[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 399
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We all spit on the range.
It is known that if you spit from the window of a speeding train, the range of the "projectile" (without taking into account the drift along the carriage) will be much less than if you do the same operation with a stationary train.
Question: How is this possible?
This may be due to increasing air friction since the friction force depends on the surface area and the mass of the body. In this case, the mass of the body will be the force of the lateral wind flow, which will increase the friction. That's about it.
The drag force increases because:
1) The velocity of the air flow around the flying saliva increases.
2) The midsectional area of the flying saliva increases due to its deformation due to the drag force.
I'm not so sure about point 2.
Now the granddaughter of a school employee called and asked for help with a physics problem. :)
There are 8 metal balls of the same size. One of them is hollow.
The question is how to find the hollow ball with the help of 2 weighings on a lever scale.
I had to think about it! The grandfather was happy when we solved it.
First option: Put three balls on the scales each (the first weighing), if the scales are balanced, then the hollow ball is one of the remaining two, which will reveal the second weighing.
Second option: We put three balls on the scales each (first weighing); if the scales are out of balance, the hollow ball is one of the three. We take two of them at random and carry out the second weighing; if the scales are in equilibrium, the hollow ball is the one remaining alone. If the scales are not balanced, the lighter one is.
Both options are two-way and there are no more options.
Now the granddaughter of a school employee called and asked for help with a physics problem. :)
There are 8 metal balls of the same size. One of them is hollow.
The question is how to find the hollow ball with the help of 2 weighings on a lever scale.
I had to think about it! The grandfather was happy when we solved it.
tell your granddaughter that she can now solve the problem even if there are nine balls
tell your granddaughter that she can now solve this problem even if there are 9 balls
On this forum, with the help of all the esteemed forum members, I think any problem can be solved! :)
It seems to me that the problem is inaccurate. It is given that there are 8 balls, although the methodology given here clearly shows that it can be solved for 9 too. If my granddaughter declares at school that she can also solve for 9 balls, and not only for 8 as in the problem, she will get a bonus for the answer.
It seems to me that the problem is inaccurate. It is given that there are 8 balls, although the methodology given here clearly shows that for 9 also can be solved. If my granddaughter declares at school that she can solve for 9 balls, and not only for 8 as in the problem, she will get a bonus for the answer.
Exactly right, the problem is a hundred years old and the idea of the ninth has never even occurred to her.)
In this case, the mass of the body would be the force of the lateral wind flow...
Well, that's a bit of an overreaction, dear boy! Force and mass have different dimensions.
The correct answer (assuming that the shape of the body remains unchanged) is non-linear drag force F(V) depends on the speed of oncoming flow V: F(V)=k*V^2, where k is drag coefficient- a constant. Now, if to write accurately the value of force acting on body from air stream in direction to carriage, we have F=k*V^2=>Fx=F*sin(a)= k*V^2*Vx/|V|=k*V*Vx=k*Vx*SQRT(Vx^2+Vy^2)=k*Vx^2*SQRT(1+(Vy/Vx)^2), where a-angle in a right angle triangle with the cathetuses formed by the flow rate along the car and spitting speed.
Now, you can clearly see that Fx=Vx^2*SQRT(1+(Vy/Vx)^2), that the drag force across the car movement depends not only on the spitting speed Vx (as for stationary train), but also on the train speed Vy. This fact does not allow us to spit further than usual from the open window :-) In other words, the ratio of drag forces in direction of the spitting train for the case with moving train and at rest is: SQRT(1+(Vy/Vx)^2) and not 1 as one would assume.
AlGor:
The drag force increases, since:
1) The velocity of the air flow around the flying spit increases.Hence, this is a correct assumption.
P.S. Apparently, the fact that it is rare to land from the heart in the field in windy weather has the same non-linear effect.
This is all called Bernoulli's law.
The atmospheric pressure in the layer between the stationary air and the layer entrained by the train is the lowest of these 'three' layers (in fact, the pressure naturally varies continuously and smoothly). Consequently, any body that enters the pressure gradient area is subject to a force that tends to move it into this intermediate layer.
It's the same story with "pissing" :))) -- physics won't allow it.
Can any mathematician tell me which function in the script can be used to calculate the logarithm (not the natural one!)?
Thanks in advance.