Scope, Sequence, and Coordination

A Framework for High School Science Education

Based on the National Science Education Standards

Law of Conservation of Momentum

Conservation of Momentum
During the interaction of two systems, A and B, the force exerted by A on B is equal and opposite to the force exerted by B on A. Since the duration of the interaction provides the time interval, and the forces are equal in magnitude, the changes in momentum of the two systems must also be identical, but oppositely directed. The total momentum must therefore remain the same. This is the law of conservation of momentum.

Further Description:

During the time of an interaction between two objects, the forces acting between the objects may be of various kinds: contact, gravitational, electrical, or even nuclear. Contact forces are fundamentally electrical in nature. Similarly, elastic forces, like those exerted by a rubber band or spring, are electrical. Molecular forces are also electrical.

During an interaction, Newton’s third law requires that the impulse delivered by one system be equal and opposite to the impulse delivered by the other system. This behavior requires that the magnitude of the change in momentum of each system be the same. Since they are oppositely directed, their sum is zero. In two or three dimensions, where there are three or more interacting systems, the sum must be a vector, where the vector represents the total of the momenta of the interacting systems.

The law of conservation of momentum is one of the major laws of nature, and for any closed system that includes all interacting objects it always holds. Thus, regardless of the nature of the force and of other constraints on objects in the system, like energy considerations, the total momentum is conserved. If there is a net external force on the system, then the total momentum of the system changes at a rate equal to that force. This law is of great interest in applications like sports, safety devices for cars and planes, rockets, and jet propulsion.

Observationally, the total momentum after an event occurs in a closed system equals its total momentum before the event, but only within the uncertainty of measurement.

Concepts Needed:

Grade 9

Interaction, action at a distance

Grade 10

Action and reaction pairs, impulse and momentum

Grade 11

Vector momenta and impulse (two dimensions), system

Grade 12

Free-body diagrams, three-dimensional vector momenta and impulse

Empirical Laws or Observed Relationships:

Newton=s third law, law of conservation of momentum

Theories or Models:

Physical systems and free-body diagrams

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Micro-Unit Description:

Law of Conservation of Momentum
At this level, students learn to distinguish between forces acting on an object and forces exerted by the object. They need to examine pairs of real objects, identifying the forces on each object and their points of application and direction. They should consider qualitative questions or problems, like the horse-cart "paradox." A qualitative understanding of single mass emission rockets should be developed. These are best illustrated with "exploding carts" of different masses.

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