Optimizing Steel Cable Strength for Stopping a 17,000 lb Vehicle at 10mph

[swoodbury]

I have a complicated problem I'd like some assistance with.

I have a 17,000 lb vehicle traveling at 10mph and impacting a series of 4000lb jersey barriers connected by a 1" steel cable through the inside of the jersey barriers. The cable will be anchored at each end by 22,000lb blocks. The spacing in between the jersey barriers is 30 inches. Total length of jersey barrier and cable configuration is 100ft. What is the tensile strength of the steel cable I need to stop the vehicle? Distance required to stop the vehicle is negligible, I just need it to stop! Assume modulus of elasticity of the steel in tension is 28 x 10^3 ksi.

I'm stumped and any help would be greatly appreciated!

 

[siddharth23]

A diagram would or figure would be greatly appreciated..! ;-)

 

[Simon Bridge]

Welcome to PF;
The distance required to stop the vehicle is never negligible - the shorter the distance the more energy is expended: to stop a vehicle dead in zero distance requires infinite force.

But you should be able to work the problem in terms of conservation of momentum.
This should give you an idea pf the energies involved and thus the energy that needs to get absorbed by the cable and thus the tensile strength.

 

[sophiecentaur]

The answer to any problem such as this one will depend upon the time taken for the interaction. This is because the Momentum change is Force times time (Impulse). You would need a lot of experimenting if you wanted to find out the actual forces involved. There are so many unknowns in your model, so far.

The OP reads as if it could be seeking to analyse what went on in an accident. To make any argument stand up in court, you need a highly paid 'expert' to convince a Judge. The sum total of PF knowledge of the subject will never convince that guy. (Just so that you won't be disappointed, later.)

 

[russ_watters]

Since we have elastic cables, I think you need both conservation of momentum and energy.

 

[sophiecentaur]

In the case of such a collision, can we really expect the impacting vehicle to rebound with a significant amount of KE? That would sound to be a very dodgy way to design a barrier. Boing! boing!