SYMBOLIC PROBLEM: Bob picks up a bucket of water by a rope and swings it around

Question

SYMBOLIC PROBLEM:

Bob picks up a bucket of water by a rope and swings it around in a vertical plane. The bucket passes through the top of the circle with a speed v1.
(Note: You may neglect air resistance.)

a.) At point 1 (top of the loop):

How large is centripetal acceleration of the bucket? (Express as a multiple of g.)
ac,1 = _____ g

How much is the tension in the rope? (Express as a multiple of the bucket's weight.)
T1 = _____ mg

b.) At point 2 (bucket at same height as the center of the circle):

What is the speed of the bucket? (Express as a multiple of v1.)
v2 = _____ v1

How large is centripetal acceleration of the bucket?
ac,2 = _____ g

How much is the tension in the rope?
T2 = ______ mg

c.) Repeat when the bucket is at point 3 (bottom of the swing):
v3 = _____ v1
ac,3 = _____ g
T3 = ______ mg

SYMBOLIC PROBLEM: Bob picks up a bucket of water by a rope and swings it around in a vertical plane. The bucket passes through the top of the circle with a speed v1. (Note: You may neglect air resistance.) a.) At point 1 (top of the loop): How large is centripetal acceleration of the bucket? (Express as a multiple of g.) ac,1 = _____ g How much is the tension in the rope? (Express as a multiple of the bucket's weight.) T1 = _____ mg b.) At point 2 (bucket at same height as the center of the circle): What is the speed of the bucket? (Express as a multiple of v1.) v2 = _____ v1 How large is centripetal acceleration of the bucket? ac,2 = _____ g How much is the tension in the rope? T2 = ______ mg c.) Repeat when the bucket is at point 3 (bottom of the swing): v3 = _____ v1 ac,3 = _____ g T3 = ______ mg

Explanation / Answer

1. (A) at top of the circle v=sqrt (g

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