How Do You Design an Automobile Bumper to Absorb Impact?

[James22]

Homework Statement

I have posted the assignment hand out. The weight of the car will be 3702lbs.

Homework Equations

The Attempt at a Solution

Right now I am overwhelmed with this project, I am not really sure where to start. Here is my thoughts on where to start.

The weight of the car will be 3702lbs. I think I need to find the kinetic energy of the automobile traveling at 5 mi/h. Now knowing the kinetic energy, would the next step be to decide upon the number of springs and their coefficient needed to stop the auto in 3" or slightly more?

Thank you in advance and sorry if this seems elementary. Dynamics related work doesn't come easy to me to say the least.

 

[James22]

I worked on this project some more and calculated the kinetic energy as;

E=1/2 mv^2
0.5 x (3702/32.2) x 7.33ft/s^2 = 3091.38 ft-lb

I have chosen to use a 6" crumple zone and 4 springs to absorb the impact.

This is where I run into trouble trying to get my head around the concept.

I know for the spring
U=0.5*k*s^2

where;
k = Spring co-efficient
s = spring displacement


Since I am trying to stop the car in 6" do I have to treat the kinetic energy as double? Then divide it over the 4 springs that I will be using to stop the car?

Thanks,
Kyle