Question

Вагон массой 30 тон, движущийся со скорость 10м/с, сталкивается с неподвижным вагоном массой 20 тонн, после чего они вмести продолжают движение. Определите их скорость после воздействия.

Answer 1

MV1+mV2=(m1+m2)*V3;
300000=50000V3;
V3=6м/с

Answer 2

Problem Analysis

We have two wagons colliding with each other. One wagon has a mass of 30 tons and is moving with a velocity of 10 m/s. The other wagon is stationary and has a mass of 20 tons. We need to determine their velocities 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. Mathematically, momentum (p) is defined as:

p = m * v

where p is the momentum, m is the mass, and v is the velocity.

Let's denote the initial velocity of the first wagon as v1, the final velocity of the first wagon as v1', the initial velocity of the second wagon as v2, and the final velocity of the second wagon as v2'.

According to the principle of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision:

m1 * v1 + m2 * v2 = m1 * v1' + m2 * v2'

Substituting the given values:

(30 tons * 10 m/s) + (20 tons * 0 m/s) = (30 tons * v1') + (20 tons * v2')

Simplifying the equation:

300 tons * m/s = 30 tons * v1' + 20 tons * v2'

We have two unknowns, v1' and v2', but we can solve for them using the given information.

Calculation

Let's calculate the velocities of the wagons after the collision.

Substituting the values into the equation:

300 tons * m/s = 30 tons * v1' + 20 tons * v2'

Simplifying the equation:

3000 kg * m/s = 30 tons * v1' + 20 tons * v2'

Converting the masses to kilograms:

3000 kg * m/s = 30000 kg * v1' + 20000 kg * v2'

Dividing both sides of the equation by 1000 to convert tons to kilograms:

3000 kg * m/s = 30000 kg * v1' + 20000 kg * v2'

Now we have the equation:

3000 = 30000 * v1' + 20000 * v2'

We need one more equation to solve for the velocities. This equation can be derived from the conservation of kinetic energy.

The kinetic energy of an object is given by the formula:

KE = (1/2) * m * v^2

where KE is the kinetic energy, m is the mass, and v is the velocity.

According to the conservation of kinetic energy, the total kinetic energy before the collision is equal to the total kinetic energy after the collision.

KE1 + KE2 = KE1' + KE2'

Substituting the given values:

(1/2) * (30 tons) * (10 m/s)^2 + (1/2) * (20 tons) * (0 m/s)^2 = (1/2) * (30 tons) * (v1')^2 + (1/2) * (20 tons) * (v2')^2

Simplifying the equation:

(1/2) * (30000 kg) * (10 m/s)^2 + (1/2) * (20000 kg) * (0 m/s)^2 = (1/2) * (30000 kg) * (v1')^2 + (1/2) * (20000 kg) * (v2')^2

Simplifying further:

(1/2) * (30000 kg) * (100 m^2/s^2) + 0 = (1/2) * (30000 kg) * (v1')^2 + 0

Now we have the equation:

1500000 = 15000 * (v1')^2

Simplifying the equation:

100 = (v1')^2

Taking the square root of both sides:

v1' = 10 m/s

We have found the velocity of the first wagon after the collision. Now we can substitute this value back into the equation we derived from the conservation of momentum to solve for the velocity of the second wagon.

3000 = 30000 * v1' + 20000 * v2'

Substituting the value of v1':

3000 = 30000 * 10 + 20000 * v2'

Simplifying the equation:

3000 = 300000 + 20000 * v2'

Subtracting 300000 from both sides:

-297000 = 20000 * v2'

Dividing both sides by 20000:

-14.85 = v2'

The negative sign indicates that the second wagon is moving in the opposite direction after the collision.

Answer

After the collision, the first wagon will have a velocity of 10 m/s and the second wagon will have a velocity of -14.85 m/s. The negative sign indicates that the second wagon is moving in the opposite direction.