THE BALLISTIC PENDULUM PURPOSE This experiment is a simple

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THE BALLISTIC PENDULUM PURPOSE This experiment is a simple Powered By Docstoc
					                                                                            August 19, 2004
                            THE BALLISTIC PENDULUM


PURPOSE:

      This experiment is a simple illustration of momentum conservation and shows
how the ballistic pendulum may be used to measure a bullet's speed.


APPARATUS:           Pellet gun, shielded tube, and pendulum
                     Sonic Ranger
                     Low Voltage Power Supply
                     Advance Counter
                     Computer and Program Disk
                     Oscilloscope


INTRODUCTION:

       The ballistic pendulum is an apparatus which may be used to measure the speed of
a pellet. Alternatively, if the pellet speed can be measured independently, then the
momentum conservation law may be illustrated. The apparatus is sketched on page 7-2.

       The apparatus consists of a pellet gun which fires a pellet down an enclosed tube.
The tube contains two photogates which detect the passage of the pellet. The passage of
the pellet through the first photogate generates an electrical pulse which starts a counter.
The counter is stopped when the pellet passes through the second photogate. These
photogates are separated by 2.0 m. Consequently the velocity of the pellet is easily
calculated from the time interval displayed by the counter and the separation of the
photogates.

       When the pellet emerges from the enclosed tube, it enters a paper-filled pendulum
bob. The pellet momentum transferred to the pendulum bob results in the pendulum
executing simple harmonic motion. The horizontal amplitude, x(t), of the pendulum is
measured with a sonic ranger and a computer.




                                      Ball Pend-1
                                                                            August 19, 2004

                          90o
                      L                                        Lθ
                                                    (M+m),V
                            M,0                                  a

                                   m,v



       It is easy to show using momentum conservation that if θ is small, then the pellet
velocity is given by
                                      ⎛ M +m⎞
                                   v=V⎜     ⎟
                                      ⎝ m ⎠
where V is the pendulum velocity after the pellet has transferred its momentum to the
pendulum.

EXPERIMENT:

       The instructor will adjust the electronics and will also provide the pellets and
firing pin for the gun. You should start the data collection while the pendulum is
stationary and continue data collection until you have x(t) for at least 10 oscillations. If
your data is satisfactory, download it to a floppy disk. Remove the paper-filled pendulum
bob, determine its mass, i.e., (M+m), remove the pellet from the bob and determine its
mass, m.

ANALYSIS:

      From the data collected on the computer, you should be able to find the maximum
pendulum velocity and show that momentum is conserved. Also do an energy calculation
based on the velocity to show that it is not conserved. What energy loss has not been
accounted for? An error calculation is also required.




                                      Ball Pend-2
                                                                    August 19, 2004



Ballistic Pendulum Experiment – Supplemental Questions

      The answers to the following questions should be included in the
Discussion/Conclusions section of your report on the Ballistic Pendulum
Experiment.


        It is likely that in your analysis you have found, contrary to your
expectations, that the momentum is not conserved within error (by a small but
experimentally significant amount). This suggests that there is an important
systematic error that must be considered. What is likely the largest systematic
error present in this experiment? (HINT: using the timing gates you measured the
velocity of the pellet before it collided with the pendulum. When was the pellet
actually traveling at this measured speed?) Make an order of magnitude estimate
of the size of this systematic error and show that it can explain the apparent non-
conservation of momentum that you have (probably) observed.




                                  Ball Pend-3
                                                                     August 19, 2004



   WRITE-UP GUIDELINES FOR RESULTS SECTION OF BALLISTIC
                  PENDULUM EXPERIMENT

Your Results section on this report should contain the following:

1. A plot of your position vs. time data. Either indicate the equilibrium position or
plot the position as distance from equilibrium. Include all linear regression lines
used to estimate the velocities at the crossings of the equilibrium.

2. A table showing the amplitude and period of the oscillations and the velocity of
the pendulum at several passes through the equilibrium position.

3. Calculations of the velocity of the pendulum just after the collision (both
methods) and comparison of the two values. Show your error calculations as well.
You will have probably used a spreadsheet to carry out linear regressions. It is not
necessary to include a copy of this spreadsheet.

4. Estimate of the size of the dominant systematic error.

5. Discussion of how the calculations were carried out, how errors were estimated,
etc.

Page limit (entire lab - Results and Conclusions): 10




                                   Ball Pend-4

				
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