Question

На платформе стоит недвижимо пушка массой 8т. С пушки совершается выстрел с горизонтальной скоростью снаряда 800м/с. С какой скоростью начнет двигаться платформа, если ее масса 12 т , а масса снаряда 50? Узнать время движения платформы, если коэффициент трения колес платформы с колеями - 0,01.

Answer 1

Ответ на фотографии...

Answer 2

Calculation of the Recoil Velocity of the Platform

To calculate the recoil velocity of the platform after firing a projectile, we can use the principle of conservation of momentum. According to this principle, the total momentum before the shot is equal to the total momentum after the shot.

The momentum of an object is given by the product of its mass and velocity. Therefore, we can write the equation:

Initial momentum of the system = Final momentum of the system

The initial momentum of the system is the momentum of the platform and the projectile before the shot, and the final momentum of the system is the momentum of the platform and the projectile after the shot.

Let's denote the initial velocity of the platform as v_initial, the final velocity of the platform as v_final, the mass of the platform as m_platform, the mass of the projectile as m_projectile, and the velocity of the projectile as v_projectile.

The initial momentum of the system is given by:

Initial momentum = (m_platform + m_projectile) * v_initial

The final momentum of the system is given by:

Final momentum = m_platform * v_final + m_projectile * v_projectile

Since the projectile is fired horizontally, its vertical velocity does not affect the horizontal recoil of the platform. Therefore, we can assume that the final velocity of the projectile is zero (v_projectile = 0).

Setting the initial momentum equal to the final momentum, we have:

(m_platform + m_projectile) * v_initial = m_platform * v_final

Now we can substitute the given values into the equation. The mass of the platform is 12 tons (12,000 kg), the mass of the projectile is 50 kg, and the initial velocity of the projectile is 800 m/s.

(12,000 kg + 50 kg) * v_initial = 12,000 kg * v_final

Simplifying the equation:

12,050 kg * v_initial = 12,000 kg * v_final

Dividing both sides of the equation by 12,050 kg:

v_initial = (12,000 kg * v_final) / 12,050 kg

Now we can calculate the recoil velocity of the platform by substituting the given values:

v_initial = (12,000 kg * v_final) / 12,050 kg

Calculation of the Time of Motion of the Platform

To calculate the time of motion of the platform, we need to consider the friction coefficient between the wheels of the platform and the rails. The friction force opposes the motion of the platform and affects its acceleration.

The equation that relates the force of friction, the mass of the platform, and the acceleration of the platform is:

Friction force = mass * acceleration

The friction force can be calculated using the equation:

Friction force = friction coefficient * normal force

The normal force is equal to the weight of the platform, which can be calculated as:

Normal force = mass * gravity

where gravity is the acceleration due to gravity (approximately 9.8 m/s^2).

Now we can write the equation for the friction force:

Friction force = friction coefficient * mass * gravity

The friction force is also equal to the product of mass and acceleration:

Friction force = mass * acceleration

Setting these two equations equal to each other, we have:

friction coefficient * mass * gravity = mass * acceleration

Simplifying the equation:

friction coefficient * gravity = acceleration

Now we can calculate the acceleration of the platform using the given friction coefficient:

acceleration = friction coefficient * gravity

Substituting the given friction coefficient of 0.01 and the acceleration due to gravity of 9.8 m/s^2:

acceleration = 0.01 * 9.8 m/s^2

Finally, we can calculate the time of motion of the platform using the equation:

Time = (Final velocity - Initial velocity) / acceleration

Substituting the calculated acceleration and the initial velocity of the platform (recoil velocity), we can find the time of motion.

Please note that the exact values of the recoil velocity and time of motion will depend on the specific calculations using the given values.