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h3. Part A

!pushbox2_1.png|width=300!

{excerpt}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.{excerpt}  The box accelerates horizontally at a rate of 2.0 m/s{color:black}^2^{color}.  What is the magnitude of _F_?

h4. Solution

{toggle-cloak:id=sysa} *System:*  {cloak:id=sysa}Box as [point particle].{cloak}

{toggle-cloak:id=inta} *Interactions:* {cloak:id=inta}External influences from the person (applied force) the earth (gravity) and the floor (normal force).{cloak}

{toggle-cloak:id=moda} *Model:* {cloak:id=moda}[Point Particle Dynamics].{cloak}

{toggle-cloak:id=appa} *Approach:*  

{cloak:id=appa}

{toggle-cloak:id=diaga} {color:red} *Diagrammatic Representation* {color}

{cloak:id=diaga}

Before writing [Newton's 2nd Law|Newton's Second Law] for the _x_ direction, we choose coordinates and break the applied force _F_ into x- and y-components:

!pushingboxmore1.png!

{cloak:diaga}

{toggle-cloak:id=matha} {color:red} *Mathematical Representation* {color}

{cloak:id=matha}

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

{latex}\begin{large}\[ \sum F_{x} = F\cos\theta = ma_{x}\] \end{large}{latex}

Solving for _F_:

{latex}\begin{large}\[ F = \frac{ma_{x}}{\cos\theta} = \mbox{34.6 N}\]\end{large}{latex}

{cloak:matha}
{cloak:appa}
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{card:label=Part B}

h3. Part B

!pushblock2_2.png|width=300!

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/s{color:black}^2^{color}.  What is the magnitude of _F_?

h4. Solution

{toggle-cloak:id=sysb} *System:*  {cloak:id=sysb} Box as [point particle].{cloak}

{toggle-cloak:id=intb} *Interactions:* {cloak:id=intb} External influences from the person (applied force) the earth (gravity) and the floor (normal force).{cloak}

{toggle-cloak:id=modb} *Model:* {cloak:id=modb}[Point Particle Dynamics].{cloak}

{toggle-cloak:id=appb} *Approach:*  

{cloak:id=appb}

{toggle-cloak:id=diagb} {color:red} *Diagrammatic Representation* {color}

{cloak:id=diagb}

Before writing [Newton's 2nd Law|Newton's Second Law] for the _x_ direction, we choose coordinates and break the applied force _F_ into x- and y-components:

!pushingboxmore2.png!

{cloak:diagb}

{toggle-cloak:id=mathb} {color:red} *Mathematical Representation* {color}

{cloak:id=mathb}

The free body diagram implies:

{latex}\begin{large}\[ \sum F_{x} = F\cos\theta = ma_{x}\] \end{large}{latex}

Solving for _F_:

{latex}\begin{large}\[ F = \frac{ma_{x}}{\cos\theta} = \mbox{34.6 N}\]\end{large}{latex}

{cloak:mathb}
{cloak:appb}
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