Rony fills a bucket with water and whirls it in a vertical circle to demonstrate that the water will not spill from the bucket at the top of the loop. if the length of the rope from his hand to the centre of the bucket is 1.24 m, what is the minimum tension in the rope (at the top of the swing)? how slow can he swing the bucket? explain your answer.

0 N, 3.49 m/s

Explanation:

Draw a free body diagram for the bucket at the top of the swing.  There are two forces acting on the bucket: weight and tension, both downwards.

If we take the sum of the forces in the radial direction, where towards the center is positive:

∑F = ma

W + T = m v² / r

The higher the velocity that Rony swings the bucket, the more tension there will be.  The slowest he can swing it is when the tension is 0.

W = m v² / r

mg = m v² / r

g = v² / r

v = √(gr)

Given that r = 1.24 m:

v = √(9.8 m/s² × 1.24 m)

v = 3.49 m/s

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