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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

Box as .sysA

intA Interactions: intA External influences from the person (applied force) the earth (gravity) and the floor (normal force and friction).

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

\begin{large}\[ N = F\sin\theta + mg \]\end{large}

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

\begin{large}\[ F\cos\theta - \mu_{k}\left(F\sin\theta + mg\right) = ma_{x}\]\end{large}

\begin{large}\[ F = \frac{ma_{x} +\mu_{k}mg}{\cos\theta - \mu_{k}\sin\theta} = \mbox{150 N}\]\end{large}

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

\begin{large}\[ N = mg - F\sin\theta\]\end{large}

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

\begin{large}\[ F = \frac{ma_{x} +\mu_{k}mg}{\cos\theta + \mu_{k}\sin\theta} = \mbox{88 N}\]\end{large}