Question

В ящик с песком массой 4,992 кг, подвешанный на нити, попала пуля массой 0,008 кг, летящая горизонтально со скоростью перед столкновением 500 м/с, и астряла в нём. На какую высоту поднимется ящк с пулей? на сколько изменится внутренняя энергия системы " пуля- ящик"? g = 10м/с

Answer 1

При неупругом столкновении пули с ящиком выполняется закон сохранения импульса:mv=(m+M)*v', где v-скорость пули,M-масса мешка,v'-скорость после столкновения.отсюда находим скорость v'=mv/m+M после этого находим высоту.я сделал через формулу безвременной высоты. v'^2=2gh, h=v'^2/2g

Answer 2

Given information:

- Mass of the box with sand: 4.992 kg - Mass of the bullet: 0.008 kg - Horizontal velocity of the bullet before collision: 500 m/s - Acceleration due to gravity: g = 10 m/s^2

To find the height to which the box with the bullet will rise and the change in the internal energy of the "bullet-box" system, we can apply the principle of conservation of momentum and the principle of conservation of mechanical energy.

Conservation of momentum:

Before the collision, the bullet has a horizontal velocity of 500 m/s, and the box with sand is at rest. After the collision, the bullet gets embedded in the box, so the entire system moves together with a common velocity.

The momentum before the collision is equal to the momentum after the collision. Therefore, we can write:

Initial momentum = Final momentum

`(mass of bullet) * (initial velocity of bullet) = (mass of bullet + mass of box) * (final velocity of system)`

`(0.008 kg) * (500 m/s) = (0.008 kg + 4.992 kg) * (final velocity)`

Solving for the final velocity of the system:

`final velocity = (0.008 kg * 500 m/s) / (0.008 kg + 4.992 kg)`

`final velocity ≈ 0.0798 m/s`

Conservation of mechanical energy:

The change in potential energy of the system is equal to the change in kinetic energy of the system.

The change in potential energy is given by the formula:

Change in potential energy = mass of system * g * change in height

The change in kinetic energy is given by the formula:

Change in kinetic energy = (1/2) * mass of system * (final velocity)^2

Since the initial kinetic energy is zero (the box is at rest), the change in kinetic energy is equal to the final kinetic energy.

Therefore, we can write:

Change in potential energy = Change in kinetic energy

`(mass of bullet + mass of box) * g * change in height = (1/2) * (mass of bullet + mass of box) * (final velocity)^2`

Substituting the given values and solving for the change in height:

`(0.008 kg + 4.992 kg) * 10 m/s^2 * change in height = (1/2) * (0.008 kg + 4.992 kg) * (0.0798 m/s)^2`

Simplifying the equation:

`5 kg * 10 m/s^2 * change in height = 0.5 * 5 kg * (0.0798 m/s)^2`

`50 m/s^2 * change in height = 0.5 * (0.0798 m/s)^2`

`change in height = (0.5 * (0.0798 m/s)^2) / (50 m/s^2)`

`change in height ≈ 0.00006384 m`

Answer:

The box with the bullet will rise to a height of approximately 0.00006384 meters (or 0.06384 millimeters). The change in the internal energy of the "bullet-box" system is zero because there is no change in temperature or other forms of energy.