Bob picks up a bucket of water by a rope and swings it around in a vertical plan

Question

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.)

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 the top of the loop, the bucket barely keeps from falling into the circle. Find an expression for the radius of the circle, in terms of the given variable. (What would happen if the rope were shortened/lengthened from there?) At point 1 (top of the loop): How large is centripetal acceleration of the bucket? (Express as a multiple of g.) ac,1 = x g (Found answer to be 1.) How much is the tension in the rope? (Express as a multiple of the bucket's weight.) T1 = x mg (Found answer to be 0.) 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 = x v1 How large is centripetal acceleration of the bucket? ac,2 = x g How much is the tension in the rope? T2 = x mg Repeat when the bucket is at point 3 (bottom of the swing): v3 = x v1 ac,3 = x g T3 = x mg

Explanation / Answer

a) m*v1^2/r = m*g

r = v1^2/g

b) a = g

T1 = m*g-m*a = 0

c) v2 = sqrt(v1^2+2*g*r) = sqrt(3*g*r)

v2 = sqrt(3)*v1

a2 = v2^2/r = 3*v1^2/r = 3*g

T2 = 3*m*g

d)

v3 = 5*v1

a = 5*g

T = 5*m*g

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