Part  I. 

Part II. 1.  

Physics 407 Final Exam           

December 18, 2000

Closed book.  Do all questions. 

Part I.  Do all 8 questions. 5 pts each

Use: G = 6.7 x 10-11  Nm2/kg2 
Use: pi2  = 10

1.) The correct equation for the SHM (Simple Harmonic Motion) described in the graph is

  1. x = xm cos

  2. x = xm cos

  3. x = xm sin

  4. x = xm sin

2.  If the amplitude of SHM is increased from xm to 2xm the total energy is multiplied by:

  1. 1
  2. 2
  3. 4                                              

3.)  If the frequency of SHM is increased from  f to 2f   the total energy is multiplied by:

  1. 1
  2. 2
  3. 4

4.)  If a SHO (Simple Harmonic Oscillator) is at  x = xm for  t = 0, its equation for x(t) must be

 x(t) = ______________________________________ (Fill in the correct expression)

5.) A 2 kg mass oscillates with SHM with a frequency of  f =1.0 Hz and an amplitude of  xm = 0.30m.  Its total energy is: 

  1. 0.09 J
  2. 1.89 J
  3. 11.2 J
  4. 3.6 J                              

6.)  An object released from rest on the surface of a spherical asteroid of radius R = 500 km with no atmosphere accelerates downward toward the center of the asteroid with an acceleration of  a = 0.67m/s2.  The mass of the asteroid is:

  1. 5.0 x 1015 kg
  2. 2.5 x 1019 kg
  3. 2.5 x 1021 kg
  4. 6.4 x 1024 kg

7.) In a solid uniformly dense sphere of radius R, let us look at a small mass m at the point P. To compute the net gravitational force on m we have to use:      

  1. the entire mass of the sphere
  2. only the unshaded mass                 
  3. only the shaded mass
  4. none of the mass of the sphere

8.)  Each planet can be considered a satellite moving around the sun because the sun's attractive force is much larger than any other force on any given planet.

What is a constant for all planets?   Use: r = radius of planets' orbits  

                                                            T = period of planets' orbits

                                                            v = tangential speed of planets

  1. the sun's gravitational force on the planets
  2. r2/T3
  3. 2pir/T
  4. v2r

Part II. Do both problems. 30 pts each. BE NEAT. WRITE COMPLETE EQUATIONS. SHOW ALL YOUR WORK.

1.)    A high tech tower is built with its top one earth radius above the earth's surface.  Calculate the quantities that are requested below in terms of G, m, ME, and RE.  

Note: Neglect the Earth's rotation in this problem and neglect air friction!

  1. Calculate the acceleration of (the earth's) gravity in a lab at the top of the tower and the force exerted on an object of mass m. (10)
  2. Calculate the potential energy U_h at the top of the tower and U_G on the ground. (10)
  3. Calculate the kinetic energy K and the speed v of the object just before it strikes the earth.  (10)

2.)    A simple harmonic oscillator of mass 2.0 kg oscillates according to the equation: x = 4.0 cos
Note: The time t is given in seconds and the displacement x in m!


  1. the period in s (5)
  2. the frequency in Hz  (5)
  3. the amplitude in m (5)
  4. the angular frequency in rad/s (5)
  5. the maximum speed in m/s (5)
  6. the total energy in J (5)