Classical Dynamics of Particles and Systems
5th Edition
ISBN: 9780534408961
Author: Stephen T. Thornton, Jerry B. Marion
Publisher: Cengage Learning
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Question
Chapter 1, Problem 1.37P
To determine
The value of the integral
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Students have asked these similar questions
The surface integral of V = x + yŷ + (z - 3)2 over the sphere of unit radius centred at
the origin is
Select one:
○ a. 4π
○ b. O
○ c. 4π/3
○ d. π
Q# 02:
Use Green's Theorem in a plane to evaluate the integral
S,[(2x² – y²)dx + (x² + y²)dy] Where C is the boundary in xy-
plane of the area enclosed by the x-axis and the semi-circle x² + y² = 1 in the upper
half of xy-plane.
b) Given F(x, y, z) = (x³ + cosh z) i+ (2y³ – 3r²y)j – (x² + 4y²z) k. Use
Gauss's theorem to calculate //F
.n dS where n is the outward
unit normal of o, the surface bounded by the planes, x = 0, z = 0 and
x + z = 6, and the parabolic cylinder x = 4 – y².
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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- If A = 2yz i – (x + 3y – 2)j+ (x² + z)k, evaluate SS, (V × A)· dS over the surface of intersection of the cylinders x² +y? = 1, x? + z² = 1 which is included in the first octant.arrow_forwardQUESTION 1 Give a physical interpretation of what is meant by the curl of a vector. Suppose a vector function A is given by A=-yi + xj and another vector function B is given by B = xj. 1.1 1.2 1.3 Calculate (i) the curl of A: (ii) the curl of B: V x A and Vx B. In which direction are the curls pointing? Hence what can you say about their divergence and why?arrow_forwardConsider a rectangular surface of length L and width W in the xy plane with its center at the origin: Which of the following are valid expressions for the area vector of this surface? Check all that apply. O (0,0, LW) O (W, L, 0) O (0,0, -LW) O (LW, LW, 0) O (0, LW, 0) O (L, W, 0)arrow_forward
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