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5 March, 17:16

After landing on an unfamiliar planet, a space explorer constructs a simple pendulum of length 55.0 cm. The explorer finds that the pendulum completes 108 full swing cycles in a time of 132 s. Part A What is the magnitude of the gravitational acceleration on this planet

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  1. 5 March, 19:26
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    The magnitude of the gravitational acceleration on this planet is 14.54 m/s².

    Explanation:

    given information:

    pendulum length, L = 55 cm = 0.55 m

    total swing, n = 108

    time, t = 132 s

    to calculate the gravitational acceleration of the planet, we can use the simple pendulum formula

    T = 2π√ (L/g)

    where

    T = period (s)

    L = the length of pendulum (m)

    g = gravitational force (m/s²)

    thus,

    T² = (2π) ² (L/g)

    g = (2π) ² (L/T²)

    we know that

    T = t/n

    so,

    g = (2π) ² (L/T²)

    = (2π) ²[L / (t/n) ²]

    = (2π) ²[L (n/t) ²]

    = (2π) ² [0.55 (108/132) ²]

    = 14.54 m/s²
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