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Composition Setup
Deck of Cards
idbigdeck
Wiki Markup
{composition-setup}{composition-setup} {table:border=1|frame=void|rules=cols|cellpadding=8|cellspacing=0} {tr:valign=top} {td:width=350|bgcolor=#F2F2F2} {live-template:Left Column} {td} {td} {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

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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} {td} {tr} {table} {live-template:RELATE license}
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mathb
mathb

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appb
appb