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h2. Part A

!Pushing a Box Some More^pushbox2_1.png|width=40%!

A person pushes a box of mass 15 kg along a floor by applying a force _F_ at an angle of 30° below the horizontal.  There is friction between the box and the floor characterized by a coefficient of kinetic friction of 0.45.  The box accelerates horizontally at a rate of 2.0 m/s{color:black}^2^{color}.  What is the magnitude of _F_?

System:  Box as [point particle] subject to external influences from the person (applied force) the earth (gravity) and the floor (normal force and friction).

Model: [Point Particle Dynamics].

Approach:  We begin with a free body diagram:

 FBD

With the free body diagram as a guide, we write the equations of [Newton's 2nd Law|Newton's Second Law]:

{latex}\begin{large}\[ \sum F_{x} = F\cos\theta - F_{f} = ma_{x}\] 
\[ \sum F_{y} = N - F\sin\theta - mg = ma_{y}\] \end{large}{latex}

 box of mass 15 kg along a floor by applying a force _F_ at an angle of 30° above the horizontal.  There is friction between the box and the floor characterized by a coefficient of kinetic friction of 0.45.  The box accelerates horizontally at a rate of 2.0 m/s{color:black}^2^{color}.  What is the magnitude of _F_?

System:  Box as [point particle] subject to external influences from the person (applied force) the earth (gravity) and the floor (normal force and friction).

Model: [Point Particle Dynamics].

Approach:  We again begin with a free body diagram:

 FBD

Which implies the form of [Newton's 2nd Law|Newton's Second Law]:

{latex}\begin{large}\[ \sum F_{x} = F\cos\theta - F_{f} = ma_{x}\] 
\[ \sum F_{y} = N + F\sin\theta - mg = ma_{y}\] \end{large}{latex}

}

so

{latex}\begin{large}\[ F_{f} = \mu_{k}\left(mg - F\sin\theta\right)\]\end{large}{latex}