### : Lab 2: Gauss Gun Conservation of Momentum, Work and Energy

```Physics 15a
Lab 2: Gauss Gun
Spring 2008
: Lab 2:
Gauss Gun
Conservation of Momentum, Work and Energy
Introduction
In this lab you will explore the Gauss gun, an interesting physical system that will give
you the opportunity to explore the notions of work, energy and conservation of
momentum.
The Gauss Gun is made up of magnets and steel ball bearings, and it can be used to
shoot the ball bearings at high speeds. There are many videos on YouTube about these
devices, for instance, take a look at this one: http://www.youtube.com/watch?
v=zZmCJ5eZlmo .
The details are complicated because they involve magnetic forces, which will not be
covered in this course. However, the momentum conservation does not depend on the
details of the interaction, so we can just look at the initial momentum and the final
momentum and compare them.
Although, the physics laws responsible for the interaction of the magnet and balls is
unknown to us, we can tell that there is energy associated with that interaction. It
appears that the magnetic interaction can be a source of kinetic energy, so there must
be a potential energy that gets transformed into kinetic energy.
Even though we don't have a way of measuring energy directly, we can use our
understanding of work to get at the potential energy by measuring the magnetic force
at different distances. Once we know the energies, we can explain why the kinetic
energy changes so much in the operation of the Gauss gun.
Lab Goals
I.
Explore an unfamiliar system using the concepts learned in class
II.
Study conservation of momentum, given the experimental uncertainties
III. Understand the relationship between work and force
IV. Understand the relationship between work and energy
V.
Learn how to use the video analysis capabilities of Logger Pro
Prelab Assignment
You should read through this lab handout in its entirety before your lab session. Also,
please take a look to the Lab Companion to remind yourself of what we learned last
time about significant figures and error propagation.
Do the following exercises in a separate piece of paper and turn it in at the beginning
1/7
Physics 15a
Lab 2: Gauss Gun
Spring 2008
Exercises:
I.
Do the LoggerPro tutorial: “12 Video Analysis”
A. Remember you can find the tutorials inside the sub-folder: Experiments/
Tutorials
B. Make the graph for X and Y and fit both variables. Comment on the results of
C. Print the last page and return it with the rest of your prelab assignment
II.
Watch some of the Gauss Gun YouTube videos. A good place to start is: http://
III. A ball bearing is launched horizontally off the edge of a table with speed v0. It
lands in a sandbox a distance L from the edge of the table. The table is at a height
h.
A. Determine v0 in terms of h, L, and g. You may neglect air drag.
B. If you measure, h and L with uncertainties δh and δL. What is the uncertainty of
v0, in terms of h, δh, L, δL, and g? (Assume there is no uncertainty in g.). Refer
to the lab companion for help.
IV. Design a procedure to determine whether momentum is conserved in the
operation of the Gauss gun. Write it on a separate sheet of paper from the first
pre-lab questions, and include your name, lab time, and lab TF's name. You'll need
it at the beginning of the lab, but you'll hand it in at the end of the lab. Some
A. You'll have access to the equipment listed in the material section, but if you
B. You might want to think on how to reduce the importance of friction in your
experiment, and how to keep your Gauss gun horizontal.
C. Checking momentum conservation involves comparing an initial momentum to a
final momentum. That means you should think about what state you'll consider
to be "initial" in your experiment and what state you'll consider as "final."
D. Remember that to make a statement like "momentum was conserved" or
"momentum wasn't conserved," you need to determine not only the initial and
final momentum, but also the uncertainties that go with them. This means that
you should estimate the uncertainty of any measurement you make, and use
error propagation as you learned last time.
2/7
Physics 15a
Lab 2: Gauss Gun
Spring 2008
Material
Gauss gun
You will get 3 steel ball bearings, one magnet and a low friction track with a meter
scale. You can use them to make a basic Gauss gun. We will have access to extra balls
and magnets for you to create more complex guns if you wish. However, keep in mind
that complex systems are more difficult to study.
Measuring sensors
I.
Digital video camera on tripod.
A. You can use it to record movies at 30
frames per second and then analyze
them using the video analysis in
LoggerPro (see prelab tutorial).
