If I have to let go of a glass from my hand from at least 1m so that it breaks,
With what minimum speed do I have to throw a glass of the same kind into another so that they both break?

 

If I have to let go of a glass from my hand from at least 1m so that it breaks,
With what minimum speed do I have to throw a glass of the same kind into another so that they both break?

I'd have to think about this.

But I'd also have to have interest beyond the scope of this thread: "What do I tell my daughter?"

I'll happily read your solution if you post it. I may even find it interesting and enlightening.

 

That sounds like a great learning moment for both you and your daughter! The key reason conservation of energy (CofE) doesn't work in the initial collision is that it's an inelastic collision—mechanical energy is not conserved because some of it is converted into heat, sound, and deformation.

A general rule of thumb for choosing between conservation of energy (CofE) and conservation of momentum (CofM):

• Use CofM when dealing with collisions and interactions, especially if external forces are negligible during the moment of impact.
• Use CofE when analyzing motion before and after a collision or when no non-conservative forces (like friction) are doing significant work.

For a ballistic pendulum, the correct approach is:

1. Use CofM for the bullet-block collision (since it's a brief interaction with no external horizontal force).
2. Use CofE for the block’s subsequent swing, since gravity is a conservative force acting on the system.

To check if you’ve used the right principle:

• If kinetic energy before and after a collision doesn’t match → it’s inelastic, so CofE doesn’t apply.
• If no external force acts significantly during impact → CofM applies.
• If the motion after impact involves only conservative forces (like gravity), then CofE is valid.

 

The reason why the actions of the third sister, Amanda, cannot be known for sure is that the problem, as stated, does not logically necessitate any specific action for her. Here's why:

1. The Implicit Assumption That Amanda Must Be Playing Chess
The trick behind the question is the assumption that chess requires two players, and thus, if Alice is playing a match of chess, she must be playing against someone else in the room. Given that there are only three sisters in the room, one might assume that Amanda must be the opponent.

However, this assumption is not guaranteed because:

• Alice could be playing chess against a computer or an online opponent.
• Alice could be playing by herself (e.g., solving chess puzzles, practicing moves, analyzing a game, or even using a physical chessboard to visualize strategies).
• There could be an unmentioned fourth person in the room playing against Alice.

Thus, logically speaking, we lack definitive proof that Amanda must be the opponent.

2. Why the LLM's Answer is Correct
The LLM (like OpenOrca Platypus2 13B) does not make unwarranted assumptions. It correctly recognizes that the information provided does not conclusively determine Amanda’s activity.

When the person clarifies that Alice is playing "a match of chess against someone in the room," the LLM still doesn't immediately conclude that it must be Amanda because it lacks explicit confirmation:

• The problem never states that only the three sisters are in the room (there could be someone else).
• It never states that Alice must be playing against one of her sisters.

Thus, an LLM that strictly follows logic (instead of assuming unstated facts) would avoid concluding that Amanda must be playing chess.

3. Why Humans Might Answer Differently
A human might quickly assume that Amanda is playing chess because we tend to fill in missing details based on typical expectations rather than strict logical necessity. If a person is told that Alice is playing a match of chess, their intuition might say, "Well, she must be playing against Amanda, since no other players were explicitly mentioned."

However, a rigorous logical approach (such as the one taken by the LLM) recognizes that the problem does not force that conclusion.

4. The Core Issue: The Problem is Ambiguous
The real issue with the problem is ambiguity:

• If the problem explicitly stated that there are only three people in the room and that Alice is playing chess against someone in the room, then logically, Amanda must be the opponent.
• But since it does not explicitly rule out other possibilities, the LLM correctly avoids jumping to conclusions.

Conclusion
The LLM’s response is actually more logically sound than assuming Amanda is necessarily playing chess. The question's wording is ambiguous, and a logically precise system will not make assumptions beyond what is given. If the question were phrased more explicitly, an LLM could reach the "expected" answer.

 

The reason why the actions of the third sister, Amanda, cannot be known for sure.....

