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23 April, 20:51

A 4 kg object hangs below a 6 kg object by a string of negligible mass. If the 6 kg object is pulled upward by a force of 440 N, what is the tension in the string?

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  1. 23 April, 20:54
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    176 N

    Explanation:

    Sum of the forces on the 6 kg object:

    ∑F = ma

    F - Mg - T = Ma

    Sum of the forces on the 4 kg object:

    ∑F = ma

    T - mg = ma

    Notice that since the objects are connected, they have the same acceleration.

    Solving for acceleration in both equations:

    a = (F - Mg - T) / M

    a = (T - mg) / m

    Set equal:

    (F - Mg - T) / M = (T - mg) / m

    Cross multiply and solve for T:

    m (F - Mg - T) = M (T - mg)

    mF - mMg - mT = MT - mMg

    mF - mT = MT

    mF = mT + MT

    mF = (m + M) T

    T = mF / (m + M)

    Given F = 440 N, m = 4 kg, and M = 6 kg:

    T = (4) (440) / (4 + 6)

    T = 176 N
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