Question

Два вагона массами 20 т и 30 т движутся навстречу друг-другу со скоростями : 4 м/с и 8 м/с. При столкновении они приходят в сцепку, а затем движутся как одно целое. Определить их скорость движения после сцепки.

Answer 1

дано m1=20т     m2=30т     V1=4м\с    V2=8м\с

m2*V2-m1*V1=V*(m1+m2)

V=(240-80)\50=160\50=3,2 м\с ( в направлении куда двигался вагон m2)

Answer 2

Problem Analysis

We have two wagons with masses of 20 tons and 30 tons, respectively, moving towards each other with velocities of 4 m/s and 8 m/s. After colliding, they become coupled and move as one unit. We need to determine their velocity after the collision.

Solution

To solve this problem, 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, the total momentum before the collision is the sum of the individual momenta of the two wagons.

Let's calculate the total momentum before the collision:

Wagon 1 momentum before collision: Mass of wagon 1 = 20 tons Velocity of wagon 1 = 4 m/s Momentum of wagon 1 = mass * velocity = 20 tons * 4 m/s = 80 ton*m/s

Wagon 2 momentum before collision: Mass of wagon 2 = 30 tons Velocity of wagon 2 = -8 m/s (negative because it is moving in the opposite direction) Momentum of wagon 2 = mass * velocity = 30 tons * (-8 m/s) = -240 ton*m/s

Total momentum before collision: Total momentum = momentum of wagon 1 + momentum of wagon 2 = 80 ton*m/s + (-240 ton*m/s) = -160 ton*m/s

After the collision, the two wagons become coupled and move as one unit. Let's assume their combined mass is M and their velocity after the collision is V.

Total momentum after collision: Total momentum = combined mass * velocity = M * V

According to the principle of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. Therefore, we can equate the two expressions for total momentum:

-160 ton*m/s = M * V

Now, we need to find the combined mass M. The combined mass is simply the sum of the masses of the two wagons:

Combined mass M = mass of wagon 1 + mass of wagon 2 = 20 tons + 30 tons = 50 tons

Substituting the values into the equation, we can solve for the velocity V:

-160 ton*m/s = 50 tons * V

V = -160 ton*m/s / 50 tons = -3.2 m/s

Answer

The velocity of the two wagons after the collision is -3.2 m/s.