2011 Honors Vibrations and Waves

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					2011 Honors Notes Chapter 13


                            Vibrations and Waves
   1. How does the force on a spring is related to the distance a spring is stretched?




          a. What is Hooke’s Law?




          b. If a spring is cut in half, what happens to its spring constant?



          c. If you know the force on the block below, how can you determine the
             acceleration of the block? Is it constant?




          d. For each of the pictures draw the force and acceleration directions. Label
             the equilibrium point and the amplitude. In which picture is the force
             maximum? Minimum?
2011 Honors Notes Chapter 13


   2. What is the period of the motion?




          a. Through what total distance does the block travel in one period?
                   A/2             A              2A              4A


   3. What is the frequency of the motion?




   4. The motion of Earth going around the Sun is
      periodic with a period of 1 year. Is this motion
      simple harmonic?




   5. How is it possible to find the work done by a variable force?




          a. What is the potential energy stored by a spring?
2011 Honors Notes Chapter 13


           b. What does the potential energy change to as the block moves?




           c. Is mechanical energy conserved in this system?




           End


                    0

                  midpoint


                    0


                             End


                    0
Fill in the chart with constant, max or zero

             Velocity     Kinetic      Potential    Force      Acceleration ETotal
                          Energy       energy
mid

End


   6. Find the velocity as a function of the position.
2011 Honors Notes Chapter 13


                7. A mass of 0.5 kg oscillates with amplitude of 0.2 meters on a
                   horizontal spring with spring constant of 100 N/m.
                       a. What is the total energy?




          b. What is the velocity at a position of 0.1 meters from equilibrium?




   8. A slingshot consists of a light leather cup, containing a stone that is pulled back
      against two parallel rubber bands. It takes a force of 15 N to stretch either one of
      these bands 1.0 cm.
          a. What is the potential energy stored in the two bands together when a 50 g
              stone is placed in the cup and pulled back 0.20 m from the equilibrium
              position?




          b. With what speed does the stone leave the slingshot?




   9. At an outdoor market, a bunch of bananas is set into oscillatory motion with an
      amplitude of 20.0 cm on a spring with a spring constant of 16.0 N/m. It is
      observed that the maximum speed of the bunch of bananas is 40.0 cm/s. What is
      the weight of the bananas in Newton’s?
2011 Honors Notes Chapter 13


      10. Comparing simple harmonic motion with uniform circular motion




            a. Draw a clock hand at 1 o’clock.




            b. Draw a line from the end of the clock hand to the x axis. Describe the
               motion of the point on the x-axis as the clock hand travels
               counterclockwise.




            c. Relate the amplitude (the length of the clock hand) of the motion to the
               position of the point on the x axis.




            d. Draw a graph of the position of the point on the x axis as a function of
               time.
    xmax
x
                                                       t

                     ½T                 T
-xmax
-


            e. Write the equation for the two motions given in class.
2011 Honors Notes Chapter 13



          f. What if the blocks don’t travel at the same angular velocity?




          g. Substitute angular displacement to relate to angular velocity/frequency.
             Substitute in for angular velocity/frequency so that it is terms of period.




          h. Write the equations for the two motions given in class.




          i. What if the motion starts with an angular displacement?




          j. Write the equations for the two motions given in class.
2011 Honors Notes Chapter 13



    11. The position of a 0.2 kg object attached to a spring is described by
                           x= (0.5m) cos(0.5πt+π/2)
           a. What is the position of the object at 2 seconds? At 0 seconds?

            b. What is the spring constant?


            c. What is the frequency?



    12. Start with the velocity equation as a function of position. Find velocity as a
        function of time.




            a. Graph velocity as a function of time.


    vmax
v
                                                       t

                     ½T                 T
    -vmax



    13. How is angular velocity/frequency related to the spring constant and mass?
2011 Honors Notes Chapter 13


   14. Find the period of simple harmonic motion.




   15. Find the period of a simple pendulum.

             
             




   16. A pendulum clock that works perfectly on Earth is taken to the Moon. Does it run
       fast or slow there?
2011 Honors Notes Chapter 13


   17. A simple pendulum is 5.00m long.
           a. What is the period of simple harmonic motion for this pendulum if it is
              located in an elevator accelerating upward at 5.00 m/s2?




              b. What is the period if the elevator is accelerating downward at 5.00 m/s2?




   18. What is a wave?




   19. What is a medium?




   20. What is an example of waves transferring energy?




  21. Types of Waves
               Mechanical Waves                         Electromagnetic waves
Mediums

What
oscillates?
Examples
2011 Honors Notes Chapter 13



   22. Types of Mechanical Waves

                Longitudinal Waves        Transverse waves
Mediums

Direction of
oscillations
Examples



   23. Describing waves
          a. Frequency




           b. Amplitude




           c. Wavelength




           d. Wave speed




   24. How are the terms above related?
2011 Honors Notes Chapter 13


   25. In a long line of people waiting to buy tickets at a movie theater, when the first
       person leaves, a pulse of motion occurs as people step forward to fill in the gap.
       The gap moves through the line of people. What determines the speed of this
       pulse? Is it transverse or longitudinal?




   26. Speed of waves on strings




   27. In mechanics, massless strings are often assumed. Why is this not a good
       assumption when discussing waves on strings?




   28. A simple pendulum consists of a ball of mass 5.00 kg hanging from a uniform
       string of mass 0.060 kg and length L. If the period of oscillation for the pendulum
       is 2.00s, determine the speed of a transverse wave in the string when the
       pendulum hangs vertically.
2011 Honors Notes Chapter 13


   29. Interference of Waves
           a. Constructive interference




          b. Destructive interference




   30. Reflection of waves
          a. What happens at a fixed end?




          b. What happens at a free end?

				
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