Classical Mechanics - Taylor. Prob 2.24, 2.27: Quadratic Air Resistance
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Загружено: 2026-01-14
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Classical Mechanics - John R. Taylor
Chapter 2: Projectiles and Charged Particles
2.4: Quadratic Air Resistance
Prob 2.24: Consider a sphere (diameter D, density rho_sph) falling through air (density rho_air) and assume that the drag force is purely quadratic.
(a) Use Equation (2.84) from Problem 2.4 (with kappa = 1/4 for a sphere) to show that the terminal speed is
v_ter = sqrt{8Dgrho_sph/3rho_air}.
(b) Use this result to show that of two spheres of the same size, the denser one will eventually fall faster.
(c) For two spheres of same material, show that the larger one will eventually fall faster.
Prob 2.27: I kick a puck of mass m up an incline (angle of slope = theta) with initial speed v_0. There is no friction between the puck and the incline, but there is air resistance with magnitude f(v) = cv^2. Write down and solve Newton's second law for the puck's velocity as a function of t on the upward journey. How long does the upward journey last?
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