Pure maths, physics, logic (braingames.ru): non-trade-related brain games - page 106

 
Mischek:
That's the thing, it will and the speed of the cart won't.

It will, at least I agree with that. Why won't the speed of the cart drop?

The snow has taken away some of the momentum. So some of the momentum has been taken away from the cart.

I don't know about cart speed, I don't count it. I'm counting the momentum of the cart!

 

Well, I am reading about these carts and cannot understand anything. Here is an example with a car - no positive/negative impulse it cannot return to the hand (car), because its acceleration vector is directed perpendicularly to the vector of car motion.

Here's an even more colourful example: we drive a car, point the barrel of the gun perpendicular to the motion of the car. We shoot. Where will the recoil go? (This example is useful as there is no sweep, everything is strictly perpendicular).

And again to the carts - shoot from the cart, as a variant the cart will turn over, but not backwards or forwards, but to the side opposite to shooting.

 
fyords: Well, I'm reading about these carts and I can't understand anything. Here is an example with a car - no positive/negative momentum it cannot return to the hand (car), because its acceleration vector is directed perpendicular to the motion vector of the car.

Whose acceleration? I don't understand you. Let's try to be more precise, with physical reasoning.

 
Mathemat:

Whose acceleration? I don't understand you. Let's try to be more precise, with physical reasoning.

The acceleration vector of the stone.
 
fyords: The acceleration vector of the stone.

I'll try to explain it to you as well. Let's not talk about acceleration, let's talk about velocities.

You are driving in a car (speed V) and you throw a stone strictly perpendicular to the motion of V at speed v.

Where is the vector of motion of the stone directed? It is v+V. It is the sum of the two vectors, which can no longer be strictly perpendicular to V.

Consequently, you have actually thrown the stone slightly forward. This means that you have slowed the car down.

You won't feel it on an intuitive level, but it's physics.

 
Mathemat:

I'll try to explain it to you as well. Let's not talk about acceleration but about velocities.

You are driving in a car (velocity V) and you throw a stone strictly perpendicular to the motion of V with velocity v.

Where is the vector of motion of the stone directed? It is v+V. It is the sum of the two vectors, which can no longer be strictly perpendicular to V.

Consequently, you have actually thrown the stone slightly forward. This means that you have slowed the car down.

You won't feel it on an intuitive level, but it's physics.

A is the motion vector of the car.

B - the rock's acceleration vector.

C is the resultant vector.

The car is moving and we assume that the motion is uniform not accelerated.

We are throwing a stone perpendicular to the motion. We are throwing the stone, we are in the car and we are moving in the same direction.

The stone rolls perpendicular to the car's movement, but as we had an initial speed perpendicular to the throw, part of this speed is transmitted to the stone and it flies parallel to us, but it moves away. If standing, same effect: vector A=0, so the resulting C=B.

 
fyords:

A - the motion vector of the car

B - rock acceleration vector

C - resultant vector

The car is moving and we assume that the motion is uniform and not accelerated.

We are throwing a stone perpendicular to the motion. We are throwing the stone, we are in the car and we are moving in the same direction.

The stone rolls perpendicular to the car's movement, but as we had an initial speed perpendicular to the throw, part of this speed is transmitted to the stone and it flies parallel to mum, but it moves away. If standing, same effect: vector A=0, so the resulting C=B.

Correct. Further we consider that the stones fly out not in portions, but as a continuous flow, a pump.

Where does the pump push the machine? Backwards!

 
Mathemat:

Correct. Next, consider that the stones do not fly out in portions, but in a continuous flow, a pump.

Where does the pump push the car? Backwards!

Read the condition.

One is constantly clearing the cart of snow (dumping the shovel to the side perpendicular to the path of travel)...

it's a shovel, so it's individual pulses, not a stream. So it's slowing down?

It doesn't have 10 shovels, flow won't work ))

 
fyords:

Read the condition.

it's dumping in spades, so it's individual pulses, not a stream. So it's slowing down?

He doesn't have 10 shovels, it won't work in a stream.)

It will, because it's a megamotor, it'll work. Otherwise the movement would be jerky and even harder to describe.

The principle is that the megamosque throws some of the momentum forward. So it takes some of the momentum away from the cart. So its momentum is reduced. And that's modelled by the reactive braking force created by the work of the megamotor. It's just the recoil force.

P.S. By the way, the moderator informed me that the cart moves on rails, so its trajectory is not curved.

 
Mathemat:

It will work, as it's a megamotor, it will twist out. Otherwise the movement would be jerky and even harder to describe.

Consequently, the throw itself has no effect on speed. It remains to examine the snow itself.

Not forward, but along vector B. The resulting direction of the snow will be directed slightly forward (vector C), relative to the drop point, and if you consider that the cart is going slowly, vector A will be quite small.

We solved it and arrived at the same thing. )