Tethered bullet problem

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In summary, a problem was posed involving a string of unknown length and a bullet attached to one end. The string had a maximum load of ~13 N and weighed 1kg per kilometer. The question was to determine the minimum value of L so that the string could swing the bullet in a circular arc without exceeding the maximum load. The problem was complicated by the string being heat and blast resistant, but also having a spring-like quality. Suggestions were made to break down the problem into smaller parts and to approximate the situation as a thin, ideal, rigid rod.
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Magnolial
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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.

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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
 
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Magnolial said:

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?
 
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1. What is the "Tethered Bullet Problem"?

The "Tethered Bullet Problem" is a theoretical physics problem involving a bullet tethered to a fixed point by a string. The question is whether the bullet will hit the ground or continue to rotate around the fixed point when released.

2. What are the key factors that affect the outcome of the "Tethered Bullet Problem"?

The key factors that affect the outcome of the "Tethered Bullet Problem" include the length and tension of the string, the initial velocity of the bullet, and the gravitational force acting on the bullet.

3. What is the significance of the "Tethered Bullet Problem"?

The "Tethered Bullet Problem" has real-world applications in fields such as ballistics and space exploration. It also serves as a thought experiment to help understand the principles of angular momentum and conservation of energy.

4. What are some possible solutions to the "Tethered Bullet Problem"?

Possible solutions to the "Tethered Bullet Problem" include using mathematical equations to calculate the trajectory of the bullet, conducting experiments in a controlled environment, and using computer simulations to model the problem.

5. How does the "Tethered Bullet Problem" relate to other physics concepts?

The "Tethered Bullet Problem" is closely related to concepts such as projectile motion, rotational motion, and centripetal force. It also illustrates the importance of considering both linear and angular momentum in a system.

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