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Deck of Cards
idprobparts
h2.

Part

A

Suppose

a

person

with

a

weight

of

686

N

is

in

an

elevator

which

is

accelerating

downwards

at

a

rate

of

3.0

m/s

{color:black}{^}

2

{^}{color}

.

What

is

the

person's

apparent

weight?

h4. Solution {

Solution

Card
labelPart A
Wiki Markup
Toggle Cloak

:

id

=

Asys

} *

System:

* {

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} {

Amod

.

Toggle Cloak

:

id

=

Aapp

} *

Approach:

* {cloak:id=Aapp} {

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
=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~ = \

ay = -3.0

m/s

{color:black}{^}

2

{^}{color}

,

giving:

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

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

{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:Amath}
{cloak:Aapp}
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