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Part A

A 4460 lb Ford Explorer traveling 35 mph has a head on collision with a 2750 lb Toyota Corolla, also traveling 35 mph. What .

Excerpt
hiddentrue

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

Composition Setup
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labelPart A
Part A
Assuming that the automobiles become locked together during the collision, what is the speed of 
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the combined mass immediately after the collision?
Solutions
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Explorer plus Corolla as point particles.
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Impulse resulting from external influences will be neglected, as we assume that the collision 
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is instantaneous.
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  Diagrammatic Representation 
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We begin by sketching the situation and defining a coordinate system.
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Initial State
Final State
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  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:
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\begin{large}\[ p^{TC}_{x,i} + p^{FE}_{x,i} = p^{system}_{x,f} \]\end{large}
or, in terms of the masses:
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\begin{large}\[ m^{TC}v^{TC}_{x,i} + m^{FE}v^{FE}_{x,i} = (m^{TC}+m^{FE})v_{x,f} \]\end{large}
which gives:
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\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}
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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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 Corolla and Explorer as separate  systems.
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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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Part C
Assuming the collision lasted for 0.060 seconds, find the time-averaged force exerted on each vehicle.
Solution
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 Corolla and Explorer as separate  systems. 
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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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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.
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idsysd
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First, the Corolla and Explorer as separate  systems, then the passengers as separate  systems.
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idintd
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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: Momentum and Impulse.
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