Body motion in a one-dimensional resistive medium

American Journal of Physics

Volumn 66, Issue 11, 1998, Pages 973-974

  Molina, M I ^a  

^a UNIVERSITY OF CHILE   (Chile)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032336948     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.19009     Document Type: Article

References (8)

1. For a nice discussion on the ranges of validity of Stokes's law and Newton's law expressions for the drag force with respect to Reynolds number and turbulent flow see F. X. Hart and C. A. Little III, "Student investigation of models for the drag force," Am. J. Phys. 44, 872-878 (1976). See also G. W. Parker, "Projectile motion with air resistance quadratic in the speed," ibid. 45, 606-610 (1977) for a discussion on the origin of the quadratic dependence on velocity for a body moving at high Reynolds number.
2. For a nice discussion on the ranges of validity of Stokes's law and Newton's law expressions for the drag force with respect to Reynolds number and turbulent flow see F. X. Hart and C. A. Little III, "Student investigation of models for the drag force," Am. J. Phys. 44, 872-878 (1976). See also G. W. Parker, "Projectile motion with air resistance quadratic in the speed," ibid. 45, 606-610 (1977) for a discussion on the origin of the quadratic dependence on velocity for a body moving at high Reynolds number.
3. V. K. Gupta, Gauri Shanker, and N. K. Sharma, "Experiment on fluid drag and viscosity with an oscillating sphere," Am. J. Phys. 54, 619-622 (1986).
4. See, e.g., J. B. Marion and S. T. Thornton, Classical Dynamics of Particles and Systems (Saunders College Publishing, Philadelphia, 1995), 4th ed., pp. 60-71. See also Parker's article in Ref. 1, pp. 606-608.
5. An interesting treatment of the general two-body collision that leads to a convenient geometrical visualization is found in Gordon P. Ramsey, "A simplified approach to collision processes," Am. J. Phys. 65, 384-389 (1997). For multiple one-dimensional, elastic collisions, a matrix formalism is advisable. See R. H. Romer, "Matrix Description of Collisions on an Air Track," ibid. 35, 862-868 (1967) and also Richard L. Garwin, "Kinematics of an Ultraelastic Rough Ball," ibid. 37, 88-92 (1969).
6. An interesting treatment of the general two-body collision that leads to a convenient geometrical visualization is found in Gordon P. Ramsey, "A simplified approach to collision processes," Am. J. Phys. 65, 384-389 (1997). For multiple one-dimensional, elastic collisions, a matrix formalism is advisable. See R. H. Romer, "Matrix Description of Collisions on an Air Track," ibid. 35, 862-868 (1967) and also Richard L. Garwin, "Kinematics of an Ultraelastic Rough Ball," ibid. 37, 88-92 (1969).
7. An interesting treatment of the general two-body collision that leads to a convenient geometrical visualization is found in Gordon P. Ramsey, "A simplified approach to collision processes," Am. J. Phys. 65, 384-389 (1997). For multiple one-dimensional, elastic collisions, a matrix formalism is advisable. See R. H. Romer, "Matrix Description of Collisions on an Air Track," ibid. 35, 862-868 (1967) and also Richard L. Garwin, "Kinematics of an Ultraelastic Rough Ball," ibid. 37, 88-92 (1969).
8. The one dimensionality makes our model aerodynamically very poor, since all collisions are of the "head-on" type and the body compresses the air in front of it as it moves. In two and three dimensions, the presence of glancing collisions between the body and the air molecules would decrease the forward momentum loss rate in comparison with the one-dimensional case, thus reducing the quadratic dependence on speed for the resistive force on the moving body.