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Deck of Cards
id
bigdeck
Card
label
Part A
Wiki Markup
h2.
Part
A
!thatnormal1.png|width=500!
A person holds a 10 kg box against a smooth
A
Image Added
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 .
Toggle Cloak
id
inta
Interactions:
Cloak
id
inta
External influences from the earth (gravity), the wall () and the person ().
Toggle Cloak
id
moda
Model:
Cloak
id
moda
.
Toggle Cloak
id
appa
Approach:
Cloak
id
appa
Toggle Cloak
id
diaga
Diagrammatic Representation
Cloak
id
diaga
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
id
matha
Mathematical Representation
Cloak
id
matha
From the free body diagram, we can write the equations of Newton's 2nd Law.
Latex
* {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}\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}
Cloak
matha
matha
Cloak
appa
appa
Card
label
Part B
unmigrated-wiki-markup
h2.
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
id
sysb
System:
Cloak
id
sysb
Box as .
Toggle Cloak
id
intb
Interactions:
Cloak
id
intb
External influences from the earth (gravity), the wall () and the person ().
Toggle Cloak
id
modb
Model:
Cloak
id
modb
.
Toggle Cloak
id
appb
Approach:
Cloak
id
appb
Toggle Cloak
id
diagb
Diagrammatic Representation
Cloak
id
diagb
We begin with a free body diagram for the box:
Image Added
Cloak
diagb
diagb
Toggle Cloak
id
mathb
Mathematical Representation
Cloak
id
mathb
From the free body diagram, we can write the equations of Newton's 2nd Law.
Latex
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}\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}
Cloak
mathb
mathb
Cloak
appb
appb
Card
label
Part C
Wiki Markup
h2.
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
id
sysc
System:
Cloak
id
sysc
Box as .
Toggle Cloak
id
intc
Interactions:
Cloak
id
intc
External influences from the earth (gravity), the ceiling () and the person ().
Toggle Cloak
id
modc
Model:
Cloak
id
modc
.
Toggle Cloak
id
appc
Approach:
Cloak
id
appc
Toggle Cloak
id
diagc
Diagrammatic Representation
Cloak
id
diagc
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
id
mathc
Mathematical Representation
Cloak
id
mathc
From the free body diagram, we can write the equations of Newton's 2nd Law.
Latex
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}\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}
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).