Pure maths, physics, logic (braingames.ru): non-trade-related brain games - page 107
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It does. Both on speed and, more importantly, on momentum.
If you consider that the cart travels slowly, vector A will be very small.
The snow is dumped little by little, differentially, but continuously. The effect accumulates and becomes finite.
It will work, as it is a megamotor, it will work out. Otherwise the movement would be jerky and even harder to describe.
The principle is that the megamotor throws some of the momentum forward. So it takes some of the momentum away from the cart. So its momentum goes down. And that's modelled by the reactive braking force created by the work of the megamotor. It's just the recoil force.
So what's the deal with budding carts in a vacuum? Recall the question.
A space cart flies (with speed V). Then by budding it splits in half. The daughter carts (equal in mass) are repelled perpendicularly to the motion (with microscopic speed v).
Is the speed halved?
So what is it about budding carts in a vacuum? Remind me of the question.
A space cart flies. Then by budding it splits in half. The daughter carts (equal in mass) are repulsed perpendicular to the motion...
Does the speed halve?
No, it does not. The carts fly further at an angle (not 180), but their velocities in the direction of motion are the same as before. Law of conservation of momentum.
Where did you get the double?
It does. Both on speed and, more importantly, on momentum.
Well, how does it affect me. Either I'm stupid, or the skis aren't moving.
The gun example - the bullet goes out perpendicular to the movement, but as its speed is much higher than the speed of the cart, the resulting vector of motion of the bullet will be almost perpendicular.
No, it doesn't. The trolleys fly further at an angle (not 180), but their velocities in the direction of travel are the same as before. Law of conservation of momentum.
Where did you get double that from?
We have not a bullet, but slowly falling snow. And it is just as slowly being swept back.
OK, let it be snow, but when we give acceleration to the SNOW, we do not waste the PULSE of the cart, because the acceleration vector is perpendicular to the movement. As long as it does not matter where the snow will fly, the main thing is that at the point of detachment from the shovel, it will fly to the side where the shovel gave it (snow) impetus.
Right?
OK, let it be snow, but when we give acceleration to the SNOW, we do not waste the PULSE of the cart, because the acceleration vector is perpendicular to the movement. The main thing is that at the point of breakaway from the shovel, the snow flies away to the direction where the shovel gave it (the snow) impulse.
Right?
Well, you drew the picture yourself. In the system connected to the ground. Right? Are you going to tell me not to believe my eyes?
It does not matter where the snow flies, the main thing is that at the point of breakaway from the shovel, it flies to the side where the shovel gave it (the snow) an impulse.
In the system associated with the cart, the snow will fly away strictly perpendicular to the cart. In a system connected to the ground, it will fly next to the cart and move away until it hits the ground.
Is "you" OK?
Well, each half has lost half of its momentum, strictly according to your logic.
You're making something up. They haven't lost anything.
I'm only talking about the part of the impulse that's in the direction of the movement. What happens strictly perpendicular to it is of no interest to me.
In the case of your cosmotelega, it's very simple: the momentum is conserved, so both parts will fly further in the direction of the original motion, but will fly apart. But the vector of the total momentum of the system will remain the same.
Believe me, I didn't get that conclusion for nothing either. You are a witness: I resisted at first.
Well, you're the one who painted it. In a system connected to the earth. Didn't you? So you're gonna tell me not to believe my own eyes?
"Is 'on you' OK?
No problem.
In the system connected to the cart, the snow would be perpendicular to the cart. In a system connected to the ground, it will fly next to the cart and move away until it hits the ground.
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 have elapsed. 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 at the 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 megamotor throws forward momentum dp = v*dm - in the same time dt.
Hence, it throws an impulse dp = v*alpha*dt in the time dt. I'm only talking about the motion-directed component. At what speed he tosses the snow perpendicular to the motion - even at the third cosmic speed - I don't care at all.
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 a megamotor is not a person, but a pump that sweeps the snow off the cart.