Momentum And Colliding Spheres

Robert Watkins                 Beethoven Elementary School
                               25 W. 47 Street
                               Chicago IL 60609
                               (312) 535-1480

Objective:

Student will be able to understand that mass x velocity equals momentum.
Student will be able to understand the impacts of collisions and their results.
Student will be able to determine the vector of an incident. 

Materials:

Paper, Chalk, Iron Spheres, Marker, Meter Sticks, and String.

Strategy:

The student is asked to think about the content of an object.  The student will 
probably think in terms of the object's weight.  The student will learn that 
weight is the force upon a body due to gravity and that force is usually a push 
or a pull.  Mass is introduced to the student.  The student will learn that mass 
is the quantity of matter in a body.  A rolling sphere is shown to class.  The 
student learns that its mass is the matter that makes up this object.  After 
rolling the sphere across a table, the student is asked what happened?  At this 
point velocity is introduced.  The student learns that velocity is the 
specification of the speed of a body and its direction of motion. 

The student is told that when we think of mass and velocity together, we call 
this action momentum.  The student learns that momentum is the idea of inertia 
in motion.  Momentum refers to moving things, that is, the mass of an object 
multiplied by its velocity.  Two spheres are shown with the same amount of mass. 
The student is asked what would happen if both spheres were moving at the same 
speed toward a wall?  At this point, the student is asked what would happen if 
the two spheres were moving toward each other at the same speed?  The teacher 
advises that when two objects with the same mass are moving toward each other at 
the same speed and hit each other, we call this activity a collision.  We say 
that both objects had the same momentum and at impact their momentum has been 
shared equally. 
 
At this point, the teacher demonstrates a collision using spheres of equal mass.  
The spheres are hung from a ceiling and paper is placed underneath.  One sphere 
is stationary while the second sphere is held at a short distance.  The student 
is asked what will happen when the two spheres collide?  The student will give a 
variety of responses yet the idea of both spheres colliding and being held as 
they reach their peak in flight will be emphasized.  The teacher demonstrates a 
few trial collisions and tells the student to place an X at the point of release 
of the moving sphere.  An X is also placed at the point of the stationary 
sphere.  The sphere is released and collides with the stationary sphere.  Both 
spheres are caught at their peaks and arrows are placed at each point.  The word 
Vector is written on the board and the student is told that the momentum of each 
sphere can be expressed involving a technique called vector addition.  The 
student learns that the magnitude of the sphere and its direction are the two 
elements used to find net momentum.  Using a meter stick, the released point is 
measured to the stationary point.  Next, the two points at the sphere's peak are 
measured.  Using meter sticks to draw the lines at a right angle, a 
parallelogram is drawn.  The released point to the stationary point should equal 
the stationary point to the end of parallelogram after drawing a diagonal line. 

The student is asked to start at a given point and walk in one direction 
counting ten steps.  He walks in a second direction and counts ten steps.  The 
student is asked how many steps would it take to return to the starting point. 
The student will probably feel that if he adds ten plus ten, then the correct 
answer will be twenty.  The student is told that the diagonal line to the 
starting point is usually greater.  After a few trial runs the student learns 
that although the sides of a figure are equal, the diagonal point to the 
starting point is usually greater.  A second demonstration is given using 
spheres of unequal mass.  The stationary sphere is one half the mass of the 
moving sphere.  After the collision and after the parallelogram is made, the 
student is told to take one half the length of the sides of the parallelogram 
due to the unequal mass.  Afterwards the student will determine that the 
distance from the release point to the impact point should equal the distance 
from the impact point to the length of the diagonal line. 

Summary:

The understanding of momentum should help the student in preparing for 
additional activities in PHYSICS.  To introduce the meaning of inertia at the 
beginning of a momentum lesson is helpful.  The student learns the meaning of 
force and is introduced to mass.  The next step is to define velocity and share 
that momentum is mass multiplied by velocity.  Hands on activities are excellent 
ways to help the student see the reality of what is happening.  After vector 
addition is introduced the student is helped to recognized points of importance.  
The release point, the impact point and the peak points are placed with an X so 
the student can recall distance recognition.  In conclusion, the student is 
helped to developed a parallelogram.  This method of discovery and development 
should encourage the student to continue his interest in Science activities. 

References:

Hewitt, G. Paul, Conceptual Physics : Momentum. Little, Brown and Company
Boston, Mass. Fifth Edition.