Using physics to solve stunt challenge

[DKTKD]

Hello All,

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 andhad 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

 

[AndyW]

Hello!

my approach to this problem would be to first gather all the necessary information and make any necessary assumptions. In this case, the weight and speed of the cart, the type of surface it will be stopping on, and the materials provided for the stunt have been given. I would also assume that the cart is moving in a straight line and that the surface is level.

Next, I would use the equations for conservation of energy and momentum to calculate the initial kinetic energy and momentum of the cart. From there, I would determine the necessary stopping force and distance needed to bring the cart to a complete stop within 5 ft after passing the reference point. This would involve taking into account the friction coefficient between the metal container and the surface, as well as the elongation of the steel cables due to the weight of the cart and container.

Based on the information provided, it seems that using two 5/8" steel cables would be sufficient for stopping the cart within 5 ft. However, I would also consider the option of using additional sand bags or concrete barriers if needed to ensure the safety of the stunt performer and those around them.

In terms of the length of the steel cables, I would need to know the exact distance between the cart and the reference point in order to calculate the necessary length. I would also need to know the maximum elongation allowed for the cables and the strength of the fastening points in order to determine the appropriate length.

Overall, it is important to carefully consider all factors and make sure that the stunt can be performed safely and successfully. I hope this helps with your calculations and I am interested to hear about other approaches to this problem. Good luck with the stunt!

 

[sir-pinski]

Hello,

It sounds like you were given quite a challenging stunt to calculate! Using physics to solve this stunt challenge is definitely the right approach. Based on the information provided, here is how I would approach the problem:

1. Calculate the initial kinetic energy of the cart using the mass and velocity given: KE = 1/2 * m * v^2. This will give you the minimum amount of energy that needs to be dissipated in order to stop the cart.

2. Use the conservation of energy principle to determine the amount of energy that can be dissipated by the sand bags and metal container. This will depend on the friction coefficient between the metal container and the asphalt, as well as the height at which the sand bags are dropped into the container.

3. Determine the amount of energy that needs to be dissipated by the steel cables. This will depend on the elongation of the cables and the Young's modulus of the steel. You can use the equation for elastic potential energy: PE = 1/2 * k * x^2, where k is the spring constant and x is the elongation of the cables.

4. Use the conservation of momentum principle to determine the velocity of the cart after the sand bags and metal container have stopped it. This will give you the final velocity that the steel cables need to stop in order to keep the cart within 5 ft.

5. Finally, calculate the minimum tension force required in the steel cables to stop the cart within 5 ft. This will depend on the mass of the cart, its final velocity, and the distance over which the cables need to stop it.

Based on these calculations, it seems like it may be possible to stop the cart within 5 ft with the given materials. However, it will require precise calculations and careful planning to ensure that the steel cables and other materials can withstand the tension and forces involved. It may also be helpful to conduct some experimental tests to determine the best combination of materials and configurations for the stunt.

I hope this helps with your calculations and approach to the stunt challenge. Good luck with your calculations and let us know how it goes!