Question

Вагон массой 80т, двигавшийся со скоростью 0,8м/с, столкнулся с неподвижной платформой массой 10т. С какой скоростью двигался после столкновения вагон, если платформа приобрела скорость 1.2 м/с

Answer 1

M1V1=m1v2+m2V2
отсюда 
80000*0,8=80000*V2+10000*1.2
V2=0.65

Answer 2

Problem Analysis

We have a wagon with a mass of 80 tons (80,000 kg) moving with a velocity of 0.8 m/s. It collides with a stationary platform with a mass of 10 tons (10,000 kg). After the collision, the platform acquires a velocity of 1.2 m/s. We need to calculate the velocity of the wagon 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 of the object, and - v is the velocity of the object.

Before the collision, the total momentum is the sum of the momentum of the wagon and the momentum of the platform. After the collision, the total momentum is the sum of the momentum of the wagon and the momentum of the platform.

Let's denote the velocity of the wagon after the collision as v_wagon_after and the velocity of the platform after the collision as v_platform_after.

According to the conservation of momentum principle, we have:

m_wagon * v_wagon_before + m_platform * v_platform_before = m_wagon * v_wagon_after + m_platform * v_platform_after

where: - m_wagon is the mass of the wagon, - v_wagon_before is the velocity of the wagon before the collision, - m_platform is the mass of the platform, - v_platform_before is the velocity of the platform before the collision, - v_wagon_after is the velocity of the wagon after the collision, and - v_platform_after is the velocity of the platform after the collision.

We are given the following values: - m_wagon = 80,000 kg - v_wagon_before = 0.8 m/s - m_platform = 10,000 kg - v_platform_before = 0 m/s - v_platform_after = 1.2 m/s

Substituting these values into the conservation of momentum equation, we can solve for v_wagon_after.

Calculation

Let's calculate the velocity of the wagon after the collision.

m_wagon * v_wagon_before + m_platform * v_platform_before = m_wagon * v_wagon_after + m_platform * v_platform_after

Substituting the given values:

(80,000 kg) * (0.8 m/s) + (10,000 kg) * (0 m/s) = (80,000 kg) * v_wagon_after + (10,000 kg) * (1.2 m/s)

Simplifying the equation:

64,000 kg·m/s = 80,000 kg·v_wagon_after + 12,000 kg·m/s

Rearranging the equation to solve for v_wagon_after:

80,000 kg·v_wagon_after = 64,000 kg·m/s - 12,000 kg·m/s

80,000 kg·v_wagon_after = 52,000 kg·m/s

v_wagon_after = (52,000 kg·m/s) / (80,000 kg)

v_wagon_after ≈ 0.65 m/s

Answer

After the collision, the wagon is moving with a velocity of approximately 0.65 m/s.