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Excerpt
hiddentrue

Finding apparent weight using normal force.

...

...


cloak.memory.duration = 0

...

width70%

...

One

...

way

...

that

...

we

...

perceive

...

weight

...

is

...

the

...

normal

...

force

...

we

...

experience

...

from

...

the

...

ground.

...

In

...

physics

...

problems,

...

when

...

you

...

are

...

asked

...

to

...

determine

...

apparent

...

weight,

...

the

...

quickest

...

method

...

is

...

usually

...

to

...

compute

...

the

...

normal

...

force

...

provided

...

by

...

the

...

"ground".

...

One

...

way

...

to

...

experience

...

a

...

reduced

...

apparent

...

weight

...

is

...

to

...

strap

...

into

...

a

...

harness

...

of

...

ropes

...

and

...

have

...

someone

...

(or

...

some

...

weight)

...

pull

...

down

...

on

...

the

...

other

...

end

...

like

...

they

...

do

...

in

...

theater

...

or

...

films.

...

Another

...

way

...

is

...

to

...

jump

...

into

...

a

...

swimming

...

pool,

...

where

...

the

...

water

...

lifts

...

up

...

on

...

you.

...

Another

...

possibility,

...

which

...

we

...

explore

...

in

...

this

...

problem,

...

is

...

to

...

enter

...

an

...

environment

...

where

...

the

...

"ground"

...

is

...

capable

...

of

...

moving,

...

such

...

as

...

an

...

elevator.

{:=
Deck of Cards
id
probparts
} {:=
Card
label
Part
A
} h2.

Part

A

Suppose

a

person

with

a

weight

of

686

N

is

in

an

elevator

which

is descending at a constant rate of 1.0 m/s and speeding up at a rate of

is accelerating downwards at a rate of 3.0

m/s

{color:black}^2^{color}. What is the

2. What is the person's

apparent

weight?

h4. Solution {

Solution

Toggle Cloak

:

id

=

Asys

} *

System:
Cloak
idAsys

Person as a .

Toggle Cloak
idAint
Interactions:
Cloak
idAint

External influences from the earth (gravity) and the floor of the elevator (normal force).

Toggle Cloak
idAmod
Model:
Cloak
idAmod

.

Toggle Cloak
idAapp
Approach:

Cloak
idAapp

Toggle Cloak
idAFBD
Diagrammatic Representations

Cloak
idAFBD

The physical picture and free body diagram for the person is:

Image Added

Image Added

Physical Picture

Free Body Diagram

Cloak
AFBD
AFBD

Toggle Cloak
idAmath
Mathematical Representation

Cloak
idAmath

which leads to the form of Newton's 2nd Law for the y direction:

Latex
*  {cloak:id=Asys}Person as a [point particle].{cloak}

{toggle-cloak:id=Aint} *Interactions:* {cloak:id=Aint}External influences from the earth (gravity) and the floor of the elevator (normal force).{cloak}

{toggle-cloak:id=Amod} *Model:*  {cloak:id=Amod}[Point Particle Dynamics].{cloak}

{toggle-cloak:id=Aapp} *Approach:*
{cloak:id=Aapp}  

{toggle-cloak:id=AFBD} {color:red}*Diagrammatic Representations*{color}
{cloak:id=AFBD}The physical picture and free body diagram for the person is:

|!elevator1.gif!|!elevator2.gif!|
||Physical Picture||Free Body Diagram||
{cloak:AFBD}

{toggle-cloak:id=Amath} {color:red}*Mathematical Representation*{color}
{cloak:id=Amath}which leads to the form of [Newton's 2nd Law|Newton's Second Law] for the _y_ direction:

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

In

our

coordinates,

the

acceleration

of

the

person

is

_

a

_~y~

y =

-3.0

m/s2, giving:

Latex
{color:black}^2^{color}, giving:

{latex}\begin{large}\[ N = ma_{y} + mg = \mbox{476 N} \]\end{large}{latex}
{cloak:Amath}

{toggle-cloak:id=Acheck} {color:red}*Is the answer sensible?*{color}
{cloak:id=Acheck}
{tip}This result for the normal force is less than the person's usual weight, in agreement with our expectation that the person should feel lighter while accelerating downward.{tip}
{cloak:Acheck}
{cloak:Aapp}
{card}
{card:label=Part B}

h2. Part B

Suppose a person with a weight of 686 N is in an elevator which is ascending at a constant rate of 1.0 m/s and slowing down at a rate of 3.0 m/s{color:black}^2^{color}.  What is the person's apparent weight?

h4. Solution

{toggle-cloak:id=Bsys} *System, Interactions and Model:* {cloak:id=Bsys}As in Part A.{cloak}

{toggle-cloak:id=Bapp} *Approach:*  {cloak:id=Bapp}As in Part A, the acceleration is negative in our coordinates.  The free body diagram is also the same, and so we find the same result:

{latex}\begin{large}\[ N = \mbox{476 N} \]\end{large}{latex}
{cloak}
{card}
{card:label=Part C}

h2. Part C

Suppose a person with a weight of 686 N is in an elevator which is ascending at a constant rate of 1.0 m/s and speeding up at a rate of 3.0 m/s{color:black}^2^{color}.  What is the person's apparent weight?

h4. Solution

{toggle-cloak:id=Csys} *System, Interactions and Model:*  {cloak:id=Csys}As in Part A.{cloak}

{toggle-cloak:id=Capp} *Approach:*  {cloak:id=Capp}The free body diagram and form of Newton's 2nd Law is the same as in Part A, except that the relative size of the forces will be different.  We can see this by writing Newton's 2nd Law for the y-direction:

{latex}\begin{large}\[ N = ma_{y} + mg \]\end{large}{latex}

This time, however, the acceleration is positive (_a_~y~ = + 3.0 m/s{color:black}^2^{color}) giving:

{latex}\begin{large}\[ N = \mbox{896 N} \] \end{large}{latex}
{tip}Upward acceleration increases the perceived weight.{tip}

{cloak}
{card}
{deck}

Tip

Is it clear why the acceleration must have a minus sign?

Tip

This result for the normal force is less than the person's usual weight, in agreement with our expectation that the person should feel lighter while accelerating downward.

Cloak
Amath
Amath

Cloak
Aapp
Aapp

Card
labelPart B

Part B

Suppose a person with a weight of 686 N is in an elevator which has been ascending at a constant rate of 1.0 m/s and is now slowing down at a rate of 3.0 m/s2. What is the person's apparent weight?

Solution

Toggle Cloak
idBsys
System, Interactions and Model:
Cloak
idBsys

As in Part A.

Toggle Cloak
idBapp
Approach:

Cloak
idBapp
Card
labelPart C

Part C

Suppose a person with a weight of 686 N is in an elevator which is ascending, speeding up at a rate of 3.0 m/s2. What is the person's apparent weight?

Solution

Toggle Cloak
idCsys
System, Interactions and Model:
Cloak
idCsys

As in Part A.

Toggle Cloak
idCapp
Approach:

Cloak
idCapp
Column
width30%
{table:align=right|cellspacing=0|cellpadding=1|border=1|frame=box} {tr} {td:align=center|bgcolor=#F2F2F2}{*}[Examples from Dynamics]* {td} {tr} {tr} {td} {pagetree:root=Examples from Dynamics} {search-box} {td} {tr} {table}
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