Question

Вагон массой 20 т при движении со скоростью 0,6 м/с сталкивается с неподвижным вагоном массой 10 т, сцепляется с ним, и далее они движутся вместе. Чему равно количество теплоты, выделившееся при сцеплении вагонов?

Answer 1

Ek=mv^2/2
Ek=20000kg*(0,6m/s)^2/2=20000*0,36/2=3600J

Answer 2

Calculation of the Heat Released during the Collision of Wagons

To calculate the amount of heat released during the collision of the wagons, we need to consider the principle of conservation of mechanical energy. According to this principle, the total mechanical energy before the collision is equal to the total mechanical energy after the collision.

The mechanical energy of an object can be calculated using the formula:

E = (1/2)mv^2

Where: - E is the mechanical energy - m is the mass of the object - v is the velocity of the object

Let's calculate the mechanical energy before and after the collision and find the difference, which represents the heat released during the collision.

Calculation:

1. Calculation of the mechanical energy before the collision:

The first wagon has a mass of 20 tons (20,000 kg) and a velocity of 0.6 m/s. Using the formula, we can calculate its mechanical energy:

E1 = (1/2) * m1 * v1^2

E1 = (1/2) * 20,000 kg * (0.6 m/s)^2

2. Calculation of the mechanical energy after the collision:

After the collision, the two wagons are coupled and move together. The total mass of the coupled wagons is the sum of the masses of the individual wagons, which is 20 tons (20,000 kg) + 10 tons (10,000 kg) = 30 tons (30,000 kg). The velocity of the coupled wagons is the same as the velocity of the first wagon before the collision, which is 0.6 m/s. Using the formula, we can calculate the mechanical energy:

E2 = (1/2) * m2 * v2^2

E2 = (1/2) * 30,000 kg * (0.6 m/s)^2

3. Calculation of the heat released during the collision:

The heat released during the collision is equal to the difference in mechanical energy before and after the collision:

Heat released = E1 - E2

Let's calculate the values:

E1 = (1/2) * 20,000 kg * (0.6 m/s)^2

E1 = 3,600,000 J

E2 = (1/2) * 30,000 kg * (0.6 m/s)^2

E2 = 5,400,000 J

Heat released = E1 - E2

Heat released = 3,600,000 J - 5,400,000 J

Heat released = -1,800,000 J

The negative sign indicates that heat is released during the collision.

Therefore, the amount of heat released during the collision of the wagons is -1,800,000 J.

Please note that the negative sign indicates the direction of heat flow, which is from the system (wagons) to the surroundings.