Recent content by Quantum Psi Inverted

I believe that this is due to context of application, but now, I'm starting to doubt myself. For example, a helicopter lifting itself has positive PE change. I really don't intuitively understand how this works. Can someone kindly explain this to me?

Oops, yes. Yes, it does. Thank you!

Yes, thank you for poi I would like to understand how the idea that F_3f(a)=F_2f(a+b) came to be. I'm very confused about what motivates this, as it's neither stated in the book, nor anywhere else. I'm not quite interested in why f(x)=x nor the sum of f_if(x_i); I can see those working out...

In particular the author shows that f(x)=x by first considering F_3f(a)=F_2f(a+b) and F_3f(b)=f(a+b). Combining these two with the fact that F_3=F_2+F_1, we result with f(a)+f(b)=f(a+b) over the positive reals, which is known as Cauchy's Functional Equation. The method that I used here to prove...

In the given solution, it states that F_3f(a)=F_2f(a+b) is a "reasonable assumption". However, I don't see how we can just assume that. I can very clearly see that F_i for i=1,2,3 is likely proportional to a and b in some kind of way, but I can not clearly establish a line of reasoning for this...

Ah! When you put it that way, everything makes sense now. Thank you very much.

A rope wraps an angle θ around a pole. You grab one end and pull with a tension T0. The other end is attached to a large object, say, a boat. If the coefficient of static friction between the rope and the pole is µ, what is the largest force the rope can exert on the boat, if the rope is not to...