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30 August, 23:05

A dog sits 1.22 m from the center of a merrygo-round with an angular speed of 1.07 rad/s. If the magnitude of the force that maintains the dog's circular motion is 32.3 N, what is the dog's mass?

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  1. 30 August, 23:06
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    24.74 kg

    Explanation:

    The formula of centripetal force is given as

    F = mv²/r ... Equation 1

    Where F = Force, m = mass of the dog, v = velocity of the dog, r = radius of the circle

    Also,

    v = ωr ... Equation 2

    ω = angular velocity

    Substitute equation 2 into equation 1

    F = m (ωr) ²/r

    F = mω²r ... Equation 3

    Make m the subject of the equation,

    m = F/ω²r ... Equation 4

    Given: F = 32.3 N, r = 1.22 m, ω = 1.07 rad/s

    Substitute into equation 4

    m = 32.3 / (1.22*1.07)

    m = 24.74 kg.

    Thus the mass of the dog = 24.74 kg
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