Question

Используя закон сохранения импульса, найти скорость тел после неупругого соударения, если тела двигались навстречу друг другу. Первое тело имело массу 300 г и двигалось со скоростью 2м/с; второе тело имело массу 100 г и двигалось со скоростью 3м/с.

Answer 1

Calculation of the final velocity using the law of conservation of momentum

To find the final velocity of the objects after an inelastic collision, we can use the law of conservation of momentum. According to this law, the total momentum before the collision is equal to the total momentum after the collision.

The momentum of an object is calculated by multiplying its mass by its velocity. Therefore, the momentum of the first object before the collision is given by:

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

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

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

Since the objects are moving towards each other, the velocity of the second object can be considered negative.

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

According to the law of conservation of momentum, the total momentum after the collision is equal to the sum of the momenta of the two objects before the collision:

Total momentum after collision = (mass of first object + mass of second object) * final velocity

Setting the two expressions for momentum equal to each other, we can solve for the final velocity:

(mass of first object * velocity of first object) + (mass of second object * velocity of second object) = (mass of first object + mass of second object) * final velocity

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

Given: - Mass of first object (m1) = 300 g = 0.3 kg - Velocity of first object (v1) = 2 m/s - Mass of second object (m2) = 100 g = 0.1 kg - Velocity of second object (v2) = -3 m/s

Substituting these values into the equation, we have:

(0.3 kg * 2 m/s) + (0.1 kg * (-3 m/s)) = (0.3 kg + 0.1 kg) * final velocity

Simplifying the equation:

0.6 kg m/s - 0.3 kg m/s = 0.4 kg * final velocity

0.3 kg m/s = 0.4 kg * final velocity

Dividing both sides of the equation by 0.4 kg:

0.3 kg m/s / 0.4 kg = final velocity

Simplifying:

0.75 m/s = final velocity

Therefore, the final velocity of the objects after the inelastic collision is 0.75 m/s.