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QUESTION: A clothes line is installed joining two pulleys whose centres are 12 m apart. Each pulley has a radius of 10 cm. How long (in cm) will the string need to be? (Round your answer to the nearest unit.)

ANSWER: Not sure I understand what is being asked in this question. Is the length of a line between the centers of the pulleys wanted? Please clarify.

Randy

---------- FOLLOW-UP ----------

Similar image to word problem
Similar image to word  
QUESTION: I think it wants to know the length of the string that will attach the two pulleys together as well as going around both of them. So the string will go around both wheels.
(The image that I have sent to you along with this follow-up question is not the same, but it is similar to the one represented in my Math book)

Answer
It looks like we want to know the length of the string that goes around both pulleys in a single loop. From the picture, the top and bottom of the loop are the same length and are equal to 12m = distance between the centers of the pulleys. Added to this length are the lengths of string that goes around the pulleys. But each pulleys only has the string go around it halfway, or half the circumference. Since there are 2 pulleys, the total length of these pulley-segments will be a whole circumference or 2pi(10cm). So the total length of the string needed is

L = 2(12m) + 2pi(0.1m).

I'll let you do the artihmetic. Note that I've converted the radius of the pulleys to meters so that the units are consistent in the formula. Very important!

Randy

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randy patton

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college mathematics, applied math, advanced calculus, complex analysis, linear and abstract algebra, probability theory, signal processing, undergraduate physics, physical oceanography

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26 years as a professional scientist conducting academic quality research on mostly classified projects involving math/physics modeling and simulation, data analysis and signal processing, instrument development; often ocean related

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J. Physical Oceanography, 1984 "A Numerical Model for Low-Frequency Equatorial Dynamics", with M. Cane

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M.S. MIT Physical Oceanography, B.S. UC Berkeley Applied Math

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