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{
Wiki Markup
Composition Setup
 Deck of Cards
idbigdeck
}{composition-setup}
{deck:id=bigdeck}
{card:label=Part A}

h3. Part 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:*  

{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}
 Card
labelPart A
Part A
Image Added
 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.
 The box accelerates horizontally at a rate of 2.0 m/s2. What is the magnitude of F?
Solution
 Toggle Cloak
idsysa
 System: 
 Cloak
idsysa
Box as .
 Toggle Cloak
idinta
 Interactions: 
 Cloak
idinta
External influences from the person (applied force) the earth (gravity) and the floor (normal force).
 Toggle Cloak
idmoda
 Model: 
 Cloak
idmoda
.
 Toggle Cloak
idappa
 Approach: 
 Cloak
idappa
 Toggle Cloak
iddiaga
  Diagrammatic Representation 
 Cloak
iddiaga
Before writing Newton's 2nd Law for the x direction, we choose coordinates and break the applied force F into x- and y-components:
Image Added
 Cloak
diaga
diaga
 Toggle Cloak
idmatha
  Mathematical Representation 
 Cloak
idmatha
Using the free body diagram, we can write the relevant x-component of Newton's 2nd 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}
{card}
{card:label=Part B}

h3. Part B

!pushblock2_2.png|width=400!

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}
 Cloak
matha
matha
 Cloak
appa
appa
 Card
labelPart B
Part B
Image Added
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/s2. What is the magnitude of F?
Solution
 Toggle Cloak
idsysb
 System: 
 Cloak
idsysb
 Box as .
 Toggle Cloak
idintb
 Interactions: 
 Cloak
idintb
 External influences from the person (applied force) the earth (gravity) and the floor (normal force).
 Toggle Cloak
idmodb
 Model: 
 Cloak
idmodb
.
 Toggle Cloak
idappb
 Approach: 
 Cloak
idappb
 Toggle Cloak
iddiagb
  Diagrammatic Representation 
 Cloak
iddiagb
Before writing Newton's 2nd Law for the x direction, we choose coordinates and break the applied force F into x- and y-components:
Image Added
 Cloak
diagb
diagb
 Toggle Cloak
idmathb
  Mathematical Representation 
 Cloak
idmathb
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}
{card}
{deck}

 Cloak
mathb
mathb
 Cloak
appb
appb