Question

1.Рассчитайте массу Земли , если Луна движется вокруг Земли со скоростью 1 км/с , а средний радиус ее орбиты составляет 384000 км.2.Вагон массой 10 т движется со скоростью 1 м/с и сталкивается с неподвижной платформой массой 5 т . Чему равна скорость их движения после того , как сработает автосцепка?Помогите пожалуйста!

Answer 1

Задача 2 на закон сохранения импульса. Делаешь рисунок тел до и после столкновения.
Записываешь закон m1V1=(m1+m2)*V
Остается подставить числа и подсчитать V=0,66 м/с

Answer 2

5.7*10^6кг масса земли
m=v^2*R/G=5.7*10^6 масса земли преобразуется до этой формулы

Answer 3

Calculation of Earth's Mass

To calculate the mass of the Earth, we can use the formula for centripetal force:

F = (m * v^2) / r

Where: - F is the centripetal force - m is the mass of the Moon - v is the velocity of the Moon - r is the radius of the Moon's orbit

Given that the Moon's velocity is 1 km/s and the radius of its orbit is 384,000 km, we can substitute these values into the formula.

F = (m * (1 km/s)^2) / 384,000 km

To find the mass of the Earth, we need to know the mass of the Moon. The mass of the Moon is approximately 7.35 x 10^22 kg.

Substituting the values into the formula, we get:

F = (7.35 x 10^22 kg * (1 km/s)^2) / 384,000 km

Simplifying the equation, we find:

F = 1.91 x 10^17 kg km/s^2

Therefore, the mass of the Earth is approximately 1.91 x 10^17 kg.

Calculation of Final Velocity after Collision

To calculate the final velocity of the wagon and the platform after the collision, we can use the principle of conservation of momentum.

According to the principle of conservation of momentum, 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.

Before the collision, the momentum of the wagon is given by:

Momentum of wagon before collision = mass of wagon * velocity of wagon

After the collision, the momentum of the wagon and the platform combined is given by:

Momentum of wagon and platform after collision = (mass of wagon + mass of platform) * final velocity

Since the platform is initially at rest, its velocity is 0 m/s.

Using the principle of conservation of momentum, we can equate the two expressions:

mass of wagon * velocity of wagon = (mass of wagon + mass of platform) * final velocity

Given that the mass of the wagon is 10 tons (10,000 kg) and the mass of the platform is 5 tons (5,000 kg), and the initial velocity of the wagon is 1 m/s, we can substitute these values into the equation.

10,000 kg * 1 m/s = (10,000 kg + 5,000 kg) * final velocity

Simplifying the equation, we find:

10,000 kg = 15,000 kg * final velocity

Dividing both sides of the equation by 15,000 kg, we get:

final velocity = 10,000 kg / 15,000 kg

Simplifying further, we find:

final velocity = 0.67 m/s

Therefore, the final velocity of the wagon and the platform after the collision, when the auto coupling is activated, is approximately 0.67 m/s.