SOLUTION: Water is taken from a well 11m deep in a bucket, the rope winding on to a drum 35cm in diameter. Through what angle does the handle turn in winding up 1m of rope? If the arm of the
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Question 1134297: Water is taken from a well 11m deep in a bucket, the rope winding on to a drum 35cm in diameter. Through what angle does the handle turn in winding up 1m of rope? If the arm of the handle is 42cm long, how far does the handle of the winder travel when bringing the bucket up from the bottom? Answer by ikleyn(52784) (Show Source):
The formula S = for the arc length " S " via the radius " r " and the central angle " " (in radians) works
in both cases when the angle is between 0 and and when the angle is greater (larger) than , describing many rotations.
For the first question, the arc length is 1 meter, the radius r = = 0.175 meters.
So, the angle the handle turn in winding up 1 m of the rope is
= = = 5.714 radians = 329 degrees. ANSWER
For the second question, you may continue through this way, but more short way is to use a proportion
=
to find the distance " x " the handle of the winder travel when bringing the bucket up 11 meters from the bottom.
From the proportion, x = = 26.4 meters. ANSWER
