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posted by  jjn000 on 11/5/2009 12:32:53 AM  |  status: Closed  |  Earned Karma: 66

Will rate Lifesaver... Tension and Period of motion

Course Textbook Chapter Problem Needs by
General Physics Fundamentals of Physics Extended (8th) by Halliday, Resnick, Walker N/A N/A 11/5/2009 at 1:00:00 AM
Question Details:
The figure below shows a "conical pendulum", in which the bob (the small object at the lower end of the cord) moves in a horizontal circle at constant speed. (The cord sweeps out a cone as the bob rotates.) The bob has a mass of 0.055 kg, the string has length L = 0.60 m and negligible mass, and the bob follows a circular path of circumference 0.88 m.
(a) What is the tension in the string?
1Your answer is incorrect. N

(b) What is the period of the motion?
2 s
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posted by esther_jyothi on 11/5/2009 1:04:48 AM  |  status: Live
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posted by Mobiusdick on 11/5/2009 1:13:24 AM  |  status: Live
Asker's Rating: Lifesaver   
Response Details:
a) The centripetal force causes the bob to deviate from hanging straight down at an angle determined by the ratio of its force to the force of gravity. This angle is also represented by the string.

sin θ = Fg / T                 cos θ = r / L
sin θ = .055*9.8/T         cos θ = (.88/2π)/.6  =>    θ = 76.5 deg
T = .055*9.8/sin(76.5deg)
T = .554 N

b) Fc/T = cos θ     Fc = T*cosθ = .554*cos(76.5) = .129N
Fc = m*(v2)/r = .055*(v2)/(.88/2π) = .129N
v2 = .329
v = .573 m/s

T = 2πr/v = .88/.573 = 1.534s
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