**ERIC Number:**EJ818430

**Record Type:**Journal

**Publication Date:**2008-Jul

**Pages:**8

**Abstractor:**As Provided

**Reference Count:**11

**ISBN:**N/A

**ISSN:**ISSN-0143-0807

Newton on Objects Moving in a Fluid--The Penetration Length

Saslow, Wayne M.; Lu, Hong

European Journal of Physics, v29 n4 p689-696 Jul 2008

We solve for the motion of an object with initial velocity v[subscript 0] and subject only to the combined drag of forces linear and quadratic in the velocity. This problem was treated briefly by Newton, after he developed a theoretical argument for the quadratic term, which we now know is characteristic of turbulent flow. Linear drag introduces a time [tau], and the two drag forces are equal at a critical velocity v[subscript c]; this defines a characteristic distance R = v[subscript c][tau]; details are discussed for spheres and for cylinders moving along their axis. For v[subscript 0]/v[subscript c] [approximately] 1 the role of quadratic drag is largely to reduce the velocity to v[subscript c], below which linear drag dominates. The penetration length is given by L[subscript N] = Rln(1 + v[subscript 0]/v[subscript c]). As noted by Gamow, L[subscript N] is relevant to the range of non-self-propelled projectiles, such as artillery shells, bullets, ground penetration bombs and spears shot from spearguns; it is also relevant to windmills and fans. (Contains 6 footnotes.)

Descriptors: Mechanics (Physics), Motion, Science Instruction, Equations (Mathematics), Scientific Principles, Models, Problem Solving, College Science, Undergraduate Study

Institute of Physics Publishing. The Public Ledger Building Suite 929, 150 South Independence Mall West, Philadelphia, PA 19106. Tel: 215-627-0880; Fax: 215-627-0879; e-mail: info@ioppubusa.com; Web site: http://www.iop.org/EJ/journal/EJP

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

**Education Level:**Higher Education

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A