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 3, Problem 3.45P
A grandfather clock has a pendulum length of 0.7 m and mass bob of 0.4 kg. A mass of 2 kg falls 0.8 m in seven days to keep the amplitude (from equilibrium) of the pendulum oscillation steady at 0.03 rad. What is the Q of the system?
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A 0.500 kg sphere moving with a velocity given by (2.00î – 2.60ĵ + 1.00k) m/s strikes another sphere of mass 1.50 kg moving with an initial velocity of (−1.00î + 2.00ĵ – 3.20k) m/s.
(a) The velocity of the 0.500 kg sphere after the collision is (-0.90î + 3.00ĵ − 8.00k) m/s. Find the final velocity of the 1.50 kg sphere.
R =
m/s
Identify the kind of collision (elastic, inelastic, or perfectly inelastic).
○ elastic
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O perfectly inelastic
(b) Now assume the velocity of the 0.500 kg sphere after the collision is (-0.250 + 0.850ĵ - 2.15k) m/s. Find the final velocity of the 1.50 kg sphere.
✓ =
m/s
Identify the kind of collision.
O elastic
O inelastic
O perfectly inelastic
(c) Take the velocity of the 0.500 kg sphere after the collision as (−1.00ỉ + 3.40] + ak) m/s. Find the value of a and the velocity of the 1.50 kg sphere after an elastic collision. (Two values of a are possible, a positive value and a negative value. Report each with their
corresponding final velocities.)
a…
A cannon is rigidly attached to a carriage, which can move along horizontal rails, but is connected to a post by a large spring, initially unstretched and with force constant k = 1.31 x 104 N/m, as in the figure below. The cannon fires a 200-kg projectile at a velocity of 136 m/s directed 45.0°
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45.0°
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m/s
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m
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Passage Problems
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Chapter 3 Solutions
Classical Dynamics of Particles and Systems
Ch. 3 - Prob. 3.1PCh. 3 - Allow the motion in the preceding problem to take...Ch. 3 - Prob. 3.3PCh. 3 - Prob. 3.4PCh. 3 - Obtain an expression for the fraction of a...Ch. 3 - Two masses m1 = 100 g and m2 = 200 g slide freely...Ch. 3 - Prob. 3.7PCh. 3 - Prob. 3.8PCh. 3 - A particle of mass m is at rest at the end of a...Ch. 3 - If the amplitude of a damped oscillator decreases...
Ch. 3 - Prob. 3.11PCh. 3 - Prob. 3.12PCh. 3 - Prob. 3.13PCh. 3 - Prob. 3.14PCh. 3 - Reproduce Figures 3-10b and c for the same values...Ch. 3 - Prob. 3.16PCh. 3 - For a damped, driven oscillator, show that the...Ch. 3 - Show that, if a driven oscillator is only lightly...Ch. 3 - Prob. 3.19PCh. 3 - Plot a velocity resonance curve for a driven,...Ch. 3 - Let the initial position and speed of an...Ch. 3 - Prob. 3.26PCh. 3 - Prob. 3.27PCh. 3 - Prob. 3.28PCh. 3 - Prob. 3.29PCh. 3 - Prob. 3.30PCh. 3 - Prob. 3.31PCh. 3 - Obtain the response of a linear oscillator to a...Ch. 3 - Calculate the maximum values of the amplitudes of...Ch. 3 - Consider an undamped linear oscillator with a...Ch. 3 - Prob. 3.35PCh. 3 - Prob. 3.36PCh. 3 - Prob. 3.37PCh. 3 - Prob. 3.38PCh. 3 - Prob. 3.39PCh. 3 - An automobile with a mass of 1000 kg, including...Ch. 3 - Prob. 3.41PCh. 3 - An undamped driven harmonic oscillator satisfies...Ch. 3 - Consider a damped harmonic oscillator. After four...Ch. 3 - A grandfather clock has a pendulum length of 0.7 m...
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