Peter

Your statement contains a strong criticism of your employer, and cannot is difficult to prove. Some may think it proves you are not exercising discretion or dignity.

@Mari-LouA, In Australia, the US and the UK most native English speakers have only very limited exposure to other languages. Is this the case in India? And would you describe an Indian who learned English as a second (or even an additional first) language a native speaker?

Here is an article on dummy subjects that might be helpful. learnenglish.britishcouncil.org/grammar/…

To me (Aus) what nerve is often synonymous with what courage, while what a nerve is more likely to mean what a rude thing to do.

Centrifugal force not regarded as a real force, while centipetal force is. Changing this word may help your question to be re-opened. Also, consider changing the final question to ask why the energy is greater. The short answer is because you did work when you changed the system, and you can see the reverse (due to friction) if you set it up and then watch it slow down

How does a guitarist learn what the notes are to tune the strings to without at least a book or a magazine article? (the pre-internet versions of a web site/social media).

Yes it looks like we have sorted it all out.

Anyway, it's after midnight for me so I need to go to bed. Thanks for your contributions. I hope OP learned something.

I suppose another example might be a book pushed by a hand on a long rough bench where friction would stop the book (almost) instantly if the force ceased. In both directions the hand force would do positive work, while friction would do negative work. Total work of all forces would be zero with 200J done by the hand and -200J done by friction.

Do you think my car from A to B and back is a reasonable example for the problem (though it is the wrong order of magnitude by a long way)?

I think so. I think we were at cross-purposes with the use of "displacement".

Yes. OP's problem appears to be that he thought getting 200J was not compatible with going back to the starting point. For a constant force situation (like gravity) that would be a problem. When the force varies anything could happen - you need to calculate it. My car suggestion is the only half-realistic example I could think of. BTW I suspect some moderator is likely to delete this whole conversation, especially as the question has been closed.

@TejasDahake Firstly, I said if, not only if. A car accelerating around a circular track will have changed energy back at the start. Secondly, displacement during an interval is not the position vector but the change in the position vector (ie $\Delta x$). I know the word displacement is sometimes used to mean the displacement from the origin (ie position vector), but that is clearly not what is meant here. An example meeting the description of the problem would be a car accelerating from A to B, performing a U-turn without changing speed, then accelerating further from B back to A.

No. Displacement is change in position, ie final position - initial position. During the first segment displacement is A to B (B - A) and the force is also in the direction from A to B so the work done is positive. During the second segment the displacement is from B to A (A - B) and the work done is also from B to A, so the work is again positive. If the force is constant then zero displacement results in zero work, but the force is not constant - its direction reverses.

Probably not on topic for Physics SE, but the short answer might be that a complete self-replicating machine would need to contain a computer chip factory.

In British English "fag" was already in use for a junior student acting as a servant to a senior student. Even though the fagging system ended the meaning persisted, eg "fagged out" for very tired.

@Tom_C, there is a third reason why 3rd valve is normally a tone and a half. It is beacause that way the fingerings are more consistent between the bottom and top octaves. D5 is normally fingered 1, D4 is fingered 1+3 instead of 2+3.

@Tom_C there are 2 reasons for 3rd valve to be approximately equivalent to 1st + 2nd. One is alternative fingerings. The other is that theoretically lowering by a tone (say) means adding a percentageto the length. So lowering by a second tone means that the length to be added should be a little more. Using 1st and 2nd valves the effect is small, but it is greater with the 3rd valve combinations. The 3rd valve tubing is a bit longer than 1st +2nd so as to help the combinations (2,3), (1,3), (1,2,3) to be better in tune.

The difficulty for me in this question was the arccos function. I used x basically as a way to get some leverage on it. My argument is that because we have a good (hopefully) approximation to cosx we can use it backwards to approximate x when the cosine is known. The sum is the sum of x_n, and because x_n is small its convergance should be well determined by the convergance of root6 times the sum of the power series.