Question

Два шара с массами 2 кг и 8 кг движутся навстречу друг другу со скоростями 6 и 4 м/с соответственно. Найти модули скоростей, с которыми будут двигаться шары после абсолютно неупругого центрального удара?

Answer 1

Calculation of the final velocities of the balls after an inelastic collision

To find the final velocities of the balls after an inelastic collision, 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 momentum of the first ball (with mass 2 kg) before the collision is given by:

Momentum of ball 1 before collision = mass of ball 1 * velocity of ball 1

Similarly, the momentum of the second ball (with mass 8 kg) before the collision is given by:

Momentum of ball 2 before collision = mass of ball 2 * velocity of ball 2

Since the balls are moving towards each other, we can consider the velocity of ball 1 as positive and the velocity of ball 2 as negative.

After the collision, the two balls stick together and move with a common final velocity. Let's denote this final velocity as V.

The total momentum after the collision is given by:

Total momentum after collision = (mass of ball 1 + mass of ball 2) * final velocity

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 set up the following equation:

(mass of ball 1 * velocity of ball 1) + (mass of ball 2 * velocity of ball 2) = (mass of ball 1 + mass of ball 2) * final velocity

Now we can substitute the given values into the equation and solve for the final velocity.

mass of ball 1 = 2 kg velocity of ball 1 = 6 m/s mass of ball 2 = 8 kg velocity of ball 2 = -4 m/s

Substituting these values into the equation, we get:

(2 kg * 6 m/s) + (8 kg * (-4 m/s)) = (2 kg + 8 kg) * final velocity

Simplifying the equation:

12 kg m/s - 32 kg m/s = 10 kg * final velocity

-20 kg m/s = 10 kg * final velocity

Dividing both sides of the equation by 10 kg:

final velocity = -2 m/s

Therefore, the balls will move with a final velocity of -2 m/s after the inelastic collision.

Please note that the negative sign indicates that the balls will move in the opposite direction compared to their initial motion.