Question 174715This question is from textbook Amsco's Preparing for the Regents Examination Mathematics B
: (15) Melba is building a grandfather clock and needs to know the minimum width of the case. If the pendulum;s arc subtends a central angle of 1.2 radians and the lenght of the pendulum itself is 18 inches, what is the minimum width of the clock case, to the nearest tenth of an inch, needed?
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This question is from textbook Amsco's Preparing for the Regents Examination Mathematics B
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! (15) Melba is building a grandfather clock and needs to know the minimum width of the case. If the pendulum;s arc subtends a central angle of 1.2 radians and the lenght of the pendulum itself is 18 inches, what is the minimum width of the clock case, to the nearest tenth of an inch, needed?
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When the pendulum is at its farthest excursion, it forms a right triangle with its centerline. The hypotenuse is 18" and the angle at the top (the pivot of the pendulum) is 0.6 rads. The horizontal leg is 18*sin(0.6), and the width of the case has to be twice that, = 36*sin(0.6) inches.
Minimum width = 20.3 inches.
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BTW, pendulums never swing more than about 8º off center, usually less.
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