ASPIRE - Momentum - Introduction

Momentum Teacher Overview
Level: 9-12
Science 3640- Physics
Utah State Core Standard: 3640-02 Students will investigate the laws of motion.
Utah State Core Objective: 3640-0204 Apply principles of momentum to motion.
Utah State Core Intended Learning Outcomes:

1. Use Basic Science Process Skills

Make observations and measurements (uses instruments as appropriate).

2. Use Integrated Science Process Skills

Identify variables and describe relationships between them.
Formulate research questions and hypotheses.
Plan field studies, controlled experiments, and other investigations.
Collect and record data using procedures designed to minimize error.
Analyze data and draw warranted inferences.
Evaluate causal inferences in terms of the plausibility of rival explanations.
Construct models and simulations to describe and explain natural phenomena.

5. Understand Science Concepts, Principles, and Systems

Know science terminology appropriate to grade level.
Understand natural and human-produced systems in science (appropriate to grade level):

Explain how the parts of a system are interconnected and function together as a unit.
Predict how changes in one part of a system will likely affect the rest of the system.

Solve problems by applying science principles and procedures.

6. Communicate Effectively Using Science Language and Reasoning

Use the language and concepts of science as a means of thinking and communicating.
Prepare written and oral reports describing the findings of investigations and the reasoning which led to the conclusions.
Report results honestly. Avoid embellishing or exaggerating the results, and include a full description of any negative findings.
Construct tables, graphs, charts, diagrams, and models to describe and summarize data.
Provide relevant evidence to support inferences put forth to be accepted by others.
Present results of research in appropriate forums, and accept suggestions and reasoned criticism from qualified, external reviewers.
Evaluate the findings and conclusions reported by other investigators using relevant and defensible criteria.

Background: Momentum is a concept that is often misunderstood. One common misconception is that momentum is a force. The use of these four lessons will allow students to explore the concept of momentum by considering the behavior of various objects in terms of mass and velocity. The idea of momentum is introduced as the product of mass times velocity, and is then developed to show how momentum is conserved under a closed system.
Activity One:: The concept of linear momentum is introduced as the product of mass and velocity (mv). Mass is measured in kilograms, and velocity is measured in meters/second. Momentum is denoted by the letter p, where p = mv (in units of mass times velocity, kg-m/s).
Activity Two:: This activity develops the idea of conservation of momentum via an explosion of a single object into two pieces. This allows students to discover that momentum is conserved within a system. Each object has zero momentum initially and the explosion will give each object equal momentum in opposite directions from each other. The velocity of each object will depend on its mass.
Activity Three:: This lab will develop the idea of how momentum and kinetic energy are related in a collision of two objects. The idea of systems of objects is further developed. There are two fundamentally different types of collisions. In the first type, both system momentum and system kinetic energy are conserved. In other words, the system momentum and the system kinetic energy are the same before and after the collision. The second type of collision occurs where system momentum is conserved, but system kinetic energy is not conserved. Both types of collisions are explored in this activity.
Activity Four:: Principles of momentum are applied to explain cosmic ray acceleration.
The concept of linear momentum is the product of mass and velocity (mv). Mass is measured in kilograms, and velocity is measured in meters/second. Momentum is a vector quantity, therefore consists of both magnitude and direction, provided by the velocity (mass being a scalar quantity). Momentum is a conserved quantity, that is the final momentum of any closed system after some interaction (force, collision, etc.) must be the same as the initial system momentum before the interaction. In mathematical terms, initial system mv must equal final system mv (where a system consists of one or more particles). Momentum is denoted by the letter p, where p = mv (in units of mass times velocity, kg-m/s).
There are two types of collisions that may occur between objects. Elastic collisions occur if the system momentum and system kinetic energy are conserved. Inelastic collisions occur if system momentum is conserved, but system kinetic energy is not. Note that this lab does not mention the concept of angular momentum, which may be introduced in subsequent lessons.
When multiple particles (objects) collide, the total momentum of the particles is the same before and after the collision. Mathematically, this can be expressed as:

The interaction between cosmic rays and large masses (usually gas/dust clouds) in space exhibits the same conservation of momentum observed in Lab Three, however, it is conservation of angular momentum that is generally considered. For our purposes, angular momentum is left for future consideration in subsequent labs. We will simply define a cosmic ray-large mass interaction as an elastic collision.
As cosmic rays travel through space, they encounter massive objects in their path. As they interact (collide) with these objects, the system momentum is conserved, with the cosmic ray gaining momentum, and the large mass losing momentum. Assuming system mass remains constant, these interactions result in an increased velocity of the cosmic ray, and a decreased velocity of the mass. Since the mass of the gas cloud is many orders of magnitude larger than the mass of the cosmic ray, the velocity loss of the large mass is scarcely noticeable. Statistically, the velocity gain of the cosmic ray is cumulative, and given enough time for zillions of collisions, the velocity, and hence the kinetic energy (1/2mv²) increases immensely.