Demostrations of Law of Conservation of Linear Momentum

Tisdale, Robert W.                  Percy L. Julian High School
                                    821-2571
                           

Objectives:

My objectives are to - (1) give a graphic demonstration of what the 
momemtum of an object really is; (2) review some of the more commonly 
available laboratroy equipment used to study momentum; (3) and produce 
as well as use some momentum equipment that is very simple, cheap, and 
easy to use. 

Apparatus needed:

The apparatus consisted of an air track, air table, momentum machine, 
billiard balls, small rubber ball, rope, steel pipe, seltzer water, 
rubber stopper, two wheel chairs, and small springs. 

Recommended strategy:

The first step is to establish what momentum is.  This is done with a 
little twist of humor by telling a story of how three little boys 
attempt to kill a big ferocious bear by using projectiles of different 
size mass and different velocities.  Of course only the projectile with 
sufficient mass and velocity is able to do the job.  

From their we move on to establish what it means to conserve momentum. 
We first observe a stationary pipe sealed on one end and with a rubber 
stopper on the opposite end.  The students are asked to tell what the 
momentum of this system is and with no exception all of them say the 
momentum is zero.  After seltzer water is placed in the pipe the rubber 
stopper flies out one way and the pipe another way.  The students are 
once again asked to give the momentum of this new system and most will 
say that the momentum has changed, changed to some nonzero or positive 
value.  

We then proceed with the concept of positive and negative velocity and 
how the sum of the two momentums resulting from this reaction add up to 
zero.  Hence, momentum is conserved and the law of conservation of 
momentum is supported. 

From this point we examine some of the equipment that is traditionally 
used to study comservation of linear momentum: air tables, air tracks, 
and the momentum device.  A small demonstration is performed with this 
equipment.  I also bring out that the equipment is expensive and easily 
damaged.  I introduce the idea of using simpler materials to illustrate 
conservation of momentum. 

One piece of equipment consists of two balls with a spring glued to at 
least one of the balls.  You use both balls to compress the spring 
about one meter directly above a point on the floor.  Very quickly you 
release the balls.  Both balls should have equal momentum.  If they are 
of equal mass then they should have equal velocities which will lead to 
to them landing equal horizontal distances from from the point on the 
floor.  If they are of unequal mass they will still have the same 
momentum but the more massive ball will have a smaller velocity the 
less massive ball.  This results in the more massive ball traveling a 
smaller horizontal distance than the less massive ball.  The results 
for this experiment don't give good quantitative data but the results 
do produce qualitative data that is good enough to support the point. 

Another demonstration involved three momentum carts of equal size.  One 
of the carts is securely taped on top of another cart.  The result is 
two carts, one which is roughly twice the mass of the other cart.  A 
spring is placed between these two carts to propel them in opposite 
directions.  Because of the law of conservation of momentum, we can 
assume that both carts will be given equal momentum.  We can also 
assume that the velocity of the lighter cart will be exactly twice the 
velocity of the heavier cart.  This is the only way two masses, one 
which is half the mass of the other, can have equal linear momentum. If 
the velocity of small cart is twice that of the larger cart then the 
small cart should be able to cover 2 times more distance in any given 
period of time.  We place a block of wood some arbitrary distance, say 
2 meters, from the smaller cart and another block of wood one half of 
former distance, 1 meter in this case, from the larger cart.  Both 
carts should arrive at their finish lines at the same time.  It will be 
clearly observable to the students when the carts crash at the same 
time.  This experiment works very well to be so simple in design. 

A third experiment involves the use of wheel chairs.  Two students, one 
much larger than the other, face each other seated in the wheel chairs 
about about 15 to 20 feet apart while while holding the opposite ends 
of rope.  Before they start pulling they have a total momentum of zero.  
To maintain a state of zero momentum after they start pulling the 
larger student will move at a smaller velocity and, therefore, not 
travel as far.  The smaller student will move at a much higher velocity 
and, consequently, roll for a greater distance.  It is important that 
the wheels of the wheel chair be aligned correctly before the pulling 
starts and that some one be there to catch the students before they 
crash in to each other.  There are a lot of variations that one can do 
with this.  Two students of similar size can pull.  Students can push 
off of each others hands instead of pull.  The results will probally 
not be good enough to make good quantitative measurements but they will 
be quite sufficient for making a qualitative estimate of what should 
take place.