Question

при выстреле из пистолета вылетает пуля массой m со скоростью v. какую по модулю скорость приобретает после выстрела пистолет если его масса в 100 раз больше массы пули?

Answer 1

Calculation of the Pistol's Velocity

To calculate the velocity acquired by the pistol after firing a bullet, 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.

Let's assume the mass of the bullet is m and its velocity is v. The mass of the pistol is 100 times greater than the mass of the bullet, so the mass of the pistol is 100m.

Before the shot, the total momentum is given by the sum of the momentum of the bullet and the momentum of the pistol, which is initially at rest:

Total momentum before the shot = momentum of the bullet + momentum of the pistol

The momentum of an object is calculated by multiplying its mass by its velocity:

Momentum = mass x velocity

Since the pistol is initially at rest, its momentum is zero:

Momentum of the pistol = 0

Therefore, the total momentum before the shot is equal to the momentum of the bullet:

Total momentum before the shot = momentum of the bullet

After the shot, the bullet is expelled with a velocity v and the pistol acquires a velocity V. The total momentum after the shot is given by the sum of the momentum of the bullet and the momentum of the pistol:

Total momentum after the shot = momentum of the bullet + momentum of the pistol

Using the principle of conservation of momentum, we can equate the total momentum before the shot to the total momentum after the shot:

Total momentum before the shot = Total momentum after the shot

Momentum of the bullet = Momentum of the bullet + Momentum of the pistol

Simplifying the equation, we get:

Momentum of the pistol = 0

Therefore, the momentum of the bullet after the shot is equal to the momentum of the bullet before the shot:

Momentum of the bullet = Momentum of the bullet

Since momentum is equal to mass times velocity, we can write:

m x v = m x V

Simplifying the equation, we find:

v = V

This means that the velocity acquired by the pistol after firing the bullet is equal to the velocity of the bullet.

Therefore, the pistol will acquire a velocity v after the shot, which is the same as the velocity of the bullet.

Please note that this calculation assumes an ideal scenario without considering factors such as recoil, friction, and energy losses. It provides a simplified understanding of the relationship between the bullet's velocity and the pistol's velocity.