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h2. Part A

!pushbox2_1.png|width=40%!

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/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).

Model: [Point Particle Dynamics].

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

This 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}

h4. Part B

!pushbox2pushblock2_2.png|width=40%!

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_?

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

Model: [Point Particle Dynamics].

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

This 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}