Question

Горизонтально летящая пуля массой M, застревая в подвешенном на нити деревянном шарике такой же массы, сообщает ему скорость v. Определи, какую скорость v′ сообщит та же пуля при тех же условиях деревянному шарику массой 10M. В ответе укажи отношение v′v. Горизонтально летящая пуля массой M, застревая в подвешенном на нити деревянном шарике такой же массы, сообщает ему скорость v. Определи, какую скорость v′ сообщит та же пуля при тех же условиях деревянному шарику массой 10M. В ответе укажи отношение v′v.

Answer 1

Ответ:

$\frac{v'}{v}=\frac{2}{11}$

Объяснение:

Закон сохранения импульса:

Mv₀=(M+M)v          Mv₀=(M+10M)v′

Mv₀=2Mv               Mv₀=11Mv′

v₀=2v                     v₀=11v′

2v=11v′

$v'=\frac{2v}{11}$

$\frac{v'}{v}=\frac{2}{11}$

Answer 2

Problem Analysis

We are given a scenario where a horizontally flying bullet with mass M gets stuck in a wooden ball of the same mass M, which is suspended by a string. The bullet imparts a velocity v to the ball. We need to determine the velocity v' that the same bullet would impart to a wooden ball with a mass of 10M under the same conditions. We are asked to provide the ratio v'/v.

Solution

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

Let's denote the velocity of the bullet after the collision as v' and the velocity of the wooden ball after the collision as V. Since the bullet gets stuck in the wooden ball, their final velocities will be the same.

Using the conservation of momentum, we can write the equation:

M * v = (10M + M) * V

Simplifying the equation, we get:

v = 11M * V

Now, we can solve for V:

V = v / (11M)

Since the bullet and the wooden ball have the same mass, we can substitute v with v' in the equation:

V = v' / (11M)

Therefore, the ratio v'/v is:

v'/v = V / (v / (11M)) = 11M

Answer

The ratio of the velocity v' that the same bullet would impart to a wooden ball with a mass of 10M to the velocity v it imparts to a wooden ball with a mass of M is 11M.