Classical Dynamics Of Particles And Systems
5th Edition
ISBN: 9788131518472
Author: Stephen T. Thornton, Jerry B. Marion
Publisher: Cengage Learning India
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Chapter 1, Problem 1.24P
To determine
The proof for
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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 general it is best to conceptualize vectors as arrows in space, and then to make calculations with them using their components. (You must first specify a coordinate system in order to find the components of each arrow.) This problem gives you some practice with the components. Let vectors A = (1,0, -3), B = (-2, 5, 1), and C = (3,1,1). Calculate the following, and express your answers as ordered triplets of values separated by commas.arrow_forwardIn general it is best to conceptualize vectors as arrows in space, and then to make calculations with them using their components. (You must first specify a coordinate system in order to find the components of each arrow.) This problem gives you some practice with the components. Let vectors A = (1,0, −3), B = (-2, 5, 1), and C = (3,1,1). Calculate the following, and express your answers as ordered triplets of values separated by commas.arrow_forwardOnly Part C.) is necessaryarrow_forward
- Only Part B.) is necessaryarrow_forwardA (3.60 m) 30.0°- 70.0° x B (2.40 m)arrow_forwardIn general it is best to conceptualize vectors as arrows in space, and then to make calculations with them using their components. (You must first specify a coordinate system in order to find the components of each arrow.) This problem gives you some practice with the components. Let vectors A = (1,0, -3), B = (-2, 5, 1), and C = (3,1,1). Calculate the following, and express your answers as ordered triplets of values separated by commas.arrow_forward
- fine the magnitude of the vector product express in sq meters what direction is the vector product in -z or +zarrow_forward4) Three point charges of magnitude Q1 = +2.0 μC, Q2 = +3.0 μС, Q3 = = +4.0 μС are located at the corners of a triangle as shown in the figure below. Assume d = 20 cm. (a) Find the resultant force vector acting on Q3. (b) Find the magnitude and direction of the force. d Q3 60° d Q1 60° 60° Q2 darrow_forwardThree point charges of magnitudes Q₁ = +6.0 μС, Q₂ = −7.0 μС, Qз = −13.0 μC are placed on the x-axis at x = 0 cm, x = 40 cm, and x = 120 cm, respectively. What is the force on the Q3 due to the other two charges?arrow_forward
- Two point charges of +30.0 μС and -9.00 μC are separated by a distance of 20.0 cm. What is the intensity of electric field E midway between these two charges?arrow_forwardTwo point charges of +7.00 μС and +10.0 μС are placed inside a cube of edge length 0.100 m. What is the net electric flux due to these charges?arrow_forwardA conducting hollow sphere has a charge density of σ = 12.2 μC/m². If the sphere has a radius of 25 cm, what net charge is on the sphere?arrow_forward
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