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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.

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A
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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 3.0 m/s{color:black}^2^{color}.  What is the person's apparent weight?

h4. Solution

{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}

{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~ = -3.0 m/s{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}
Card
labelPart B

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/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 at a constant rate of 1.0 m/s and 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

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