Page History

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A

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4460

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lb

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Ford

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Explorer

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traveling

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35

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mph

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has

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a

...

head

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on

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collision

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with

...

a

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2750

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lb

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Toyota

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Corolla,

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also

...

traveling

...

35 mph.

Excerpt

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Compare the forces on the occupants of two cars in a 1-D totally inelastic collision.

Composition Setup

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mph. Assuming that the automobiles become locked together during the collision, what is the speed of the combined mass immediately after the collision? System: Explorer plus Corolla as [point particles|point particle]. External influences will be neglected, as we assume that collision forces dominate. Model: [Momentum and Impulse]. Approach: We begin by sketching the situation and defining a coordinate system. Since we assume that external forces are negligible during the collision, we set the external impulse to zero which gives: {latex}

Card

label	Part A

Part A

Assuming that the automobiles become locked together during the collision, what is the speed of the combined mass immediately after the collision?

Solutions

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System:

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Explorer plus Corolla as point particles.

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Interactions:

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

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Model:

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.

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Approach:

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Diagrammatic Representation

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

Initial State	Final State
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id	matha

Mathematical Representation

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Since we assume that external forces are negligible during the collision, we set the external 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, the Corolla has a negative x-velocity before the collision.{warning} h2. Part B Find the impulse that acted on each of the vehicles during the collision. h2. Part C Assuming the collision lasted for 0.060 seconds, find the average force exerted on each vehicle. h2. 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 average force exerted on these people.

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

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Part B

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

Solution

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Systems:

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Corolla and Explorer as separate systems.

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Interactions:

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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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Model:

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Approach:

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Card

label	Part C

Part C

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

Solution

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id	sysc

Systems:

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Corolla and Explorer as separate systems.

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id	intc

Interactions:

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

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Model:

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Approach:

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Card

label	Part 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.

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Systems:

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

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id	intd

Interactions:

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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.

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Model:

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.

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Approach:

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Versions Compared

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Key

Part A

Solutions

Part B

Solution

Part C

Solution

Part D