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Composition Setup
 Deck of Cards
idbigdeck
 Wiki Markup
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}
 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}

h4. Part B

!pushbox2_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}
 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
mathb
 Cloak
appb
appb