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15 April, 03:58

The friends now feel ready to try a problem. Suppose an Atwood machine has a mass of m1 = 2.5 kg and another mass of m2 = 8.5 kg hanging on opposite sides of the pulley. Assume the pulley is massless and frictionless, and the cord is ideal. Determine the magnitude of the acceleration of the two objects and the tension in the cord.

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  1. 15 April, 04:45
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    a = 5.34 m/s²

    T = 37.86 N

    Explanation:

    This is the case where two masses are hanging vertically on sides of the pulley. In such case, the formula for acceleration of objects is derived to be:

    a = g (m₂ - m₁) / (m₂ + m₁)

    where,

    a = acceleration of both masses = ?

    g = 9.8 m/s²

    m₂ = heavier mass = 8.5 kg

    m₁ = lighter mass = 2.5 kg

    Therefore,

    a = (9.8 m/s²) (8.5 kg - 2.5 kg) / (8.5 kg + 2.5 kg)

    a = (9.8 m/s²) (6 kg) / (11 kg)

    a = 5.34 m/s²

    The formula for tension in cable is derived to be:

    T = 2m₁m₂g / (m₁ + m₂)

    T = (2) (2.5 kg) (8.5 kg) (9.8 m/s²) / (2.5 kg + 8.5 kg)

    T = 37.86 N
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