II.
LabPro Hardware
A. LabPro Interface: The LabPro interface is
the blue box that allows you to connect a
wide variety of different sensors to the
computer via the Logger Pro software.
There are connections for two digital
sensors on one side and four analog
sensors on the top. Today we will use one analog sensor.
B. Force sensor: This is a small box with a hook that can measure
forces applied to the hook. It is mounted in a horizontal bar.
1. The force sensor connects to the computer via the LabPro
interface and the data can be read into a computer using the
Logger Pro software. The sign of the force reading is
considered to be positive if you pull on the hook, and
negative if you push on it.
2. There is a switch on the force sensor which toggles between
force ranges of ±10 N and ±50 N. The ±10 N setting has
higher sensitivity and is more desirable to use most of the
time, but if you are measuring forces larger than 10 N,
obviously you will have to use the ±50 N setting. When you
flip the switch, Logger Pro will ask you to either change it
back or use the sensor setting; click the option to use the
sensor setting.
3. One steel ball bearing is hanging from the hook, so you can
measure forces between the ball bearing and a magnetic system.
4. The force sensor needs to be zeroed by pressing the
before you start taking data.
3/7
button
Physics 15a
Lab 2: Gauss Gun
Spring 2008
Other miscellaneous tools
I.
Meter stick
A. Remember that, in the best case scenario, the uncertainty is half the smallest
division of the ruler. The actual uncertainty in your length measurement can be
larger since it depends on the conditions you perform the measurement.
II.
Dial caliper (same as used in Lab 1)
III. Precision digital balance (same as used in Lab 1)
A. Remember that the reading uncertainty in a digital device is typically one unit of
the least significant digit. For this balance, it should be 0.01 g.
B. The magnet can potentially interact with the metal parts of the balance. Hint: if
you use the balance to measure the mass of the magnet, make sure to keep the
magnet away from the plate. Suggestion: use some “tall” light stand to place the
magnet on the balance. Re-zero the balance before putting the magnet on the
top.
IV. Carbon paper sheets
V.
Lubricant oil
A. If you feel that it is important, you can use this to reduce the sliding friction by
applying a small fraction to the track.
VI. Tubing clamp
A. The tubing clamp consists of a clear plastic tube open at both
ends, and a clamp to tighten around the tube.
B. We'll use the tubing clamp in this lab to hold one ball and one
magnet. There are two possible configurations: either the magnet
is on the end and the ball is on the inside (as shown in the
picture), or the ball is on the end and the magnet is on the inside.
Both configurations will be used in the lab (for different measurements); but in
either case, you should make sure to clamp both the ball and the magnet inside
the tube, so that neither one can move without undoing the clamp.
VII. Shim stock
A. Pieces of aluminum or plastic cut to a certain thickness. You can use them to
separate the magnet from a ball by a certain amount. (Unlike steel, aluminum
does not affect the magnetic interaction.) The shims ordered by increased
thickness are: orange, green, blue, A, B, C,...
Procedure
The lab consists of two parts. You will start using your own procedure to study the
conservation of momentum in the gauss gun collision. Then, you will try to find out
how the Gauss gun works by measuring the work of the forces involved in the collision
and the energy transfer.
Conservation of momentum
You will find a LoggerPro file (Lab2-momentum.cmbl) ready to operate your video
camera .... just in case you need it.... Please save it immediately with a different name
4/7
Physics 15a
Lab 2: Gauss Gun
Spring 2008
partners. Play around with the magnet, the ball bearings and the different instruments,
and see what you can set up. Once your group agrees on a procedure, write it out in
full detail in your lab report. Then, discuss your plan with your lab TF to see if he has
any helpful advice. Be sure to keep track of any uncertainties, explain what you intend
to measure and how you going to do it.
I.
It might be a good idea to repeat the measurement several times in order to get a
more precise result. Keep in mind what you learned in the first lab about random
uncertainties.
II.
Occasionally, when the balls and magnet collide, there is some lateral motion
which will result in a bad measurement since you will likely assume onedimensional motion only. It is better to discard these collisions.
