Question

Снаряд массой 20 кг, летевший горизонтально со скоростью 500 м/с, попадает в неподвижную платформу с песком массой 10 т и застревает в песке. С какой скоростью начинает двигаться платформа? Со всеми формулами, прошу!

Answer 1

mv =(m+M)u

u=mv /(m+M)

u=20*500 /(20+10000)=0,9980039920159681 м/с= 1 м/с

ответ :1 м/с

Answer 2

Problem Analysis

We are given the following information: - Mass of the projectile, m = 20 kg - Initial velocity of the projectile, v = 500 m/s - Mass of the platform with sand, M = 10 tons (1 ton = 1000 kg)

We need to find the velocity at which the platform starts moving after the projectile gets embedded in the sand.

To solve this problem, we can use the principle of conservation of momentum.

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.

Mathematically, we can express this as:

Initial momentum = Final momentum

Initial Momentum

The initial momentum is the momentum of the projectile before the collision. It can be calculated using the formula:

Initial momentum = mass of the projectile × initial velocity of the projectile

Final Momentum

The final momentum is the momentum of the system (projectile + platform) after the collision. Since the projectile gets embedded in the platform, the final momentum is the momentum of the platform.

Calculation

Let's calculate the initial momentum and final momentum to find the velocity at which the platform starts moving.

Initial Momentum Calculation

Initial momentum = mass of the projectile × initial velocity of the projectile

Substituting the given values: Initial momentum = 20 kg × 500 m/s

Final Momentum Calculation

The final momentum is the momentum of the platform. Since the platform was initially at rest, its initial momentum is zero. After the collision, the platform starts moving with a certain velocity. Let's assume this velocity as V.

Final momentum = mass of the platform × velocity of the platform

Substituting the given values: Final momentum = (10 tons) × V

Conservation of Momentum Equation

According to the principle of conservation of momentum, the initial momentum is equal to the final momentum.

Initial momentum = Final momentum

20 kg × 500 m/s = (10 tons) × V

Now, let's solve this equation to find the velocity at which the platform starts moving.

Solution

To solve the equation, we need to convert the mass of the platform from tons to kilograms.

1 ton = 1000 kg

Mass of the platform = 10 tons = 10 × 1000 kg = 10000 kg

Substituting the values into the equation:

20 kg × 500 m/s = 10000 kg × V

Simplifying the equation:

V = (20 kg × 500 m/s) / 10000 kg

V = 10000 kg·m/s / 10000 kg

V = 1 m/s

Therefore, the platform starts moving with a velocity of 1 m/s after the projectile gets embedded in the sand.

Summary

After the projectile with a mass of 20 kg and an initial velocity of 500 m/s gets embedded in a stationary platform with sand, the platform starts moving with a velocity of 1 m/s.

Formulas Used

- Initial momentum = mass of the projectile × initial velocity of the projectile - Final momentum = mass of the platform × velocity of the platform