Question

Два вагони масами 20т і 50т, що рухаються назустріч один одному по горизонтальній прямолінійній ділянці шляху зі швидкостями 8м/с і 2,5м/с, відповідно, зчіплюються після зіткнення. Нехтуючи опором руху, визначити модуль і напрямок швидкості вагонів після зчеплення.

Answer 1

Ответ: 0,5м/с; движение продолжится в сторону движения вагона m1

Объяснение:

Дано:

m1=20т

m2=50т

V1=8м/с

V2=2,5м/с

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V-?

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

V=(m1*V1-m2*V2)/(m1+m2)=(8*20-2,5*50)/(20+50)=0,5м/с

Вагоны продолжат движение в сторону движения вагона m1

Answer 2

Problem Analysis

We have two wagons with masses of 20 tons and 50 tons, respectively, moving towards each other on a horizontal straight track. The wagons have velocities of 8 m/s and 2.5 m/s, respectively. After the collision, the wagons couple together. We need to determine the magnitude and direction of the velocity of the wagons after coupling, neglecting any resistance to motion.

Solution

To solve this problem, we can apply 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 momentum of the first wagon before the collision is given by:

Momentum of first wagon before collision = mass of first wagon * velocity of first wagon

Similarly, the momentum of the second wagon before the collision is given by:

Momentum of second wagon before collision = mass of second wagon * velocity of second wagon

Since the wagons are moving towards each other, we can consider the velocity of the second wagon as negative. Therefore, the momentum of the second wagon before the collision can be written as:

Momentum of second wagon before collision = (-1) * mass of second wagon * velocity of second wagon

The total momentum before the collision is the sum of the individual momenta:

Total momentum before collision = Momentum of first wagon before collision + Momentum of second wagon before collision

After the collision, the wagons couple together and move with a common velocity. Let's denote this common velocity as V. The total momentum after the collision is given by:

Total momentum after collision = (mass of first wagon + mass of second wagon) * velocity of coupled wagons

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:

Momentum of first wagon before collision + Momentum of second wagon before collision = (mass of first wagon + mass of second wagon) * velocity of coupled wagons

Now we can solve this equation to find the magnitude and direction of the velocity of the wagons after coupling.

Calculation

Let's substitute the given values into the equation and solve for the velocity of the coupled wagons.

Mass of first wagon = 20 tons = 20,000 kg Velocity of first wagon = 8 m/s

Mass of second wagon = 50 tons = 50,000 kg Velocity of second wagon = -2.5 m/s

Substituting these values into the equation, we have:

(20,000 kg * 8 m/s) + (50,000 kg * (-2.5 m/s)) = (20,000 kg + 50,000 kg) * velocity of coupled wagons

Simplifying the equation, we get:

160,000 kg*m/s - 125,000 kg*m/s = 70,000 kg * velocity of coupled wagons

35,000 kg*m/s = 70,000 kg * velocity of coupled wagons

Dividing both sides of the equation by 70,000 kg, we find:

velocity of coupled wagons = 35,000 kg*m/s / 70,000 kg

velocity of coupled wagons = 0.5 m/s

Therefore, the magnitude of the velocity of the wagons after coupling is 0.5 m/s.

Since the wagons were moving towards each other, the direction of the velocity after coupling is in the opposite direction to the initial motion. Therefore, the direction of the velocity after coupling is to the left.

Answer

The magnitude of the velocity of the wagons after coupling is 0.5 m/s, and the direction of the velocity is to the left.