Versions Compared

Key

  • This line was added.
  • This line was removed.
  • Formatting was changed.
Comment: Migration of unmigrated content due to installation of a new plugin

Excerpt
hiddentrue

Several examples illustrating how to find the normal force in

...

not-so-common

...

situations.

{excerpt} {
Composition Setup
Deck of Cards
idbigdeck
Card
labelPart A

Part A

Image Added

A person holds a 10 kg box against a smooth

}{composition-setup} {deck:id=bigdeck} {card:label=Part A} h2. Part A !thatnormal1.png|width=500! A person holds a 10 kg box against a smooth

(i.e.

frictionless)

wall

(as

it

slides

down)

by

applying

a

perfectly

horizontal

force

of

300

N.

What

is

the

magnitude

of

the

normal

force

exerted

on

the

box

by

the

wall?

h4. Solution {

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 earth ([gravity|gravity (near-earth)]), the wall ([normal force]) and the person ([applied 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} We begin with a free body diagram for the box: !thatfbd1.jpg! {note}It is important to note that any surface has the potential to exert a normal force and that the normal is always perpendicular to the plane of the surface. If the wall did not exert a normal force, the box would simply pass through it.{note} {cloak:diaga} {toggle-cloak:id=matha} {color:red} *Mathematical Representation* {color} {cloak:id=matha} From the free body diagram, we can write the equations of [Newton's 2nd Law|Newton's Second Law]. {latex}

Cloak
idsysa

Box as .

Toggle Cloak
idinta
Interactions:
Cloak
idinta

External influences from the earth (gravity), the wall () and the person ().

Toggle Cloak
idmoda
Model:
Cloak
idmoda

.

Toggle Cloak
idappa
Approach:

Cloak
idappa

Toggle Cloak
iddiaga
Diagrammatic Representation

Cloak
iddiaga

We begin with a free body diagram for the box:

Image Added

Note

It is important to note that any surface has the potential to exert a normal force and that the normal is always perpendicular to the plane of the surface. If the wall did not exert a normal force, the box would simply pass through it.

Cloak
diaga
diaga

Toggle Cloak
idmatha
Mathematical Representation

Cloak
idmatha

From the free body diagram, we can write the equations of Newton's 2nd Law.

Latex
\begin{large}\[\sum F_{x} = F_{A} - N = ma_{x}\]
\[ \sum F_{y} = - mg = ma_{y}\]\end{large}
{latex}

Because

the

box

is

held

against

the

wall,

it

has

no

movement

(and

no

acceleration)

in

the

_

x

_

direction

(

_

a

_~x~

x =

0).

Setting

_

a

_~x~

x =

0

in

the

_

x

_

direction

equation

gives:

{

Latex
}
\begin{large}\[ N = F_{A} = \mbox{300 N} \]\end{large}
{latex} {cloak:matha} {cloak:appa} {card} {card:label=Part B} h2. Part B !thatnormal2.jpg|width=500! A person moves a 10 kg box up a smooth wall by applying a force of 300 N. The force is applied at an angle of 60° above the horizontal. What is the magnitude of the normal force exerted on the box by the wall? 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 earth ([gravity|gravity (near-earth)]), the wall ([normal force]) and the person ([applied 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} We begin with a free body diagram for the box: !thatfbd2.jpg! {cloak:diagb} {toggle-cloak:id=mathb} {color:red} *Mathematical Representation* {color} {cloak:id=mathb} From the free body diagram, we can write the equations of [Newton's 2nd Law|Newton's Second Law]. {latex}
Cloak
matha
matha

Cloak
appa
appa

Card
labelPart B

Part B

Image Added

A person moves a 10 kg box up a smooth wall by applying a force of 300 N. The force is applied at an angle of 60° above the horizontal. What is the magnitude of the normal force exerted on the box by the wall?

Solution

Toggle Cloak
idsysb
System:
Cloak
idsysb

Box as .

Toggle Cloak
idintb
Interactions:
Cloak
idintb

External influences from the earth (gravity), the wall () and the person ().

Toggle Cloak
idmodb
Model:
Cloak
idmodb

.

