A bucket of mass 2.00 is whirled in a vertical circle of radius 1.45 . At the lo

Question

A bucket of mass 2.00 is whirled in a vertical circle of radius 1.45 . At the lowest point of its motion the tension in the rope supporting the bucket is 24.0 . part A: Find the speed of the bucket. part B: How fast must the bucket move at the top of the circle so that the rope does not go slack?

Explanation / Answer

(a) At bottom, =>T = mv^2/r + mg =>24 = 2 x v^2/1.45 + 2 x 9.8 =>24 = 2v^2 + 21.05 =>2v^2 = 24-21.05 = 2.95 =>v^2 = 2.95/2 = 1.475 =>v = sqrt1.475 = 1.21 m/s (b) At top, =>T = mv^2/r - mg [ for T = 0] =>mv^2/r = mg =>v = sqrt(r x g) = sqrt (1.45 x 9.8) = 3.76 m/s

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