Question

Железнодорожная платформа, движущаяся со скоростью 7 м/с, сцепляется с неподвижным вагоном массой 10 т. После этого платформа с вагоном стали двигаться со скоростью 2 м/с. Чему равна масса платформы?

Answer 1

Если двигался с 7 м/с а стал с 2 м/с, т. е. в 3 с половиной раза медленнее, значит масса тоже увеличилась в 3 с половиной раза 
(учитывая то, что вагон стоял) . В итоге общая масса 
х+10=3.5*х; перенеся х получим 2.5*х=10, откуда х=4.

Answer 2

Calculation of the Platform's Mass

To calculate the mass of the platform, we can use the principle of conservation of momentum. According to this principle, the total momentum before the coupling is equal to the total momentum after the coupling.

Before the coupling, the platform is moving with a speed of 7 m/s, and the wagon is stationary. After the coupling, the platform and the wagon move together with a speed of 2 m/s.

Let's assume the mass of the platform is m (in kilograms) and the mass of the wagon is 10,000 kg (10 tons).

The total momentum before the coupling is given by the product of the mass of the platform and its velocity:

Momentum before coupling = m × 7

The total momentum after the coupling is given by the sum of the momenta of the platform and the wagon:

Momentum after coupling = (m + 10,000) × 2

According to the principle of conservation of momentum, the total momentum before the coupling is equal to the total momentum after the coupling:

m × 7 = (m + 10,000) × 2

To find the mass of the platform, we can solve this equation for m.

Let's calculate it:

7m = 2(m + 10,000)

7m = 2m + 20,000

5m = 20,000

m = 4,000 kg

Therefore, the mass of the platform is 4,000 kg.