Help? using physics to predict stunt outcome

[DKTKD]

Hello All,
I reposted this b/c i think i put it in the wrong forum.

Recently I was asked to help provide some off the cuff
calcuations for a stunt being peformed by a friend.
It was a bit of challenge for me since I haven't cracked open a
physics books in a long time.
I used the Newtons laws, standard conservations of energy,
conservation of momentum etc etc.

But I felt like my calculations were missing something.
Either b/c my approach was wrong or I wasn't given
enought info and had to make to many assumptions.

So I wanted to see how everyone here would have
approached the problem and compare notes.

Thanks. Now for the Stunt.

The goal of the stunt was to stop a cart on wheels
(weighing about 4000 lbs) traveling about 40 mph within
5 ft after passing a designated reference point.
At the 5ft mark there is a barrier that we don't want to hit.
Assume the cart/wheel interaction is frictionless.

You are provided with steel cable. Diameter and length have
not been determine as availability is unknown. It is up to you
to help decide what size diameter to use that and what length.
Remember to use your youngs modulus to make sure the
elongation of the steel cable is taken into account for you
5ft stopping distance.

It was only after I performed the calculations that I was told that
I may have two 5/8" steel cables that are about 1000ft long.

At the other end of the steel cable, you are providing with a
metal container with about 10,000lbs of sand bags. Assume
metal container is on asphalt for your friction coefficient.
Extra sand bags (about 1000lbs) are provided in front of the
metal container to be scooped into the container to help absorb
some of the momentum/energy.

And if the sandbags and metal containers were not sufficent
to stop the the cart within 5 ft, large blocks of concrete barriers
up to 30,000 lbs are aviable to stop the metal container.

Also, assume that the metal container will not deform and
that you have spread the ends of the steel cables evenly
as not to overload the fastening points.

Can you stop the cart within 5 ft?
I found this difficult b/c I had even less info to go on originally.

Good luck, let me know what your approach was to solving the problems
or if you have any questions.

Thanks again,
ME

 

[andrevdh]

Assuming that the system is decelerated at a constant rate by the frictional force over the distance d (that is the mass of sand on the container does not change during the deceleration). We get from the constant acceleration equation
$$v^2 = u^2+2ad$$
that
$$a=\frac{v^2}{2d}$$
which can be evaluated for the required deceleration

Cart:
Therefore the tension in the cable on the cart side can be calculated from
$$T=ma$$

Cable:
$$T'- T = m_ca\ \<br /> \therefore T'= T+m_ca$$
Which gives the tension in the cable at the container side.
The choice of an appropiate cable mass comes in here. I may attempt the problem of choosing an appropiate cable at a later stage!

Container:
$$f-T'=m_sa$$
$$\mu m_sg-T'=m_sa$$
$$m_s=\frac{T'}{\mu g-a}$$
The required mass of sand on the container can be calculated from this. The kinetic frictional coefficient one need to determine experimentally for the specific surface and container since it's value changes for different surface combinations.