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1. Estimation. “Crumple Zone”

a. Crumple zones in cars are designed to reduce the acceleration in a collision with a stationary object. Estimate

a relation between the size of the crumple zone, the initial speed of the car, and the average stopping

acceleration of the car’s occupants using dimensional analysis. Dimensional analysis does not start with the

equations; it utilizes only the physical quantities and their dimensions to estimate. Part “b” is an actual estimate

using some numbers.

b. For a collision at 30 miles per hour, what is the minimum crumple zone size needed to keep accelerations

below (a fatal) acceleration of 20g. How does this size compare to the length of a typical car (report this in

percent)? Respond to this question it in one complete sentence?

2. Relevant equations

p = (mass) * (velocity)

impulse = (force) * (time)

(change in momentum) = (impulse)

p - p = (force) * (time)

final initial

m*v - m*v = (force) * (time)

final initial

Crumple Zone= L= length of 'crumple zone'

3. The attempt at a solution

So for part A (which is what I need to know to find out part B) I am confused on how to get the length of the crumple zone into the equation and relate all of these terms. I would like a discussion on this question, but a nudge in the right direction would be helpful.

I started by saying: vo= initial velocity and v1=0=final velocity. turning this

m*v1 - m*vo = (force) * (time)

final initial

-but then v1 is taken out of the equation since final velocity is zero. How do I relate all the size of the crumple zone (L) to vo of the car and to the average stopping acceleration of a cars occupants?

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