Question

Вагон массой 20 т. движущийся со скоростью 0,3 м/с нагоняет вагон массой 30 т. движущийся со скорость 0,2 м/с.Какова скорость вагонов после того как сработает автосцепка?

Answer 1

Дано:

m1 = 20т = 20000 кг

v1 = 0,3 м/с

m2 = 30т = 30000 кг

v2 = 0,2 м/с

____________

v - ?

  Решение: По закону сохранения импульса для неупругого взаимодействия: m1v1 + m2v2 = (m1+m2)*v, v = (m1v1 + m2v2) / (m1+m2) v = (20000*0.3+30000*0.2) / (20000+30000) = 0.24 м/с

Answer 2

Calculation of the Final Velocity of the Coupled Wagons

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

The momentum of an object is given by the product of its mass and velocity. Therefore, we can calculate the total momentum before the collision as the sum of the individual momenta of the two wagons.

Let's denote the mass of the first wagon as m1 (20 tons) and its velocity as v1 (0.3 m/s). Similarly, let's denote the mass of the second wagon as m2 (30 tons) and its velocity as v2 (0.2 m/s).

The total momentum before the collision is given by:

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

Now, let's calculate the total momentum before the collision using the given values:

Total momentum before collision = (20 tons * 0.3 m/s) + (30 tons * 0.2 m/s)

Using the given values, we can calculate the total momentum before the collision.

Calculation:

Total momentum before collision = (20 tons * 0.3 m/s) + (30 tons * 0.2 m/s)

Total momentum before collision = (6 tons m/s) + (6 tons m/s)

Total momentum before collision = 12 tons m/s

According to the principle of conservation of momentum, the total momentum after the collision will also be 12 tons m/s.

Since the wagons are coupled, their masses combine to form a single system. Let's denote the mass of the coupled wagons as M (50 tons) and the final velocity of the coupled wagons as V (to be determined).

The total momentum after the collision is given by:

Total momentum after collision = M * V

Since the total momentum before the collision is equal to the total momentum after the collision, we can equate the two expressions:

Total momentum before collision = Total momentum after collision

12 tons m/s = M * V

Substituting the value of M (50 tons) into the equation, we can solve for V:

12 tons m/s = (50 tons) * V

Simplifying the equation:

V = (12 tons m/s) / (50 tons)

Calculation:

V = (12 tons m/s) / (50 tons)

V = 0.24 m/s

Therefore, the final velocity of the coupled wagons after the activation of the automatic coupling system is 0.24 m/s.

Please note that the calculations provided are based on the given information and assumptions.