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    Part A

    A person pushes a box of mass 15 kg along a smooth floor by applying a force F at an angle of 30° below the horizontal. The box accelerates horizontally at a rate of 2.0 m/s2. What is the magnitude of F?

    Solution

    System:

    Interactions:

    Model:

    Approach:

    Diagrammatic Representation

    Before writing Newton's 2nd Law for the x direction, we choose coordinates and break the applied force F into x- and y-components:

    Mathematical Representation

    Using the free body diagram, we can write the relevant x-component of Newton's 2nd Law:

    Unknown macro: {latex}

    \begin

    Unknown macro: {large}

    [ \sum F_

    Unknown macro: {x}

    = F\cos\theta = ma_

    ] \end

    Solving for F:

    Unknown macro: {latex}

    \begin

    Unknown macro: {large}

    [ F = \frac{ma_{x}}

    Unknown macro: {costheta}

    = \mbox

    Unknown macro: {34.6 N}

    ]\end

    Part B

    A person pulls a box of mass 15 kg along a smooth floor by applying a force F at an angle of 30° above the horizontal.. The box accelerates horizontally at a rate of 2.0 m/s2. What is the magnitude of F?

    Solution

    System:

    Interactions:

    Model:

    Approach:

    Diagrammatic Representation

    Before writing Newton's 2nd Law for the x direction, we choose coordinates and break the applied force F into x- and y-components:

    Mathematical Representation

    The free body diagram implies:

    Unknown macro: {latex}

    \begin

    Unknown macro: {large}

    [ \sum F_

    Unknown macro: {x}

    = F\cos\theta = ma_

    ] \end

    Solving for F:

    Unknown macro: {latex}

    \begin

    Unknown macro: {large}

    [ F = \frac{ma_{x}}

    Unknown macro: {costheta}

    = \mbox

    Unknown macro: {34.6 N}

    ]\end

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