**ERIC Number:**EJ876104

**Record Type:**Journal

**Publication Date:**2010-Feb

**Pages:**2

**Abstractor:**As Provided

**Reference Count:**2

**ISBN:**N/A

**ISSN:**ISSN-0031-921X

Viewing Events in the Center-of-Mass System

Ruby, Lawrence

Physics Teacher, v48 n2 p112-113 Feb 2010

In elementary physics, collisions are usually studied by employing the conservation of momentum, and sometimes also the conservation of kinetic energy. However, in nuclear reactions, changes of mass that complicate the situation often occur. To illustrate the latter, we shall cite two examples of endoergic nuclear reactions, i.e., those for which energy must be supplied to make the reaction proceed. A typical situation is given by the equation A + B [arrow right] C + D + Q, (1) where particles A, B, C, and D are expressed in terms of the energy-equivalent of the particle masses, according to the Einstein relation E = mc[squared], and where Q is a negative energy quantity, corresponding to the excess of mass of (C + D) over that of (A + B). Equation (1) is just an alternate statement of the conservation of total energy. Typically, in the lab system (L), energy is supplied as kinetic energy "T" of particle A, and particle B is at rest. Thus, to conserve momentum, particles C and D must compensate for the momentum corresponding to T. Often, it is desirable to know the minimum value of T that will conserve both energy and momentum, i.e., the threshold value of T, known as T[subscript th], that will just allow the reaction to proceed. At threshold, the particles C and D will have their minimum possible kinetic energies. In the center-of-mass system of coordinates (Z) in which the input momentum is zero, at threshold, the products C and D are each stationary, and this requirement will allow us to calculate the corresponding T[subscript th] in the lab system (L). The Z system is often termed the "center-of-mass" system, but it is more properly termed the "zero-momentum" system.

Descriptors: Kinetics, Physics, Science Education, Theories, Equations (Mathematics), Energy, Teaching Methods, Scientific Concepts, Science Teachers

American Association of Physics Teachers. One Physics Ellipse, College Park, MD 20740. Tel: 301-209-3300; Fax: 301-209-0845; e-mail: pubs@aapt.org; Web site: http://scitation.aip.org/tpt

**Publication Type:**Journal Articles; Reports - Descriptive

**Education Level:**N/A

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A