You swing a 3.25 kg bucket of water in a vertical circle of radius 0.950 m. At t

Question

You swing a 3.25 kg bucket of water in a vertical circle of radius 0.950 m. At the top of the circle the speed is 3.23 m/s, at the bottom of the circle its speed is 6.91 m/s. 1. Express the angular speeds in rad/s at the top and bottom. 2. Find the tension in the rope tied to the bucket at the top of the circle. 3. Find the tension in the rope tied to the bucket at the bottom of the circle. 4. What minimum speed at the top of the arc must be necessary to complete the circle without spilling any water?

Explanation / Answer

1)at top

v=wr

w=3.23/0.950=3.4 rad/sec

at bottom

w=6.91/0.950=7.2736 rad/sec

2)tension at top

T=mv2/r-w=3.25((3.23)2/0.950 -9.8))

T=3.8415N

3)tension at bottom

T=mv2/r+w

T=195.198N

4)minimum speed less than 3.4 rad/sec

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