Some scientists have an idea to bui 1

[Abd K]

Some scientists have an idea to build an elevator that could pull the spaceship from the ground of the earth to the spaceship orbiting around the earth. However, during the mission, the sling that is used to pull the spaceship from the ground to the spaceship orbiting around the earth is broken. The NASA engineer suggests that we increase the diameter of the sling, which may take more loads. What do you think about this idea? Is it the right thing to do? Can you verify mathematically? If this idea is not good, can you suggest the alternative? Please state all necessary assumptions.

 

[ChorasDen]

Ah, you're right, I missed a critical step: I didn't state my assumptions. I assume there is no energy or momentum loss as we pass the core of the earth and arrive out the other side. We convert the entire gravitational potential energy from the earths radius to allow us to accelerate up the elevator, and magically brake and displace that energy at whatever elevation above the earth surface that we desire.

See, this is easy!

 

[waross]

I once heard an engineer give testimony in a hearing as too how a piece of switchgear FELL UP into hot terminals.
Most of us mere mortals are bound by the law of gravity, which will almost exactly remove all of the kineticl energy that was developed by the fall to the core of the earth.
Have you considered a career developing over unity devices?

 

[rb1957]

c'mon, the space elevator is a reasonably legit project ... sure it's goals are lofty (pun intended), sure it may be better suited to other places (like the Moon or Mars (read Green Mars ?) but it's no sillier than half the nonsense going on these days.

 

[waross]

Back to the original question:

Some scientists have an idea to build an elevator that could pull the spaceship from the ground of the earth to the spaceship orbiting around the earth. However, during the mission, the sling that is used to pull the spaceship from the ground to the spaceship orbiting around the earth is broken

It depends.
If the sling has broken under its own weight, increasing the diameter will increase the weight in the same ratio as the strength is increased and the sling will stillbreak under its own weight..
If the sling has broken due to the added weight of the spacecraft, then doubling the diameter of the sling will double the load carrying capacity.
Unobtanium may still be required.
However, a tapered sling may work, on paper.
However hundreds of space craft may be launched with the same energy taken to put the sling in place.
And you will need two slings.
One to tether the orbiting spacecraft and one to lift the load.

 

[Compositepro]

A cable that is limited by self-weight can be made twice as long if it is tapered.

 

[rb1957]

and more (ie longer) if the taper is non-linear. But in any case available materials are not sufficient to make a space elevator.