Fig. 6-48 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 0.038 kg, the string has length L = 1.2 m and negligible mass, and the bob follows a circular path of circumference 0.75 m. What are (a) the tension in the string and (b) the period of the motion?

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  1. The angle of the pendulum from vertical is
    A = arcsin r/L = arcsin [0.75/(2 pi L)]
    = 5.71 degrees
    You will need this angle later.

    The vertical and horizontanl equations of motion are:
    T sin A = m V^2/R
    T cos A = m g
    which tells you that
    tan A = 0.100 = V^2/gR
    V^2 = 0.100*9.8m/s^2*0.1194m = 0.1170 m^2/s^2
    V = 0.342 m/s
    (a) T = mg/cosA = 0.038kg*9.8m/s^2/.9950
    = 0.3743 Newtons
    (b) Period = (circumference)/V
    = 2 pi R/sqrt(g R tan A)
    for small angles A, tan A = R/L, so
    Period = 2 pi R /sqrt (g R *R/L)
    = 2 pi sqrt (L/g)
    which is the same as the formula for a pendulum oscillating in a plane (one dimension)
    Period = 2.2 seconds
    Check my work

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  2. Thanks!

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