GROUP WORK 1, SECTION 64 The Weighty Chain A bucket that weighs 70 lb when fille

Question

GROUP WORK 1, SECTION 64 The Weighty Chain A bucket that weighs 70 lb when filled with water is lifted at a constant rate, by a mechanical winch, from the bottom of a well that is 60 feet deep. 1. Compute the work required to lift the bucket from the bottom of the well to the top 2. Oops, we forgot to tell you! The chain that is being used to lift the bucket weighs 0.55 pounds per foot Now find the correct amount of work required to lift the bucket from the bottom of the well all the way to the top 3. Oh no! Where is our head at today? We completely forgot to mention that the bucket has a hole in the bottom. It only weighs 35 Ib when it reaches the top, due to the water leaking out at a constant rate. Now compute the real work required to lift the bucket from the bottom of the well to the top of the well (Recall that the bucket is being lifted at a constant rate, as well

Explanation / Answer

Since 35 lb reaches to the top and remaining 35lb leaks at constant rate so we can assume that 35lb reach at half distance. Similarly we can assume mass of chain at half distance.

Now, Work = 35×60+35×30+.55×60×30

Work = 4140 lb-ft

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