Demostrations of Law of Conservation of Linear Momentum

Tisdale, Robert W. Percy L. Julian High School

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.
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