III. You lab report should include the data, observations, analysis and graphs relevant
to your measurement and conclusions. In the conclusion for this part of the lab,
let us know if the momentum was conserved within your experimental uncertainty.
If not, try to interpret your result.
IV. Save your LoggerPro file when you are done.
How the Gauss gun works?
We observed that a large amount of kinetic energy is produced in the Gauss gun
collision. How is it possible that the ball acquires such large velocity? Where does all
the kinetic energy come from? Somehow, it must have to do with the nature of the
magnetic force and, although we have not studied magnetic forces yet, you must have
noticed that the force appears to diminish with the distance.
In the Gauss gun collision, we go from the initial configuration,
to the configuration,
with a third ball bearing far away in both cases.
Questions:
A. Which configuration do you think has a higher potential energy?
B. Can you make an hypothesis using concepts of energy for what happens during
the operation of the gauss gun and why does the second ball comes out so fast?
Let’s investigate your hypothesis and determine the potential energy in each
configuration by measuring the work done by the magnetic force on the ball bearing 2.
I.
Measure the magnetic force versus distance
Open the Logger Pro file Lab2-work.cmbl (inside the Lab2 folder on the Desktop). Save
the file giving it a new name including your initials. Read the instructions on page 1
and move to page 2 for you lab. You should find two tables and three graphs already
setup. The graph Force vs Time is where you will be taking your data. You should use
the two tables to record the data for the two configurations: ball-ball-magnet and ballmagnet-ball. The two other graphs will build-up automatically from the data in the
tables.
5/7
Physics 15a
Lab 2: Gauss Gun
Spring 2008
You will be using the force sensor with a ball bearing hanging by a yellow string. Make
sure to zero the sensor by pressing
.
A. Configuration: ball-ball-magnet
1. Setup the magnet and ball in the tube and clamp them tightly so that they
don’t move (only a small part of the ball needs to protrude from the end of
the tube).
2. Touch the tubing clamp ball to the hanging ball and pull straight down.
Collect some data and observe the Force vs Time graph. The maximum force
reached before release is equal to the magnetic force on the hanging ball.
3. Question: Make a force diagram for the hanging ball. What does zeroing the
sensor do?
4. Refer to the first page of the Logger Pro file for instructions on how to make
an estimation of the magnetic force.
5. Make measurements of the magnetic force for different distances using the
shims provided. Start without any shim and move on to the thicker and
thicker ones. You don’t need to use all of them as long as you get a smooth
graph and measure a magnetic force down to close to zero.
6. Attention: make sure the shim is always in contact with both balls. Also,
when using rigid shims, make sure you don’t push the ball upwards with the
shim.
B. Configuration: ball-magnet-ball
1. Change the configuration in the clamp and repeat the measurement as
above.
2. You will likely need to use thicker shims before the force drops to zero and
you can forego some of the thinner shims. Why is that?
3. Fill-out the data for this configuration in the second table.
II.
Work done by the magnetic force
A. Do not worry about error analysis for this part of the lab.
B. Use the graphs obtained above to determine the work done by the magnetic
force on ball 2 as the separation decreases from very far away to zero, for the
two configurations
1.
2.
C. What is the magnetic potential energy for each configuration, if we define that
the potential energy is zero when the ball 2 is very far away? (be careful about
signs.)
1. Is the relative size of the potential energy for the two configurations as you
expected?
D. Calculate the difference in magnetic potential energy ΔUmag between the first
6/7
Physics 15a
Lab 2: Gauss Gun
Spring 2008
and second configuration.
1. How does this difference compare with the difference in kinetic energy in the
gauss gun collision? Does it look reasonable? Discuss it. Which finding would
be more surprising?
a) |ΔK| <|ΔUmag|
b) |ΔK| =|ΔUmag|
c) |ΔK| >|ΔUmag|
The most powerful Gauss gun
Can you devise the most powerful Gauss gun possible using the magnets and ball
bearings available in the lab. How far can it shoot a ball bearing? Why does it work and
what are the limitations?
Totally extra questions: Friction
How would you go around to estimate the friction in the system. Can you estimate the
friction force in the ball-magnet-ball system? How does it compare with the magnetic
force?
7/7
```