearson Prenuce Ha c Right Displacement is negative 0 10 20 30 40 Distance m Average Velocity Speed how far an object travels in a given time interval Instantaneous Velocity The instantaneous velocity is the average velocity in the limit as the time interval becomes infinitesimally short a 60 em in 396 20 2 0 l l l 0 01 02 03 04 05 a Time h 360 These graphs show a g 0 A4 4 39 constant veIOCIty and b Le agEXe19 lty varying velocity g 20 gt O l I l I I l I 0 01 02 03 04 05 b Time h Copyright 2005 Pearson Prentice Hall Inc Acceleration Acceleration is the rate of chan e of velocity I change of velocity average acceleratlon t1me elapsed Acceleration 1 15 S at t 10 s V 15 kmh Copyright 2005 Pearson Prentice Hall Inc Acceleration Acceleration is a vector although in one dimensional motion we only need the sign The previous image shows positive acceleration here is negative acceleration 24 Acceleration There is a difference between negative acceleration and deceleration Negative acceleration is acceleration in the negative direction as defined by the coordinate system Deceleration occurs when the acceleration is opposite in direction to the velocity v2 50 ms v1 150 ms f w 7 uL I a Copyright 2005 Pearson Prentice Hall Incl 24 Acceleration The instantaneous acceleration is the average acceleration in the limit as the time interval becomes in nitesimally short Motion at Constant Acceleration The average velocity of an object during a time interval t is The acceleration assumed constant is Motion at Constant Acceleration In addition as the velocity is increasing at a constant rate we know that Motion at Constant Acceleration We can also combine these equations so as to eliminate t We now have all the equations we need to solve constantacceleration problems 1 Read the whole problem Then read it again 2 Decide on the objects under study and what the time interval is 3 Draw a diagram and choose coordinate axesref frame 4 Write down the known given quantities and then the unknown ones that you need to nd Solving Problems 5 Which equations relate the known and unknown quantities Solve algebraically for the unknowns and check dimensions 6 Calculate the solution and round it to the appropriate number of significant figures 7 Look at the result is it reasonable Does it agree with a rough estimate 8 Check the unitsdimensions again O O D 5 E 2 j N O O 9 TI D 13 9 3 r2 539 m I J 6 3 Falling Objects Copyright 2005 Pearson Prentice Hall Inc In the absence of air resistance all objects fall with the same acceleration although this may be hard to tell by testing in an environment where there is air resistance Acceleration HA I y0 y1490m After 100 s y2 m After 200 s 23 441 m After 300 s O 0 0 A E V 4 30 2 l b 0 1 2 3 s Copyright 2005 Pearson Prentice Hall Inc Falling Objects The acceleration due to gravity at the Earth s surface is approximately a g 980 msz Graphical Analysis of Linear Motion This is a graph of x vs t for an object moving with constant velocity The velocity is the slope of the xt curve Velocity 1 ms Graphical Analysis of Linear Motion On the left we have a graph of velocity vs time for an object with varying velocity on the right we have the resulting x vs tcurve The instantaneous velocity is tangent to the curve at each point 300 D 150 A B A 2 g 200 1 100 1 3 E I 4 E 100 a 5 0 C D J39Ax40 m At 40 s 0 I I I I I I I 1 l 1 1 I I I I 0 50 100 150 200 250 300 0 50 100 150 200 250 300 a Time 1 s b Time I 3 Copyright 2005 Pearson Prentice Hall Inc Velocity 7 ms Velocity 1 ms U1 O U o i U H O U o O Graphical Analysis of Linear Motion The displacement x is the area beneath the v vs tcurve a Time I S b Copyright 2005 Pearson Prentice Hall Inc

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