Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Chapter 14, Problem 23P
To determine
The relation between resonant frequencies of two spring-mass systems.
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A simple pendulum with a length of 1.73 m and a mass of 6.74 kg is given an initial speed of 2.36 m/s at its equilibrium position.
(a) Assuming it undergoes simple harmonic motion, determine its period (in s).
(b) Determine its total energy (in J).
(c) Determine its maximum angular displacement (in degrees). (For large v, and/or small /, the small angle approximation may not be good enough here.)
(d) What If? Based on your answer to part (c), by what factor would the total energy of the pendulum have to be reduced for its motion to be described as
simple harmonic motion using the small angle approximation where 0 ≤ 10°?
A 6-kg mass is attached to a spring whose stiffness constant is 150 N/m.
The damping is negligible. The mass is displaced through a distance of
2m to the left of the equilibrium position and given a velocity of - m/s
to the right. The amplitude, natural frequency of the motion and the
time when the mass return to its equilibrium position for the first time
are given by
Select one:
V401
cycles/sec and 0.93s
10
V401
cycles/sec and 0.3s.
10
V401
cycles/sec and 0.3s
10
(401
cycles/sec and 0.93s
10
The system is released from rest with no slack in the cable and with the spring stretched 290 mm. Determine the distance s traveled by
the 17-kg cart before it comes to rest (a) if m approaches zero and (b) if m = 4.9 kg. Assume no mechanical interference.
17 kg
25°
m
k = 213 N/m
Answers:
(a) With m = 0,
S =
i
(b) With m = 4.9 kg,
S =
i
Chapter 14 Solutions
Physics for Scientists and Engineers
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