Question

Два тела массами 8 кг и 4 кг движутся вдоль одной прямой, в одном направлении со скоростями 4 м/с и 3 м/с соответственно. Определите скорость этих тел после неупругого столкновения.​

Answer 1

Ответ:

Объяснение:

Сумма импульсов до взаимодействия:

p₀ = m₁·V₁ + m₂·V₂ = 8·4 + 4·3 = 44 кг·м/с         (1)

Сумма импульсов после неупругого столкновения:

p₁ = (m₁ + m₂)·U = (8 + 4)·U = 12·U кг·м/с           (2)

Приравняем (2)  и (1):

12·U  =  44

U = 44 / 12 ≈ 3,7 м/м

Answer 2

Calculation of the final velocity after an inelastic collision

To determine the final velocity of the two bodies 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 total momentum before the collision is the sum of the individual momenta of the two bodies.

Let's denote the mass of the first body as m1 (8 kg) and its initial velocity as v1 (4 m/s). Similarly, let's denote the mass of the second body as m2 (4 kg) and its initial velocity as v2 (3 m/s).

The total momentum before the collision is given by:

Total momentum before collision = m1 * v1 + m2 * v2 Substituting the given values:

Total momentum before collision = (8 kg) * (4 m/s) + (4 kg) * (3 m/s)

Simplifying the equation:

Total momentum before collision = 32 kg·m/s + 12 kg·m/s = 44 kg·m/s

Since this is an inelastic collision, the two bodies stick together after the collision. Therefore, their masses combine to form a single body with a total mass of m1 + m2.

Let's denote the final velocity of the combined body as vf.

The total momentum after the collision is given by:

Total momentum after collision = (m1 + m2) * vf

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

Total momentum before collision = Total momentum after collision

Substituting the values:

44 kg·m/s = (8 kg + 4 kg) * vf

Simplifying the equation:

44 kg·m/s = 12 kg * vf

Solving for vf:

vf = 44 kg·m/s / 12 kg

Calculating the value:

vf ≈ 3.67 m/s

Therefore, the final velocity of the two bodies after the inelastic collision is approximately 3.67 m/s.