Download Conservation of Momentum Purpose The purpose of this experiment

Conservation of Momentum
Purpose
The purpose of this experiment is to verify the conservation of momentum in two dimensions.
Introduction and Theory


The momentum of a body ( p ) is defined as the product of its mass (m) and velocity ( v ):


p  mv
When two objects collide, if the external forces are negligible relative to the internal forces, the
momentum of the system is conserved before and after the collision, or


p system , after  p system , before
This is what we will try to verify today.
Apparatus Draw a labelled diagram as Figure 1 and list all other equipment you will use, along
with any identifying numbers. (No need to draw Figure 2 on your report.)
glass
sphere
steel
sphere
Ramp # _
supporting
screw
Side View, note that the two spheres
are at the same height
Point A
Point B
y
Top View
Figure 1
Figure 2
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Data and Analysis
Measure and record the masses of the spheres, msteel and mglass with a 4-beam balance.
Setup the apparatus as in Figure 1 and place a sheet of newsprint on the floor beneath the ramp. Do
some trial runs by releasing the steel sphere from the nail position and have it collide off-centred with
the glass sphere at the bottom of the ramp (see Figure 2). Then remove the glass sphere and let the
steel sphere roll down alone.
Adjust the orientation of the supporting screw and the position of the paper so that
(1)
(2)
(3)
(4)
the steel sphere will hit the glass sphere, but not the supporting screw;
the starting positions of both spheres fall on the big paper;
after the collision, both the steel sphere and the glass sphere land on the big paper;
without the collision, the steel sphere lands on the big paper.
Also check that the two spheres are at the same height when colliding. (The bottom of the track is at
the same height as the top of the supporting screw.) If not, consult the instructor. You are not
supposed to adjust the height of the supporting screw yourself.
Once you achieve the conditions above, keep the screw and the paper in position and do not move
them. You may secure the position of the big paper with masses from the mass box.
Now, create 5 points on the big paper (Figure 3): the starting positions of both spheres (points A and
C), the landing positions of both spheres after they collide (points D and E), and the landing position of
the steel sphere without the collision (point B). Use a plumb bob to mark points A and C. Points B, D
and E are marked by covering the big paper with carbon papers, and allowing the spheres to land on
the carbon papers.
To get an idea of uncertainty, mark point B (landing of the steel sphere alone) a few times. You should
end up with something like Figure 3, where point B is a group of points.
Point B
Point D
Point A – Steel ball starting
position
Point B – Steel ball landing
spot without collision
Point E
Point C – Glass ball starting
position
Point D – Steel ball landing
spot with collision
Point E – Glass ball landing
spot with collision
Point C
Point A
Figure 3
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Now you can remove the big paper from the floor and analyse it.
First step is to find out the momentum of each sphere before and after the collision. Remember that
momentum is a vector! Before the collision, the glass sphere is stationary, so the momentum of the
steel sphere is:

AB

psteel ,before  msteel vsteel  msteel
t
After the collision, both spheres are moving, and their momentums are:


AD
CE


, and p glass ,after  mglass v glass  mglass
p steel ,after  msteel vsteel  msteel
t
t
The vector CE is quite long, showing that the glass sphere has a big velocity (not the momentum)
after the collision. To scale this vector so that it can reflect the difference in the mass, we will create
mglass
CE , so that
another vector CE  
msteel
CE msteel

p glass ,after  mglass

t
t
 mglass
 m

CE   steel CE 
t
 msteel

On your big paper, measure and record the length of CE , calculate the length CE  
mglass
msteel
CE , and
then locate point E. Vector CE  is what we need.
After we replace vector CE by vector CE  , the vectors AB , AD , and CE  are proportional to the
m
momentum vectors with the same factor steel . Therefore, we can use these vectors to represent the
t
momentum of the spheres. (Think about why the time t is the same for all.)
Our next step is to add the vectors AD and CE  to find the momentum of the system after the
collision. We will do this graphically by the “triangle method”. Move vector CE  (keeping both the
magnitude and the direction unchanged!) so that its tail is at point D and its head lands at a point – say
point F. AF is the sum vector, or AF = AD  DF  AD  CE  .
Once you locate the vector AF on the big paper, the entire data analysis is done! On your report,
combine “Data”, “Calculations” and “Uncertainty Analysis” into one “Data and Analysis” section. In
this section, first record the masses of both spheres. Then explain how you find the momentum of the
system before and after the collision. Remember that the system momentum is the vector sum of the
two spheres.
When specifying the momentums, you must use the vector form. For example, you can say that
m
“Before the collision, the momentum of the steel sphere is steel AB ”. And draw a rough sketch of the
t
big paper to show the vector AB .
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Check if the momentum vectors of the system before and after the collision agree within uncertainty.
The ideal situation is that the difference between these two vectors is less than the uncertainty circle of
B. However, if point F falls just outside the circle B, one may argue the difference is less than the total
uncertainty if we consider that point F has at least the same uncertainty as point B.
Conclusions
State whether or not the conservation of momentum is verified by your experiment.
Discussions
Did you ignore any uncertainties in your analysis? Are there other physical factors that could have
affected your results? Do you think they are significant?
Checklist
For the big paper:

Have you measured the length CE ?

Did you show the calculations of the length CE  ?

Have you located dots A through F and E?

If you are sharing the big paper with your partner, did you write both partner’s names and your
desk number?
For the “Data and Analysis” on your report:

Have you listed the masses of both spheres, together with the uncertainty?

Did you make a rough sketch of the paper, with points A through F and E marked and
explained? You should explain how you locate point E.

Did you identify (by explanations or calculations) the momentum of the system both before and
after the collision? Why is the time the same for all momentums?

How do the momentum of the system before and after the collision compare? (Is point F inside
the uncertainty circle of B? If you consider point F has its own uncertainty circle, will it
intersect with circle of B?)
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Saved: 10/17/16, printed: 10/17/16