Question

Два неупругих тела, массы которых 2 и 6 кг, движуться навстречу друг другу со скоростями 2м/с каждое. Определите модуль и направление скороти каждого из этих тел после удара.

Answer 1

дано

m1=2кг

m2=6кг

v1= - 2м/с  движение навстречу

v2=   2м/с  

----------------------

v1 -?

v2 - ?

РЕШЕНИЕ

удар неупругий

скорость одинаковая

импульс ВТОРОГО тела боьше, потомучто масса БОЛЬШЕ

понятно, что после удара они со скоростью v12 вместе начнут двигаться

в направлении скорости v2

закон сохранения импульса

m1v1 +m2v2 = (m1+m2) v12

- 2*2 +6*2 = (2+6) v12

v12 = 8/8 = 1 м/с    <--- модуль скорости  каждого тела

ОТВЕТ 

v12 = 1м/с

направления скорости совпадают

 

Answer 2

Problem Analysis

We are given two objects with masses of 2 kg and 6 kg, moving towards each other with velocities of 2 m/s each. We need to determine the magnitude and direction of the velocities of each object 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:

Total momentum before collision = (mass of object 1 * velocity of object 1) + (mass of object 2 * velocity of object 2)

After the collision, the two objects will stick together and move with a common velocity. Let's denote this common velocity as V. The total momentum after the collision is:

Total momentum after collision = (mass of object 1 + mass of object 2) * V

Since the total momentum before the collision is equal to the total momentum after the collision, we can set up the following equation:

(mass of object 1 * velocity of object 1) + (mass of object 2 * velocity of object 2) = (mass of object 1 + mass of object 2) * V

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

mass of object 1 = 2 kg velocity of object 1 = 2 m/s mass of object 2 = 6 kg velocity of object 2 = -2 m/s (negative because the object is moving in the opposite direction)

Substituting these values into the equation:

(2 kg * 2 m/s) + (6 kg * (-2 m/s)) = (2 kg + 6 kg) * V

Simplifying the equation:

4 kg m/s - 12 kg m/s = 8 kg * V

-8 kg m/s = 8 kg * V

Dividing both sides of the equation by 8 kg:

-1 m/s = V

Therefore, the common velocity of the two objects after the collision is -1 m/s. Since the velocity is negative, it means that the objects will move in the opposite direction after the collision.

To determine the individual velocities of the objects after the collision, we can use the equation:

velocity of object 1 after collision = (mass of object 1 + mass of object 2) * V / mass of object 1

Substituting the given values:

velocity of object 1 after collision = (2 kg + 6 kg) * (-1 m/s) / 2 kg

Simplifying the equation:

velocity of object 1 after collision = 8 kg * (-1 m/s) / 2 kg

velocity of object 1 after collision = -4 m/s

Therefore, the velocity of object 1 after the collision is -4 m/s.

To find the velocity of object 2 after the collision, we can use the equation:

velocity of object 2 after collision = (mass of object 1 + mass of object 2) * V / mass of object 2

Substituting the given values:

velocity of object 2 after collision = (2 kg + 6 kg) * (-1 m/s) / 6 kg

Simplifying the equation:

velocity of object 2 after collision = 8 kg * (-1 m/s) / 6 kg

velocity of object 2 after collision = -4/3 m/s

Therefore, the velocity of object 2 after the collision is -4/3 m/s.

Answer

After the collision, the magnitude and direction of the velocities of the two objects are as follows: - Object 1: Magnitude: 4 m/s, Direction: Opposite to the initial direction - Object 2: Magnitude: 4/3 m/s, Direction: Opposite to the initial direction

Please note that the negative sign indicates that the objects are moving in the opposite direction after the collision.