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 1.4P
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(a) (AB)t = BtAt (b) (AB)−1 = B−1 A−1
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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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- In 2011, artist Hans-Peter Feldmann covered the walls of a gallery at the New York Guggenheim Museum with 100,000 one-dollar bills (Fig. P1.48). Approximately how much would it cost you to wallpaper your room in one-dollar bills, assuming the bills do not overlap? Consider the cost of the bills alone, not other supplies or labor costs. FIGURE P1.48arrow_forwardShow that 3, by calculating the change in volume V of a cube with sides of length L.arrow_forwardPlease only asnwer part (d) Answer of (a) : 60 Answer of (b) : 120 Answer of (c) : particle K.E. increases by 17.1Jarrow_forward
- Show that, when SI units for µ0 and ε0 are entered, the units given by the right-hand side of the equation in the problem above are m/s.arrow_forwardSuppose that a person has an average heart rate of72.0 beats/min. How many beats does he or she have in 2.0y? (b) In 2.00 y? (c) In 2.000 y?arrow_forwardWhy was m converted to cm?arrow_forward
- A study finds that the metabolic rate of mammals is proportional to m3/4, where m is the total body mass. By what factor does the metabolic rate of a 70.0-kg human exceed that of a 6.50-kg cat?arrow_forwardshow that v^2/r has dimensions of m/s^2arrow_forwardGIVEN: A= 5.00i + 2.00j B =3.00i + 1.00j – 3.00k C = 2.00i + 8.00j Find B x (AxC)arrow_forward
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