2-D Momentum Collision Lab
You will not be turning in this paper.
This is a very complex lab, so please READ ahead of time!
2/07
Purpose:To test the conservation of momentum in two dimensional collisions.
Your teacher will show you the equipment. You should have 4 balls (two steel, one padded steel, and one
marble), a protractor and two carbon papers. Raise or lower the target support screw to make sure the center of
the target and rolling balls are at the same height at the edge of the ramp. Position the paper on the floor so that
the plumb line is about 5 cm from the edge of the paper, about midway along the shorter side of the paper. Don’t
mark its position yet, since you may have to adjust it.
You must position the target support so that there is an off-center, glancing collision. Mis-selecting this
collision angle accounts for the biggest errors in this lab. A collision too close to head-on will result in a very
small velocity for the rolling ball after the collision. It may hit the target support and go off at some weird angle.
A collision that is too glancing, on the other hand, will just barely move the target ball, instead of knocking it
cleanly off the support. The target ball will then be affected by the support and go off in some strange direction.
You must select a middle case in which both rolling and target go off with significant speeds.
Try a practice run. If one of the two balls goes a relatively short distance (about half as much or less) compared
to the other, try a different support position. Try a practice run with no target ball in place. The rolling ball
should just clear the support. If you hear a “click” as it passes the support, it probably hit the support. Recheck
the support height and try again.
When you are satisfied with the collision and paper conditions:
STEEL-STEEL
A) Masking tape the paper to the floor and put your carbon paper down where you think the balls will hit.
B) Run the experiment by rolling a steel ball down the ramp and letting it hit the target.
C) Using carbon paper to let the balls leave marks on the paper, label the positions where the balls hit the paper
as “final rolling” and “final target” and label this end of the paper as “steel-steel”. These marks should be
circled as well as labeled and stray marks, extra marks etc. should be crossed out as soon as they occur.
D) Mark the plumb line position as “plumb line - initial target” since this is where the target ball was just
before the collision. The initial rolling ball position is behind and to the side of the plumb line and will be
located and marked later.
E) Set the target ball aside and let the steel ball roll down the ramp (no collision). By using carbon paper,
locate and mark where the rolling ball hits. Label it “initial rolling” since it represents what the ball was
doing just before it would have hit the target, were there a target in place. Hopefully your rolling ball will
not hit the support (listen for it) If it does, you may have to swing the support out of the way.
These labels are important, so use them throughout the lab!!!
STEEL-PADDED STEEL
Follow the steps above with the padded steel ball as your target. You can use the same big sheet of paper, just
turn it around 180°. Careful labeling will keep you from mixing up the marks. Position the target so that the
thickest part of the pad is faced toward where the rolling ball will hit it. Ensure that the tape does not catch on
the support.
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STEEL-MARBLE
Flip the paper over and follow the steps above with the marble as your target. Use the same target support
position that you used in the steel-steel collision. You may have to readjust the target support height since the
marble is slightly bigger than the steel ball that was your former target. You should take care to position the
paper so the marble will land on it. As always, try a practice run.
Analysis:
The following is also shown, in part, on the diagrams on page 4. Look at them while
reading the following. For each experiment you will calculate and draw vectors, representing the momentum,
for three different parts of the collision.
The time it takes for the balls to fall to the floor is the same for all cases so I hereby declare this time to be,
ta da, one clank. Therefore, the horizontal velocity of a ball is simply the distance along the floor that it moved
while falling, divided by the time of one clank. That makes the velocity vector the same length as the distance
vector which is convenient but possibly misleading later. Do not confuse them.
Momentum is this velocity times the mass which, for a steel ball, is one “bmu” or ball mass unit. This means
that for all but one vector, the momentum vectors will be the same length as the distances measured out on the
paper. Remember, we are now dealing with a scale diagram of MOMENTUM, not distance.
Do not confuse them ! ! ! ! !
◊ The one exception is the target marble momentum vector which will be only one-third of the
distance vector, since the marble mass is one-third of the steel ball mass or one-third bmu.
Read the paragraph above again!
The final target vector starts at the plumb line mark and ends at the place where the target hit the floor. Draw an
arrow to show this. In fact, all vector lines should end with arrowheads, indicating the end of the vector.
The final rolling ball vector and the initial rolling ball vector both end at their respective carbon paper marked
positions on the paper. These vectors do not start at the plumb line mark! Instead they both start at a spot one
ball diameter from the plumb line mark and in a direction from the plumb line mark directly opposite from
the final target vector. First draw the target line, then trace back along that line one ball diameter. This can best
be understood with the enlarged details on page 4. Forgetting this is the most common “dumb mistake” for this
lab. If you make it, your friends will laugh behind your back, facial blemishes will multiply, and the college of
your choice will put you on the automatic reject list.
The next step is to use a vector diagram to add the final target
momentum to the final rolling ball momentum (not the other way
around) and see how close the sum comes to the initial rolling ball
momentum. You will need to measure the angle between the two
final vectors (remember, add vectors tip-to-tail, see diagram on page
4). Record its value on the diagram near where the vectors meet.
Think through how to measure the angles (protractor) for your vector
addition by diagram. REMEMBER that the marble target
momentum is only one-third the length of its distance vector on the
floor.
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Measure the error distance as the distance FROM the end of the vector sum of the final momentum TO the end
of the initial rolling ball momentum. Then measure the length of the initial rolling ball momentum. Finally,
calculate the percentage error (see the equation at the bottom of this page).
Do all this on the large paper.
Do all this stuff for all three collisions right on the big piece of paper. There are no questions and you don’t need
to write a conclusion but don’t forget to:
Calculate the % error (show calculation on the big paper).
Measure and record the angle described in the diagram above (show on the big paper).
Use arrowheads to mark the end of each vector.
Record the length of each vector next to it. We will use this data to analyze kinetic energy.
Clearly label everything! (so I can figure it out EASILY without your help).
Fold the paper into quarters. Put your names, the date, and the period # on the outside surface of the folded
paper and turn it in. You will not turn in these lab instructions or any other papers, just the one big paper for
your team.
% error = error line length x 100
initial rolling ball length
See diagram #4 on the next page for the “error line length”.
When done collecting data, put the plumb line on the table top.
For some reason, the last diagram on the next page is ignored by about 20% of lab teams, who then end up
loosing points in a very embarrassing way. My advice (which I predict will be ignored by about 20% of you) is
to pay attention to it. The plumb line spot is marked by the string hanging from your apparatus. The other spot,
where the rolling ball vectors start, is in a very specific direction at a very specific distance from the plumb line.
Think it through ! ! !
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1. Collect data and carefully label,
including which collision you are
initial Rolling ball
2. Draw momentum vectors. Remember
the target marble vector is shorter.
final
Target
ball
initial Rolling ball
final
Target
ball
final Rolling
ball
final Rolling
ball
Plumb line
start for both
rolling ball vectors
3. Add the final target momentum vector
to the final rolling momentum vector.
Use scale diagram techniques.
final Target
vector copy
initial Rolling ball
final
Target
ball
Record angle
final Rolling
ball
Plumb line Start
for target ball
4. Construct, measure, and record
error line. Measure and record the
angle between the two final
momentum vectors.
error line
final Target
vector copy
Plumb line start
for target ball
initial Rolling ball
final
Target
ball
start for rolling ball
final Rolling
ball
Extend target vector
line backwards to find
this s pot
start for rolling ball
target vector
Plumb line
Plumb line start for
target ball
Magnified detail on how to
find the start for the rolling
ball vectors.
One ball diameter
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