Toggle Cloak
idappb
Approach:

Cloak
idappb

Toggle Cloak
iddiagb
Diagrammatic Representation

Cloak
iddiagb

We begin with a free body diagram for the box:

Image Added

Cloak
diagb
diagb

Toggle Cloak
idmathb
Mathematical Representation

Cloak
idmathb

From the free body diagram, we can write the equations of Newton's 2nd Law.

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

Because

Because

the

box

is

held

against

the

wall,

it

has

no

movement

(and

no

acceleration)

in

the

_

x

_

direction

(

_

a

_~x~

x =

0).

Setting

_

a

_~x~

x =

0

in

the

_

x

_

direction

equation

gives:

{

Latex
}
\begin{large}\[ N = F_{A}\cos\theta = \mbox{150 N} \]\end{large}
{latex} {cloak:mathb} {cloak:appb} {card} {card:label=Part C} h2. Part C !thatnormal3.jpg|width=500! A person scrapes a 10 kg box along a low, smooth ceiling by applying a force of 300 N at an angle of 30° above the horizontal. What is the magnitude of the normal force exerted on the box by the ceiling? h4. Solution {toggle-cloak:id=sysc} *System:* {cloak:id=sysc}Box as [point particle].{cloak} {toggle-cloak:id=intc} *Interactions:* {cloak:id=intc}External influences from the earth ([gravity|gravity (near-earth)]), the ceiling ([normal force]) and the person ([applied force]).{cloak} {toggle-cloak:id=modc} *Model:* {cloak:id=modc}[Point Particle Dynamics].{cloak} {toggle-cloak:id=appc} *Approach:* {cloak:id=appc} {toggle-cloak:id=diagc} {color:red} *Diagrammatic Representation* {color} {cloak:id=diagc} We begin with a free body diagram for the box: !thatfbd3.jpg! {note}The ceiling must push down to prevent objects from moving up through it.{note} {cloak:diagc} {toggle-cloak:id=mathc} {color:red} *Mathematical Representation* {color} {cloak:id=mathc} From the free body diagram, we can write the equations of [Newton's 2nd Law|Newton's Second Law]. {latex}
Cloak
mathb
mathb

Cloak
appb
appb

Card
labelPart C

Part C

Image Added

A person scrapes a 10 kg box along a low, smooth ceiling by applying a force of 300 N at an angle of 30° above the horizontal. What is the magnitude of the normal force exerted on the box by the ceiling?

Solution

Toggle Cloak
idsysc
System:
Cloak
idsysc

Box as .

Toggle Cloak
idintc
Interactions:
Cloak
idintc

External influences from the earth (gravity), the ceiling () and the person ().

Toggle Cloak
idmodc
Model:
Cloak
idmodc

.

Toggle Cloak
idappc
Approach:

Cloak
idappc

Toggle Cloak
iddiagc
Diagrammatic Representation

Cloak
iddiagc

We begin with a free body diagram for the box:

Image Added

Note

The ceiling must push down to prevent objects from moving up through it.

Cloak
diagc
diagc

Toggle Cloak
idmathc
Mathematical Representation

Cloak
idmathc

From the free body diagram, we can write the equations of Newton's 2nd Law.

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

Because

Because

the

box

is

held

against

the

ceiling,

it

has

no

movement

(and

no

acceleration)

in

the

_

y

_

direction

(

_

a

_~y~

y =

0).

Setting

_

a

_~y~

y =

0

in

the

_

y

_

direction

equation

gives:

{

Latex
}
\begin{large}\[ F_{A}\sin\theta  - mg - N = 0 \]\end{large}
{latex}

which

we

solve

to

find:

{

Latex
}
\begin{large}\[ N = F_{A}\sin\theta - mg = \mbox{52 N}\]\end{large}
{latex} {tip}We can check that the _y_ direction is in balance. We have N (52 N) and mg (98 N) on one side, and _F_~A,y~ on the other (150 N).{tip} {cloak:mathc} {cloak:appc} {card} {deck}
Tip

We can check that the y direction is in balance. We have N (52 N) and mg (98 N) on one side, and FA,y on the other (150 N).

Cloak
mathc
mathc

Cloak
appc
appc