Classical Dynamics of Particles and Systems
5th Edition
ISBN: 9780534408961
Author: Stephen T. Thornton, Jerry B. Marion
Publisher: Cengage Learning
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Chapter 1, Problem 1.13P
X is an unknown vector satisfying the following relations involving the known vectors A and B and the scalar ϕ,
A × X = B, A · X = ϕ.
Express X in terms of A, B, ϕ, and the magnitude of A.
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Given (Ã × B) · Ĉ.
(a) Prove that for any three vectors Ā, B, and C, AẢ · (B × C) = (Ả × B) · T
(b) Calculate (Á × B) · Ć for vector A with magnitude A = 5.00 and angle 6A = 26.0°
(measured from the +x -axis toward the +y -axis), vector B with B = 4.00 and
OB
63.0°, and vector C' with magnitude 6.00 and in the +z -direction. Vectors A
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Resolve A and B into components, and express using ijk unit vectors,
A = Axi + Ayj + A-k
B = B₂i + B₂j + B₂k
where A., Ay, A₂ and B₁, B₁, and B₂ are the calculated values of the x-, y-, and z-components of vectors A and
B, respectively.
Ā =
B =
Find the magnitude and unit vector for the cross product between A and B.
|ĀXB| =
Identify the unit vector for AX B.
j
k
Vectors A and B lie in an xy plane. A has magnitude 7.6 and angle 116° relative to +x direction: ☎ has components B, -4.14 and 8,
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Ax B, and (c) the direction of Ax (B+3.00A)?
(a) Number
154
(b) Number 90
(c) Number
150.3418858
Units
(degrees)
Units *(degrees)
Units "(degrees)
Chapter 1 Solutions
Classical Dynamics of Particles and Systems
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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