Can the bullet be much heavier than the string?

[Magnolial]

Homework Statement

Me and a friend of mine have been sitting around in a sleep deprived state unable to think properly pondering a problem I don't think either of us have the capacity to solve (we're freshmen, alright, we just started learning differential equations.) I forget how I started thinking about putting a string on a bullet but we started thinking and quickly got lost in it.

You have a string of unknown length, L. The string is heat resistant and blast resistant, but otherwise of mundane properties, with a maximum load of ~13 N that it can safely hold, and weighing 1kg per kilometer of string. One end of the string, pulled taught, is mounted at a frictionless axle L meters away. The other end of the string is attached to a large very fast bullet, with a mass of 42 g and moving at 928 m/s. The question we were asking is, assuming this takes place in a frictionless vacuum, and in a reference frame where gravity can be ignored, what is the minimum value of L so that the string can swing the bullet around in a circular arc, reversing its direction, without the total outward force on the string ever exceeding 13 N, if this is at all possible accounting for the weight of the string itself.

Homework Equations

The Attempt at a Solution

I'm honestly at a loss for this one, where to even begin. We tried thinking about how we could deal with the total outward force acting on the mass of the string plus the outward force of the bullet, but couldn't figure out a method we thought we could find a solution from

 

[Simon Bridge]

Homework Statement

Me and a friend of mine have been sitting around in a sleep deprived state unable to think properly pondering a problem I don't think either of us have the capacity to solve (we're freshmen, alright, we just started learning differential equations.) I forget how I started thinking about putting a string on a bullet but we started thinking and quickly got lost in it.

Get some sleep first then.

You have a string of unknown length, L. The string is heat resistant and blast resistant, but otherwise of mundane properties, with a maximum load of ~13 N that it can safely hold, and weighing 1kg per kilometer of string. One end of the string, pulled taught, is mounted at a frictionless axle L meters away.

Is this the same L as the length of the string?

The other end of the string is attached to a large very fast bullet, with a mass of 42 g and moving at 928 m/s. The question we were asking is, assuming this takes place in a frictionless vacuum, and in a reference frame where gravity can be ignored, what is the minimum value of L so that the string can swing the bullet around in a circular arc, reversing its direction, without the total outward force on the string ever exceeding 13 N, if this is at all possible accounting for the weight of the string itself.

To understand a problem you should break it down into parts - 1st - this is a non-idea string ... which means it is springy.

In detail you can model it as an infinite chain of ideal point masses connected by ideal massless springs.

"stretched taut" in the sense of the entire string being exactly horizontal, would take infinite force ... so would certainly break the string. So you need to define the initial tension in the string.
All you really need is for the forces to balance to a net centipetal force right? So the string does not need to be taut. Beware - the shape of a hanging string is not simple.

Apart from that, this is a tetherball problem with a spring instead of a string.

You could try approximating the situation as a thin, ideal, rigid rod , length L, mass density d, (so mass M=dL).

That help?