Pure maths, physics, logic (braingames.ru): non-trade-related brain games - page 113
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You're just drawing the wrong conclusion. You cannot draw conclusions "asymptotically", because you don't even know the type of function, and there you get a diffur, because velocity is a function of time, and you have to take an integral on it.
I simply tried to make the problem very simple - it failed.
The friction force can be disregarded altogether as it gives constant inverse acceleration to the cart regardless of its mass. Further see my very first post. The difference depends only on momentum transfer.
Wrong, Andrei. The friction force is different for a sloth and a worker: the friction force on the cart of the sloth grows (together with the support reaction), and the momentum taken away grows as much as quadratic. For the worker it is simpler: it is constant.
Wrong, Andrew. The friction force is different for a lazy person and a worker: the friction force on the cart of the lazy person grows, and the taken away momentum grows as much as quadratically. For the worker it is simpler: it is constant.
That's right. Look -- you kick two carts at the same speed -- one weighing a kilogram, the other weighing a ton. Which one stops first?
You're taking the argument to another angle. They will stop the same way, that's not the point.
The basic balance here is this: the initial kinetic energies (equal at the start) are expended differently - by the work of different friction forces and others.
It doesn't matter what happens to the kinetic energy of the sloth when the snow builds up. What matters is how fast the initial kinetic energy is expended.
So far I have reduced the problem to a comparison of two very simple integrals with a minimum of factors. But that's for later.
You're taking the argument to another angle. They'll stop the same way, that's not the point.
what ?! AGAIN ?
It doesn't matter what becomes of the sloth's kinetic energy when the snow accumulates. The important thing is how quickly the initial kinetic energy is expended.
The impact is there, but it doesn't need to be taken into account here as it affects every cart in the same way. This is what I called "dynamic snow pressure" earlier.
And we can talk about impulses, the equation of motion can be used.
OK, let's come at it from the other side.
There are two carts. One with mass M and one with mass m < M.
Both start driving at the same speed, snow falls on them. Which one will go the furthest?
OK, let's come at it from the other side.
There are two carts. One with mass M and the other with mass m < M.
Both start travelling at the same speed, and snow falls on them. Which one will go the furthest?
Try to argue to the moderator that friction should not be taken into account :)
The essence of the problem is that there are not only dissipative forces (friction), but also a blunt loss of momentum due to ejection of snow.
Therefore the usual proportionality of friction forces to the masses remains, but it is impossible to reduce them, because the loss of momentum is not proportional to the mass of the cart.
Let us discuss your variant of the solution.
P.S. I had an idea to make carts with megamoskami weightless. But something did not work out, there are infinities :)
Try to justify to the moderator that friction should not be taken into account :)
The essence of the problem is that there are not only dissipative forces (friction), but also blunt loss of momentum due to ejection of snow.
Therefore the usual proportionality of friction forces to the masses remains, but it is impossible to reduce them, because the loss of momentum is not proportional to the mass of the cart.
Spread your variant of the solution, we will parry.
P.S. I had an idea to make carts with megamotors weightless. But something did not work out for me, there are infinities there :)
Friction in the condition mentioned in passing, just as a reason for stopping the carts, without which the problem makes no sense. You have attached to the problem the sliding friction (or rolling, it does not matter now).
At the same time the cause of the carts stopping on a magnetic pillow may be friction with the air, and since the geometric shape of the carts is the same, the resistance will be the same.
It follows that friction cannot be measured in this problem; it is just an abstract condition for stopping the carts.
Without friction, the lazy cart moves on.