Question

Два вагона массами 3 тоны и 2 тонны двигаются друг другу со скоростями 2м/с и 4,5м/с соответственно.найдите скорость вагонов после сцепки

Answer 1

Импульс первого вагона равен m1*V1 = 3000*2=6000кг*м/с, импульс второго - m2*V2=2000*4,5=9000кг*м/с и он больше, чем у первого. Значит, после сцепки они будут двигаться в сторону, в которую двигался второй вагон.
По закону сохранения импульса (m1+m2)V=m2V2-m1V1,
откуда V=(m2V2-m1V1)/(m1+m2)=(9000-6000)/(3000+2000)=0,6 м/с

Answer 2

Calculation of the final velocity of the wagons after coupling

To find the final velocity of the wagons after coupling, we can use the principle of conservation of momentum. According to this principle, the total momentum before the coupling is equal to the total momentum after the coupling.

The momentum of an object is given by the product of its mass and velocity. Therefore, we can calculate the total momentum before the coupling and set it equal to the total momentum after the coupling.

Let's denote the mass of the first wagon as m1 (3 tons) and its velocity as v1 (2 m/s). Similarly, let's denote the mass of the second wagon as m2 (2 tons) and its velocity as v2 (4.5 m/s).

The total momentum before the coupling is given by:

Total momentum before coupling = (m1 * v1) + (m2 * v2)

After the coupling, the two wagons will move together as one system. Let's denote the final velocity of the wagons after coupling as vf.

The total momentum after the coupling is given by:

Total momentum after coupling = (m1 + m2) * vf

According to the principle of conservation of momentum, the total momentum before the coupling is equal to the total momentum after the coupling. Therefore, we can set the two expressions equal to each other and solve for vf:

(m1 * v1) + (m2 * v2) = (m1 + m2) * vf

Now, let's substitute the given values into the equation and solve for vf:

(3 tons * 2 m/s) + (2 tons * 4.5 m/s) = (3 tons + 2 tons) * vf

6 tons * m/s + 9 tons * m/s = 5 tons * vf

15 tons * m/s = 5 tons * vf

Dividing both sides of the equation by 5 tons, we get:

3 m/s = vf

Therefore, the final velocity of the wagons after coupling is 3 m/s.

Please note that the above calculation assumes an idealized scenario without any external forces or friction.