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    Part A

    A person pushes a box of mass 15 kg along a floor by applying a perfectly horizontal force F. The box accelerates horizontally at a rate of 2.0 m/s2. Assuming the coefficient of kinetic friction between the box and the ground is 0.45, what is the magnitude of F?

    Solution

    System:

    Interactions:

    Model:

    Approach:

    Diagrammatic Representation

    The free body diagram for this situation is:

    Mathematical Representation

    With this free body diagram, Newton's 2nd Law can be written:

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    \begin

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    [ \sum F_

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    = F - F_

    Unknown macro: {f}

    = ma_

    ]
    [ \sum F_

    Unknown macro: {y} = N - mg = ma_

    = 0 ]\end

    where we have assumed that the y acceleration is zero because the box is sliding along a horizontal floor, not moving upward or downward. This realization is important, because we know Ff = μN. Thus, because the y acceleration is zero, we can solve Newton's 2nd Law in the y direction to yield:

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    \begin

    Unknown macro: {large} [ N = mg]\end

    so that:

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    \begin

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    [ F = ma_

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    +F_

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    = ma_

    + \mu_

    Unknown macro: {k}

    N = ma_

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    + \mu_

    mg = \mbox

    Unknown macro: {96 N}

    ] \end

    Part B

    A person pushes a box of mass 15 kg along a floor by applying a perfectly horizontal force F. The box moves horizontally at a constant speed of 2.0 m/s in the direction of the person's applied force. Assuming the coefficient of kinetic friction between the box and the ground is 0.45, what is the magnitude of F?

    System, Interactions and Model:

    Approach:

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