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 1.23P
Use the εijk notation and derive the identity
(A × B) × (C × D) = (ABD)C − (ABC)D
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Report on the percentage errors (with uncertainty) between the value of 'k' from the F vs displacement plot and each of the values of 'k' from the period measurements. Please comment on the goodness of the results.
Value of k = Spring constant k = 50.00 N/m
Each of the values of k from period measurements:
Six Measurements of time for 5 osccilations: t1 = 7.76s, t2=8.00s, t3=7.40s, t4=7.00s, t5=6.90s, t6=7.10s
(t1-tavg)^2 = (7.76-7.36)^2 = 0.16%(t2-tavg)^2 =(8.00-7.36)^2 = 0.4096%(t3-tavg)^2 =(7.40-7.36)^2 = 0.0016%(t4-tavg)^2 =(7.00-7.36)^2 = 0.1296%(t5-tavg)^2 =(6.90-7.36)^2 = 0.2116%(t6-tavg)^2 =(7.10-7.36)^2 = 0.0676
No chatgpt pls will upvote
Based on the two periods (from hand timed and ultrasonic sensor), find the value of 'k' they suggest from the physics and from the value of the hanging mass. hand time period is 1.472s and ultrasonic sensor time period is 1.44s
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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