Physics 121 April 3 2008 Equilibrium and Simple Harmonic Motion Frank L H Wolfs Department of Physics and Astronomy University of Rochester Physics 121 April 3 2008 Course Information Topics to be discussed today Requirements for Equilibrium a brief review Stress and Strain Introduction to Harmonic Motion Frank L H Wolfs Department of Physics and Astronomy University of Rochester Physics 121 April 3 2008 Homework set 7 is due on Saturday morning April 5 at 8 30 am This assignment has two components WeBWorK 75 Video analysis 25 you can calculate the angular momentum quickly by using the expression for the vector product in terms of the components of the individual vectors the x and y components of the position and velocity of the puck Homework set 8 is now available This assignment contains only WeBWorK questions and will be due on Saturday morning April 12 at 8 30 am Exam 3 will take place on Tuesday April 22 Frank L H Wolfs Department of Physics and Astronomy University of Rochester Comments on Homework 7 Rolling motion causes much confusion Two views of rolling motion 1 Pure rotation around the instantaneous axis or 2 rotation and translation Frank L H Wolfs Department of Physics and Astronomy University of Rochester Comments on Homework 7 Rolling motion causes much confusion Note friction provides the torque with respect to the center of mass Frank L H Wolfs Department of Physics and Astronomy University of Rochester Homework 8 Due Saturday April 12 2008 All problems in this assignment are related to equilibrium In all cases you need to identify all forces and torques that act on the system Remember to choose the reference point in a smart way Frank L H Wolfs Department of Physics and Astronomy University of Rochester Physics 121 Quiz lecture 20 The quiz today will have 3 questions Frank L H Wolfs Department of Physics and Astronomy University of Rochester Equilibrium a quick review An object is in equilibrium is the following conditions are met Net force 0 N first condition for equilibrium This implies p constant and Net torque 0 Nm second condition for equilibrium This implies L constant Conditions for static equilibrium p 0 kg m s L 0 kg m2 s Frank L H Wolfs Department of Physics and Astronomy University of Rochester Equilibrium Summary of conditions a quick review Equilibrium in 3D F F F x 0 y 0 and z 0 x 0 y 0 z 0 Equilibrium in 2D F F x 0 y 0 z 0 Frank L H Wolfs Torque condition must be satisfied with respect to any reference point Department of Physics and Astronomy University of Rochester Stress and strain The effect of applied forces When we apply a force to an object that is kept fixed at one end its dimensions can change If the force is below a maximum value the change in dimension is proportional to the applied force This is called Hooke s law F k L This force region is called the elastic region Frank L H Wolfs Department of Physics and Astronomy University of Rochester Stress and strain The effect of applied forces When the applied force increases beyond the elastic limit the material enters the plastic region The elongation of the material depends not only on the applied force F but also on the type of material its length and its cross sectional area In the plastic region the material does not return to its original shape length when the applied force is removed Frank L H Wolfs Department of Physics and Astronomy University of Rochester Stress and strain The effect of applied forces The elongation L specified as follows 1 F L L0 E A where can be L0 original length A cross sectional area E Young s modulus Stress is defined as the force per unit area F A Strain is defined as the fractional change in length L0 L0 Frank L H Wolfs Note the ratio of stress to strain is equal to the Young s Modulus Department of Physics and Astronomy University of Rochester Stress and strain Direction matters Frank L H Wolfs Department of Physics and Astronomy University of Rochester Stress and strain A simple calculation could have prevented the death of 114 people Frank L H Wolfs Department of Physics and Astronomy University of Rochester Stress and strain A simple calculation could have prevented the death of 114 people Initial Design Actual Design Credit http www glendale h schools nsw edu au faculty pages ind arts web bridgeweb Hyatt page htm Frank L H Wolfs Department of Physics and Astronomy University of Rochester And now something completely different Harmonic motion We will continue our discussion of mechanics with the discussion of harmonic motion simple and complex This material is covered in Chapter 14 of our text book Chapter 14 will be the last Chapter included in the material covered on Exam 3 which will cover Chapters 10 11 12 and 14 Note We will not discuss the material discussed in Chapter 13 of the book dealing with fluids and this material will not be covered on our exams Frank L H Wolfs Department of Physics and Astronomy University of Rochester Harmonic motion Motion that repeats itself at regular intervals Frank L H Wolfs Department of Physics and Astronomy University of Rochester Simple harmonic motion Phase Constant Amplitude x t Acos t Angular Frequency Frank L H Wolfs Department of Physics and Astronomy University of Rochester Simple harmonic motion Instead of the angular frequency the motion can also be described in terms of its period T or its frequency The period T is the time required to complete one oscillation x t x t T or Acos t Acos t T In order for this to be true we must require 2 The period T is thus equal to 2 The frequency is the number of oscillations carried out per second 1 T The unit of frequency is the Hertz Hz Per definition 1 Hz 1 s 1 Frank L H Wolfs Department of Physics and Astronomy University of Rochester Simple harmonic motion The frequency of the oscillation is the number of oscillations carried out per second 1 T The unit of frequency is the Hertz Hz Per definition 1 Hz 1 s 1 Frank L H Wolfs Department of Physics and Astronomy University of Rochester Simple harmonic motion What forces are required Consider we observe simple harmonic motion The observation of the motion can be used to determine the nature of the force that generates this type of motion In order to do this we need to determine the acceleration of the object carrying out the harmonic motion x t Acos t v t a t Frank L H Wolfs dx dt dv dt d Acos t Asin t dt d Asin t 2 Acos t 2 x t dt Department of Physics and Astronomy University of Rochester Simple harmonic motion