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
Composition Setup

Excerpt
hiddentrue

Finding apparent weight using normal force.

Composition Setup

cloak.memory.duration = 0

...

...

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
idprobparts
h2.

Part

A

Suppose

a

person

with

a

weight

of

686

N

is

in

an

elevator

which

is

descending

accelerating downwards 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

2. What is the person's

apparent

weight?

h4. Solution {

Solution

Card
labelPart A
Wiki Markup
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}
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

is

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

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
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}
Wiki Markup