Question

Задача на импульс. Снаряд,летящий со скоростью 700 м\с, разрывается на 2 осколка массами 45 кг и 17 кг, со скоростями 710м\с и 900\с. Найти угол разлета осколков

Answer 1

M=m1+m2   P=m*V   P1=m1*V1  P2=m2*V2
По закону сохранения импульса  P=sqrt(P1^2+P2^2+P1*P2*cosa)
cosa=P^2-(P1^2+P2^2)/P1*P2  Считайте сами, затем по таблице найдете значение угла

Answer 2

Problem Analysis

We are given a projectile that is flying with a velocity of 700 m/s. The projectile breaks into two fragments with masses of 45 kg and 17 kg, and velocities of 710 m/s and 900 m/s, respectively. We need to find the angle at which the fragments separate.

Solution

To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before the explosion is equal to the total momentum after the explosion.

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

Initial momentum = Final momentum

Let's assume that the angle at which the fragments separate is θ. We can break down the initial and final momenta into their x and y components.

Initial Momentum

The initial momentum consists of the momentum of the projectile before the explosion. Since the projectile is moving in a straight line, its momentum only has an x-component.

The x-component of the initial momentum is given by:

P_initial_x = m_projectile * v_projectile

Final Momentum

The final momentum consists of the momenta of the two fragments after the explosion. Each fragment will have both x and y components of momentum.

The x-component of the final momentum is given by:

P_final_x = m1 * v1 * cos(θ) + m2 * v2 * cos(θ)

The y-component of the final momentum is given by:

P_final_y = m1 * v1 * sin(θ) + m2 * v2 * sin(θ)

Conservation of Momentum Equation

Using the conservation of momentum equation, we can equate the initial momentum to the final momentum:

P_initial_x = P_final_x

Substituting the values, we get:

m_projectile * v_projectile = m1 * v1 * cos(θ) + m2 * v2 * cos(θ)

Simplifying the equation, we get:

m_projectile * v_projectile = (m1 * v1 + m2 * v2) * cos(θ)

Now, we can solve this equation to find the value of θ.

Calculating the Angle θ

To find the angle θ, we can rearrange the equation as follows:

cos(θ) = (m_projectile * v_projectile) / (m1 * v1 + m2 * v2)

Taking the inverse cosine of both sides, we get:

θ = arccos((m_projectile * v_projectile) / (m1 * v1 + m2 * v2))

Now, we can substitute the given values into this equation to find the angle θ.

Calculation

Substituting the given values into the equation, we get:

θ = arccos((45 kg * 700 m/s) / ((45 kg * 710 m/s) + (17 kg * 900 m/s)))

Calculating this expression, we find:

θ ≈ 0.295 radians

Therefore, the angle at which the fragments separate is approximately 0.295 radians.

Answer

The angle at which the fragments separate is approximately 0.295 radians.