EBK CLASSICAL DYNAMICS OF PARTICLES AND
5th Edition
ISBN: 9780357886113
Author: Marion
Publisher: VST
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Chapter 1, Problem 1.15P
To determine
The value of
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Critical damping is the case where the mass never actually crosses over equilibrium position, but reaches equilibrium as fast as possible. Experiment with changing c to find the critical damping constant. Use the same initial conditions as in the last problem. Zoom in a bit to make sure you don't allow any oscillations to take place - even small ones.
NASA's KC-135 Reduced Gravity Research aircraft, affectionately known as the "Vomit Comet," is used in training astronauts and testing equipment for microgravity environments. During a typical mission, the aircraft makes approximately 30 to 40 parabolic arcs. During each arc, the aircraft and objects inside it are in free-fall, and
passengers float freely in apparent "weightlessness."
The figure below shows the altitude of the aircraft during a typical mission. It climbs from 24,000 ft to 30,850 ft, where it begins a parabolic arc with a velocity of 155 m/s at 45.0° nose-high and exits with velocity 155 m/s at 45.0° nose-low.
31 000
45° nose high
45° nose low
24 000
Zero g
65
Maneuver time (s)
(a) What is the aircraft's speed (in m/s) at the top of the parabolic arc?
110.0
m/s
(b) What is the aircraft's altitude (in ft) at the top of the parabolic arc?
2.04e+04
What is the initial height at the start of the parabolic arc? What is the initial velocity at this point? What is the final…
Chapter 1 Solutions
EBK CLASSICAL DYNAMICS OF PARTICLES AND
Ch. 1 - Prob. 1.1PCh. 1 - 1.2. Prove Equations 1.10 and 1.11 from...Ch. 1 - Prob. 1.3PCh. 1 - Show
(a) (AB)t = BtAt (b) (AB)−1 = B−1 A−1
Ch. 1 - Prob. 1.5PCh. 1 - Prob. 1.6PCh. 1 - Consider a unit cube with one corner at the origin...Ch. 1 - Prob. 1.8PCh. 1 - For the two vectors
find
A − B and |A –...Ch. 1 - A particle moves in a plane elliptical orbit...
Ch. 1 - Prob. 1.11PCh. 1 - Let a, b, c be three constant vectors drawn from...Ch. 1 - X is an unknown vector satisfying the following...Ch. 1 - Prob. 1.14PCh. 1 - Prob. 1.15PCh. 1 - What surface is represented by r a = const, that...Ch. 1 - Obtain the cosine law of plane trigonometry by...Ch. 1 - Obtain the sine law of plane trigonometry by...Ch. 1 - Prob. 1.19PCh. 1 - 1-20. Show that
Ch. 1 - Show (see also Problem 1–11) that
Ch. 1 - Prob. 1.22PCh. 1 - Use the εijk notation and derive the identity
(A ×...Ch. 1 - Prob. 1.24PCh. 1 - Find the components of the acceleration vector a...Ch. 1 - Prob. 1.26PCh. 1 - If r and are both explicit functions of time,...Ch. 1 - Show that
Ch. 1 - Prob. 1.29PCh. 1 - Prob. 1.30PCh. 1 - Show that
(a)
(b)
(c)
Ch. 1 - Show that (2arr+2brr)dt=ar2+br2+const. where r is...Ch. 1 - Show that (rrrrr2)dt=rr+C where C is a constant...Ch. 1 - Prob. 1.34PCh. 1 - Prob. 1.35PCh. 1 - Prob. 1.36PCh. 1 - Prob. 1.37PCh. 1 - Prob. 1.38PCh. 1 - A plane passes through the three points (x, y, z)...Ch. 1 - For what values of a are the vectors A = 2ai − 2j...
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