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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.

Box as .

External influences from the person (applied force) the earth (gravity) and the floor (normal force).

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 A

!pushbox2_1.png|width=400!

{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:*  

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

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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!

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

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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}