Pure maths, physics, logic (braingames.ru): non-trade-related brain games - page 108

 
Mathemat:
............

Believe me, I didn't come to that conclusion for nothing either. You are a witness: I resisted at first.

Sorry, I only believe Stringo.
 
Mathemat:

Not all of it. I'm stuck. But first you need someone to understand the reasoning given earlier:

I'm not good at maths and everything I wrote above is purely theoretical, but kind of true. I do not use mathematics very often, I use "simulations" in my brain more than anything else. That's it, I'm asleep. :)
 
Mathemat:

Not all of it. I'm stuck. But first you need at least someone to understand the reasoning given earlier (or argue the point):

Let the time dt has passed. During this time the snow has increased the mass of the cart by dm = alpha * dt = dm/dt * dt. We assume that the snow falls on the cart, increasing its mass with speed alpha. The mass of the cart grows according to the law m(t) = m_0 + alpha*t (if the snow is not dumped).

The cart's momentum has not changed. The friction changed but slightly. It will go back, as the cart mass will remain the same when the snow is dumped.

Now the megamotive takes the same mass of snow dm and throws it perpendicular to the motion for the same time dt. Due to the fact that the cart is moving forward with speed v, the megamosk tosses forward the momentum dp = v*dm - in the same time dt.

Hence, it throws momentum dp = v*alpha*dt in time dt. I'm only talking about the motion-directed component. How fast he tosses the snow perpendicular to the motion - even a third cosmic speed - is of no concern to me at all.

This is correct.

So, by pushing the cart back, it creates a reactive force equal to dp/dt = v*alpha and directed already against the motion. Consider that the megamotor is not a person, but a pump that sweeps the snow off the cart.

And here it isn't. Reactive thrust is always considered from the reference point of the system in which it is created. That is, it is only correct to consider it with respect to the cart.

And relative to the cart, the momentum along the motion axis is zero.

 

TheXpert:

Reactive thrust is always considered from the reference point of the system in which it is created. I.e. it is correct to consider it only in relation to the cart.

And relative to the cart, the momentum in the axis of motion is zero.

So it's not jet propulsion. Look at it yourself. The megamotor is pushing off the cart to toss the snow along the motion. The kickback would be Newton's third law of motion. Whatever you want to call it.

It is more correct: in order to throw an impulse forward, the megamotor will have to push off the cart itself and brake it.

 
Mathemat:

Well, let it not be jet propulsion. Look at it for yourself. A megamotor pushes off the cart to toss the snow along the motion. The kickback would be Newton's third law of motion. Whatever you want to call it.

It's not on the move, it's across. If he was throwing on the move, the snow would overtake the cart.
 
Mathemat:

It's more accurate: to throw the momentum forward, the megamotive has to push off the cart itself and brake it.

Why the hell not forward? The system's tied to the cart, there's no forward, there's sideways.
 
Mathemat:


Let's say the cart is standing still. MM throws the snow shovel three times. Once forwards, the cart moves backwards, once backwards, the cart moves forwards and once perpendicular, the cart does not move anywhere.

Is that correct?

 
Mischek:

Let's say the cart is standing still. MM throws the snow shovel three times. Once forwards, the cart moves backwards, once backwards, the cart moves forwards and once perpendicular, the cart does not move anywhere.

Is that right?

OK, no kickback. But momentum is lost.

Let's just consider all the processes by which the cart loses momentum. This is friction and this snow throw.

 
Mathemat:

OK, no kickback. But the momentum is lost.


What kind of momentum? Specifically
 
Mischek:
What is the momentum ? Specifically

There was a cart with snow, travelling at speed V, now an empty cart is travelling at the same speed and snow is flying - also at the same speed.

The speed of the cart has not changed, but the momentum has dropped. Finita la comedia.