Question

Винтовка массой М = 3 кг подвешена горизонтально на двух параллельных нитях. При выстреле в результате отдачи она отклонилась вверх на h = 20 см. Масса пули m = 10 г. Определить скорость v1, с которой вылетела пуля.

Answer 1

M₁*v₁ - m₂*v₂ = 0 => v₂ = m₁*v₁/m₂
m₂*v₂²/2 = m₂*g*h
m₂*m₁²*v₁²/2*m₂² = m₂*g*h
v₁ = m₂*корень(2*g*h)/m₁
v₁ = 3 кг * корень(2*10 Н/кг * 0,20 м) / 0,010 кг = 600 м/с

Answer 2

Problem Analysis

We have a rifle with a mass of M = 3 kg that is suspended horizontally by two parallel strings. When the rifle is fired, it recoils and moves upward by h = 20 cm. The mass of the bullet is m = 10 g. We need to determine the velocity v1 with which the bullet was ejected.

Solution

To solve this problem, 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 total momentum before the shot is zero because the rifle is at rest. After the shot, the bullet is moving with velocity v1, and the rifle recoils in the opposite direction with velocity v2. The total momentum after the shot is given by the sum of the momenta of the bullet and the rifle.

Let's denote the velocity of the rifle after the shot as v2. Since the rifle and the bullet move in opposite directions, we can write:

m * v1 + M * v2 = 0 (Equation 1)

where: - m is the mass of the bullet (m = 10 g = 0.01 kg) - M is the mass of the rifle (M = 3 kg) - v1 is the velocity of the bullet - v2 is the velocity of the rifle

We also know that the rifle recoils upward by h = 20 cm = 0.2 m. This means that the displacement of the rifle is equal to the negative displacement of the bullet:

h = -d (Equation 2)

where d is the displacement of the bullet.

To relate the displacement of the bullet to its velocity, we can use the equation of motion for uniformly accelerated motion:

d = v1 * t - (1/2) * a * t^2 (Equation 3)

where: - t is the time taken by the bullet to reach its maximum height - a is the acceleration of the bullet

Since the bullet is fired vertically, its acceleration is equal to the acceleration due to gravity, which is approximately 9.8 m/s^2.

We can rearrange Equation 3 to solve for t:

t = (v1 - 0) / a (Equation 4)

Substituting Equation 4 into Equation 3, we get:

d = v1 * [(v1 - 0) / a] - (1/2) * a * [(v1 - 0) / a]^2 (Equation 5)

Simplifying Equation 5, we have:

d = (v1^2) / (2 * a) (Equation 6)

Substituting Equation 2 into Equation 6, we get:

0.2 = (v1^2) / (2 * 9.8) (Equation 7)

Simplifying Equation 7, we have:

v1^2 = 0.2 * 2 * 9.8 (Equation 8)

Solving Equation 8 for v1, we get:

v1 = sqrt(0.2 * 2 * 9.8) (Equation 9)

Let's calculate the value of v1 using Equation 9:

v1 = sqrt(0.2 * 2 * 9.8) ≈ 2.8 m/s

Answer

The velocity with which the bullet was ejected is approximately 2.8 m/s.