Ballistic Lab MechII

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August 19, 2004

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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 ofthe 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.


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Ball Pend-2

(M+m),VM,0

L

90o

m,v

a

L

It is easy to show using momentum conservation that if is small, then the pellet

velocity is given by

m

m+MV=v

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 pendulumbob, 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.


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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.

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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 notnecessary 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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Ballistic Lab MechII