Practice Exam III

This practice exam is made up from parts of several exams that were given in the past to match the structure of your text.  It is long, but working through it will help you to prepare for the exam.

A few topics that might be on your exam, such as decibels are not on this exam.  I'll save the easy problems for your exam instead of putting them here.

For Chapter 17, be able to work problems that are the cousins of Examples, 17-2, 17-4 and 17-7.

1.  What is meant by the term:

  • conservative force
  • underdamped harmonic motion
  • overdamped harmonic motion
  • critically damped harmonic motion
  • resonance
  • amplitude
  • period

2.  What is the necessary and sufficient condition for Simple Harmonic Motion to occur? Do these conditions place any restrictions on the possible amplitudes of the motion of the object?

3.  Describe the three cases where the work done on an object is zero.

4.  Given a graph of a force versus position.  How would you find the work done by the force?

5.  What happens to the acceleration of a spring-mass system if the mass is doubled and the spring constant is quadrupled?

6.  Assume the local value of g is 9.8065 m/s2. What would be the length of a simple pendulum with a period of 1.0000 minute?

7.  A frictional force of 0.45 N causes a moving object to come to rest after traveling 23 m. What was the kinetic energy of the object? (assume the PE to be unchanged during the process.)

8.  An 1100 kg automobile is traveling at 20 m/s when the driver accelerates to 30 m/s in order to pass another car. How much net work was done on the car?

9.  How much mass is required to cause an oscillation with a period of 2 seconds when the mass is attached to a spring of constant 300 Nt/m?

10.  A system is experiencing Simple Harmonic Motion with a period of .4 s. At time t = 0, the mass is at rest and is located at it's maximum displacement of 0.23 m. Determine:

(a) The equation for the position at any time t.

(b) The maximum value of the velocity of the mass.

(c) The position, velocity and acceleration at time t = 0.123 s.

11.  A simple harmonic oscillator has an angular frequency of 12 rad/sec.  At t=0, its position is 9.1 cm and its velocity is 0 cm/s.  State x as a function of time.

12.  An oscillating mass-spring system has a spring constant of 45 N/m and a total energy of 100J.  a) What is its amplitude of motion?  b) How much kinetic energy does it have when it is halfway back to its equilibrium position?

13.  A 1000 kg car can accelerate from 0 to 20m/s in 6 seconds.  What is the average power produced by the engine?

14.  A man pushes a mop 3.5 meters across the floor.  He applies a force of 15 N.   The mop handle makes an angle of 60 degrees with the floor.  How much work does he do?

15.  A toy rifle fires plastic bullets (m = 5g) using a spring mechanism.  When the gun is loaded, the spring (k=50N/m) is compressed 5 cm.  The gun is held at a 30 degree angle and fired.  The bullet moves 35 cm along the barrel of the rifle before leaving the gun.  Assume there is no friction between the bullet and the rifle barrel.   Draw before and after work-energy bar charts for this situation (where "after" is just after it leaves the barrel).  How fast is the bullet moving when it leaves the gun?  Now assume there is a friction force of 0.3N between the rifle barrel and the bullet.  How does the bar chart change?

17.  A 1000 kg cart on a roller coaster is 30 m above the ground and traveling at 8 m/s. Assuming that friction is negligible, determine the following:

(a)  The total mechanical energy of the roller coaster cart.

(b)  The height of the highest hill that it can pass over.

(c) The speed of the cart when it is 2 m above the ground.

 

19.  The position of a  mass oscillating on the end of a spring can be described by the equation below.

        x(t) = 0.25 sin (3.4t )  where x is in centimeters and t is in seconds.

    What is the

  1. amplitude
  2. frequency
  3. period
  4. maximum acceleration
  5. positioin at t= 10 seconds

 

  • Discuss the Superposition Principle.
  • Compare and contrast Wavelength and Period of a periodic wave. In what ways are they similar and in what ways are they very different?
  • Sketch the third harmonic wave for the following organ pipe. Label the nodes and anti-nodes. (3 points)

    •  

     

 

  • Define: longitudinal wave, transverse wave, wave number, diffraction
  • What is the rotational equivalent of each of the following: mass, force, momentum, position
  • When does refraction occur?
  • When a sound wave travels from one place to another, what is transported? Explain.
  • The distance from equilibrium to the top of the crest of a periodic wave is called its
    • a. frequency
    • b. period
    • c. amplitude
    • d. wavelength
    • e. none of the above
  • Two point sources produce waves of the same wavelength and are completely in-phase (that is both sources produce crests at the same time). At a point that is 0.25 wavelength closer to one source than the other, you would expect to find an oscillation with
    • a. an amplitude equal to twice that of one wave alone
    • b. an amplitude equal to that of one wave alone
    • c. an amplitude that is 4 times that of one wave alone
    • d. an amplitude that is approximately zero
    • e. none of the above

 

    1.  The frequency of TV channel 2 is 54 megaHertz. The speed of EM waves is 3x108 m/s. What is the wavelength of a channel 2 EM wave?

    2.  A guitar string is 1.2 m long and has a mass of 9.7 grams. What must be the tension in the string to obtain a wave speed of 432 m/s?

    3.  Assume that you are 15.9 m away from a 500 watt street lamp. What is the intensity of the light at your location?

4.  The separation between the center maxima and first minima in a double slit experiment is .25 cm. The wavelength of the light is 628 nm, and the screen is 1.3 m away from the slits. What is the separation of the slits?

5. Red light from a laser (640 nm) passes through a single slit which is 2mm wide.   How far from the center of the screen is the third minimum if the screen is 3 meters away from the slit?

 

1.  The equation of a transverse wave traveling along a very long string is given by

        y(x,t) = .02 sin (3x +4t )  where x and y are in meters and t in seconds.

What is the a) amplitude, b) wave number, c) wavelength, d) angular frequency, e) direction of propagation, f) velocity of the section of the rope located at x=.2m at the instant t=.9 seconds, and g) the tension in the string if its linear density is .0026 kg/m?

2.  What is the longest wavelength that can be produced by a 2m organ pipe that is open at both ends?  What is the frequency of the fundamental and the fourth harmonic? 

3.  A diffraction grating is made up of slits of width 200nm which are 1,200 nm apart.   a) When light of wavelength 500nm passes through the grating, at what angle does the first (not counting the central one) maximum appear?  How many orders will be visible?

4.  A disk is rotating on a frictionless shaft of negligible radius.  The disk has a mass of 440 g and a radius of 3.0 cm. It is rotating at 180 rad/s.   Another disk that is initially not rotating is dropped on top of it and frictional forces act to bring the two disks to a common rotational speed.  If the second disk has a mass of 270 g and a radius of 2.0 cm, what is the final angular speed of the two disks?  (for a disk I = 1/2 m r2)

7.  A 0.40 meter diameter grinding wheel (I=0.80 kg m2) is spinning at 240 rev/min.  A torque of 10 N-m is applied to slow it down.  a) What is its final angular momentum, if the torque is applied for 2.0 seconds?  b) If the torque is created by a force of 60 N applied to the rim of the wheel, at what angle is the force applied?  c)  What is the acceleration of the wheel during the two seconds?   d)  How many revolutions did the wheel make during the two seconds?