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posted by  jjn000 on 11/5/2009 12:32:52 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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AAnswers:

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posted by jerry2009 on 11/5/2009 1:13:36 AM  |  status: Live
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Response Details:

    Mass of the bob, M = 0.055 kg

    Length of the string , L = 0.6 m

    Circumference , C = 0.88 m

    Radius of the circular path = R

    Tension in the string = T

    Angle made by the string with horizontal = θ

    Circumference , C = 2 π R

    Radius, R = C / 2 π

                    = 0.88 / ( 2 * 3.14 )

                    = 0.14 m

    From the figure,  Cos θ = Adjacent side to θ / hypotenuse
                                        = R / L
                                        = 0.14 / 0.6
                                        = 0.2333

                                    θ = arc cos 0.2333
                                       = 76.51 degrees

    In vertical direction , T sin θ = M g              .............(1)

    In horizontal direction, T cos θ = M ω2  R   ..............(2)

(a)

    from equ. (1)

    Tension in the string, T = M g / sin θ
                                       = 0.055  * 9.8 / 0.9724
                                       = 0.5543 N

(b)

    From equ (2)

    T cos θ = M ω2  R 

    0.5543 * 0.2333 = 0.055 * ω2  * 0.14

    Angular velocity, ω = 4.1 rad / s

    Time period, T = 2π  /  ω
                           = 2 * 3.14 / 4.1
                           = 1.53 s
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