Pure maths, physics, logic (braingames.ru): non-trade-related brain games - page 77

 
TheXpert:
You don't take friction into account.
Yes, indeed. But the truth is out there...
 
Mischek:
I don't think the spring has anything to do with it.
I mean F = (M+m)*K*g. It doesn't matter which box
 
TheXpert:
The problem for loonies -- solve the same problem if you can arbitrarily change the vector of application of the force.
pull a spring?
 
MetaDriver:
Yes, indeed. But the truth is out there...
Well... I don't know the answer to the second problem.
 
Do the drawers have to move all the time - or is it enough to move them just once?
 
Mathemat:
Do the boxes have to move all the time - or is it enough to move them just once?

Just once.
 
sergeev:
pull the spring?
No :) . No, I don't get it at all.
 

Three prisoners, A, B and C are imprisoned in solitary confinement and sentenced to death. The governor randomly chooses one of them and pardons him. The guard guarding the prisoners knows who is pardoned, but is not allowed to say so. Prisoner A asks the guard to tell him the name of the (other) prisoner who will definitely be executed: 'If B is pardoned, tell me that C will be executed. If C is pardoned, tell me that B will be executed. If they will both be executed, and I am pardoned, flip a coin, and say any name."

The guard tells prisoner A that prisoner B will be executed. Prisoner A is happy to hear this, as he believes that his probability of survival is now 1/2, instead of 1/3 as it was before. Prisoner A secretly tells prisoner C that B will be executed. Prisoner C is also happy to hear this, because he still believes that prisoner A's probability of survival is 1/3, but his probability of survival has increased to 2/3. How can this be?

It's not my problem, I'll tell you that right away. If I tell you whose it is, I'll tell you the answer.

I hope it hasn't happened yet.

/Corrected by Mathemat

 
sumkin75:

The guard tells prisoner A that prisoner B will be executed. Prisoner A is happy to hear this, because he thinks that his probability of survival is now 1/2, not 1/3 as it was before. Prisoner A secretly tells prisoner C that B will be executed. Prisoner C is also happy to hear this, because he still believes that prisoner A's probability of survival is 1/3, but his probability of survival has increased to 2/3. How can this be?

C thinks the probability that B will be executed == 1, and A knows that the probability is lower. It's a confusing problem.

The guard has third figures altogether :)

 
Mathemat:

The minimum force to move any box if there is no spring is N*K (N is the support reaction).

Obviously, it is harder to move the big box at first. OK, we apply a force to the small one in any chosen direction, it starts moving.

The big one will start moving when the spring tension or extension is greater than the minimum force to move it. And it doesn't depend on its stiffness - it will happen anyway, even if the small box is very small.

The answer is m*K*g.

I guess the point here is that if a force is applied to the small box, it will start moving with acceleration and will have variable momentum and kinetic energy. That's why you need less force than (M+m)Kg but more than mKg