You've lost me here, I confess. Is this a subtle illustration of a failure of relevance of a LLM?

 

Who's Amanda? What's she got to do with a Ballistic Pendulum? And why are bots replying to my posts?

 

I'm curious if this is analog to the case of charging one capacitor with another, the process of which always results in a loss of energy, even though charge stays the same.

Hi Joey,

You could use one of the analogies such as the force/current mechanical analogy.
The mass becomes the capacitance, the force the current, velocity is the voltage.

I was wondering, what were the differences in results using both methods you already tried on your current problem?

 

Who's Amanda? What's she got to do with a Ballistic Pendulum? And why are bots replying to my posts?

I can only guess that this is a very drawn-out example of a problem that we do not have all the details too yet and so we make assumptions, but why so long of an example.

 

I can only guess that this is a very drawn-out example of a problem that we do not have all the details too yet and so we make assumptions, but why so long of an example.

Hmmm...I thought it was the solution to a problem I didn't know I had.

 

I was wondering, what were the differences in results using both methods you already tried on your current problem?

Sorry, I don't remember. I think the CofE solution gave a resulting velocity about twice that of the CofM solution, but don't hold me to it. The equations are easy -- you could do it yourself in about 5 minutes. I'm too lazy.

 

You've lost me here, I confess. Is this a subtle illustration of a failure of relevance of a LLM?

This seems to be the 'new' world. Detailed, strange and often wrong answers to questions we didn't ask.

 

Sorry, I don't remember. I think the CofE solution gave a resulting velocity about twice that of the CofM solution, but don't hold me to it. The equations are easy -- you could do it yourself in about 5 minutes. I'm too lazy.

Ha ha.

With the electrical analogy, we would have this:
M*v=C*v
with v either velocity (left side) or voltage (right side).

I am thinking even a circuit simulator could then be used as usual.

 

You could use one of the analogies such as the force/current mechanical analogy.
The mass becomes the capacitance, the force the current, velocity is the voltage.

Brilliant! Do you have other analogies?
Mechanical ballistic pendulum:
m*v=(M+m)*v1.....
m, v, mass, bullet speed
M, v1: mass of the wooden block, its speed after the collision

Electrical Analogy:

 

Capacitor of capacity C charged to voltage U = Capacitor of capacity C+C1 (parallel grouping) charged to voltage U1
C=Q/U =>q=C*U

C*U=(C+C1)*U1

Kinetic energy:
KE=m*v^2/2=PE=m*g*h

Capacitor energy
E=C*U^2/2= U* I*(The equivalent of h the height to which the massive block of wood rises after being hit by the bullet, let it be the charging time of the capacitor?)

 

Brilliant! Do you have other analogies?
Mechanical ballistic pendulum:
m*v=(M+m)*v1.....
m, v, mass, bullet speed
M, v1: mass of the wooden block, its speed after the collision

Electrical Analogy:

Hi,

These analogies have been around probably before I was even born

I've used the "force/current" analogy several times in the past, and it allows the use of a circuit simulator to test ideas. Try that yourself and see what you can come up with, and show the results, that would be interesting.

The other analogy is the "force/voltage" analogy.

 

A variation on the problem:

 

A variation on the problem:

Is that 35000 feet per second real. That's around 5 miles per second.
Speed of sound is very roughly 1000 feet per second, which is only about 0.2 miles per second.
Still not close to the speed of light though, at over 980,000,000 feet per second.

 

Re http://hyperphysics.phy-astr.gsu.edu/hbase/balpen.html

I was helping my daughter solve a ballistic pendulum problem last night.

I'd never seen one of these before, so I saw it as an opportunity to teach her the value of starting from first principles.

In my naivete, I approached the problem first from conservation of energy. I got the wrong answer.

My second attempt used conservation of momentum, and the answer I arrived at was correct.

I am trying to come up with a simple explanation of why CofE doesn't work, and a rule or rules to use (say during an AP exam) as to whether to use CofE or CofM for a particular problem, and a method to determine that the correct choice was made.

Any suggestions? @WBahn, maybe?

High school level, BTW.