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Deck of Cards
idbigdeck
h2.

Part

A

Assuming

that

the

automobiles

become

locked

together

during

the

collision,

what

is

the

speed

of

the

combined

mass

immediately

after

the

collision?

h4. Solutions {

Solutions

Card
labelPart A
Wiki Markup
Toggle Cloak

:

id

=

sysa

} *

System:
Cloak
idsysa

Explorer plus Corolla as point particles.

Toggle Cloak
idinta
Interactions:
Cloak
idinta

Impulse resulting from external influences will be neglected, as we assume that the collision is instantaneous.

Toggle Cloak
idmoda
Model:
Cloak
idmoda

.

Toggle Cloak
idappa
Approach:

Cloak
idappa

Toggle Cloak
iddiaga
Diagrammatic Representation

Cloak
iddiaga

We begin by sketching the situation and defining a coordinate system.

Image Added

Image Added

Initial State

Final State

Cloak
diaga
diaga

Toggle Cloak
idmatha
Mathematical Representation

Cloak
idmatha

Since we assume that external forces are negligible during the collision, we set the external impulse to zero which gives:

Latex
*  {cloak:id=sysa}Explorer plus Corolla as [point particles|point particle].{cloak}

{toggle-cloak:id=inta} *Interactions:* {cloak:id=inta}[Impulse|impulse] resulting from [external influences|external force] will be neglected, as we assume that the collision is instantaneous.{cloak}

{toggle-cloak:id=moda} *Model:*  {cloak:id=moda}[Momentum and External Force].{cloak}

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

{cloak:id=appa}
{toggle-cloak:id=diaga} {color:red} *Diagrammatic Representation* {color}

{cloak:id=diaga}
We begin by sketching the situation and defining a [coordinate system|coordinate system].

|!CollisionInit.jpg|height=175!|!CollisionFin.jpg|height=175!|
||Initial State||Final State||

{cloak:diaga}

{toggle-cloak:id=matha} {color:red} *Mathematical Representation* {color}

{cloak:id=matha}

Since we assume that [external|external force] [forces|force] are negligible during the collision, we set the [external|external force] [impulse|impulse] to zero which gives:

{latex}\begin{large}\[ p^{TC}_{x,i} + p^{FE}_{x,i} = p^{system}_{x,f} \]\end{large}{latex}

or,

in

terms

of

the

masses:

{
Latex
}\begin{large}\[ m^{TC}v^{TC}_{x,i} + m^{FE}v^{FE}_{x,i} = (m^{TC}+m^{FE})v_{x,f} \]\end{large}{latex}

which

gives:

{
Latex
}\begin{large}\[ v_{x,f} = \frac{m^{TC}v^{TC}_{x,i} + m^{FE}v^{FE}_{x,i}}{m^{TC}+m^{FE}} = \mbox{3.71 m/s} = \mbox{8.3 mph}\]\end{large}{latex}

{warning}Remember that in our [coordinate system|coordinate system], the Corolla has a negative x-velocity before the collision.{warning}

{cloak:matha}
{cloak:appa}
Warning

Remember that in our coordinate system, the Corolla has a negative x-velocity before the collision.

Cloak
matha
matha

Cloak
appa
appa

Card
labelPart B

Part B

Find the impulse that acted on each of the vehicles during the collision.

Solution

Toggle Cloak
idsysb
Systems:
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idsysb

Corolla and Explorer as separate systems.

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idintb
Interactions:
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idintb

The impulse on each vehicle from the other is assumed to be the dominant interaction during the collision. Because we are now considering the vehicles separately, these are now external impulses.

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idmodb
Model:
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idmodb

.

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idappb
Approach:

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idappb
Card
labelPart C

Part C

Assuming the collision lasted for 0.060 seconds, find the time-averaged force exerted on each vehicle.

Solution

Toggle Cloak
idsysc
Systems:
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idsysc

Corolla and Explorer as separate systems.

Toggle Cloak
idintc
Interactions:
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idintc

The external force on each vehicle from the other is assumed to be the dominant interaction during the collision.

Toggle Cloak
idmodc
Model:
Cloak
idmodc

.

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idappc
Approach:

Cloak
idappc
Card
labelPart D

Part D

Suppose a 75 kg person in each vehicle underwent the same change in velocity as their automobile in the same amount of time. Find the time-averaged force exerted on these people.

Toggle Cloak
idsysd
Systems:
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idsysd

First, the Corolla and Explorer as separate systems, then the passengers as separate systems.

Toggle Cloak
idintd
Interactions:
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idintd

Each vehicle is subject to a collision force from the other. The passengers are each subject to some decelerating force, possibly a seatbelt or airbag.

Toggle Cloak
idmodd
Model:
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idmodd

.

Toggle Cloak
idappd
Approach:

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idappd