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A bucket of mass 1.00 kg is whirled in a vertical circle of radius 1.40 m.

A bucket of mass 1.00 kg is whirled in a vertical circle of radius 1.40 m. At the lowest point of its motion the tension in the rope supporting the bucket is 25.0 N.

(a) Find the speed of the bucket.

(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?

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1 Answer

a)

Draw a free body diagram, and apply Newton's second law:

T - mg = m(v2/r)

Plug in known values,

25 - 1.00*g = 1.00(v2/1.40)

Solve for v,

v = 4.61 m/sec <==Answer

 

b)

When T = 0, solve for v,

mg = m(v2/r)

v = √(rg) = √(1.40g) = 3.70 m/sec <==the minimum speed.