Classical Dynamics of Particles and Systems
5th Edition
ISBN: 9780534408961
Author: Stephen T. Thornton, Jerry B. Marion
Publisher: Cengage Learning
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Textbook Question
Chapter 1, Problem 1.12P
Let a, b, c be three constant vectors drawn from the origin to the points A, B C. What is the distance from the origin to the plane defined by the points A, B C? What is the area of the triangle ABC?
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Question 6:
Chlorine is widely used to purify municipal water supplies and to treat swimming pool
waters. Suppose that the volume of a particular sample of Cl₂ gas is 8.70 L at 895 torr
and 24°C.
(a) How many grams of Cl₂ are in the sample?
⚫ Atomic mass of CI = 35.453 g/mol
• Molar mass of Cl₂ = 2 x 35.453 = 70.906 g/mol
Solution:
Use the Ideal Gas Law:
Step 1: Convert Given Values
• Pressure: P = 895 torr → atm
PV=
= nRT
1
P = 895 ×
= 1.1789 atm
760
•
Temperature: Convert to Kelvin:
T24273.15 = 297.15 K
• Gas constant: R = 0.0821 L atm/mol. K
Volume: V = 8.70 L
Step 2: Solve for n
.
PV
n =
RT
n =
(1.1789)(8.70)
(0.0821)(297.15)
10.25
n =
= 0.420 mol
24.405
Step 3: Calculate Mass of Cl₂
Final Answer: 29.78 g of Cl₂.
mass nx M
mass=
(0.420)(70.906)
mass=
29.78 g
E1
R₁
w
0.50
20 Ω
12
R₁₂
ww
ΒΩ
R₂
60
E3
C
RA
w
15 Ω
E2
0.25
E4
0.75 Ω
0.5 Ω
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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