Question

В подвешенный мешок с песком весом 5 кг. ударилась пуля массой 10 кг. При этом мешок откачнулся на высоту 10 см. Определить скорость пули при ударе.

Answer 1

Считаем, что в исходных данных описка и масса пули равна 10г
Запишем закон сохранения импульса при ударе пули массой m в мешок массой М.
$mv_1=(M+m)*v_2; \ M>>m \to M+m \approx M; \ mv_1=Mv_2 \\ v_1= v_2\frac{M}{m};$
После удара мешок поднялся вверх на высоту h, следовательно в верхней точке вся его кинетическая энергия перешла в потенциальную:
$\frac{Mv_2^2}{2}=Mgh \to v_2= \sqrt{2gh} \\ v_1=\sqrt{2gh} \frac{M}{m}= \sqrt{2*9.8*0.1}* \frac{5}{0.01}=500 \sqrt{1.96}=500*1.4=700 (_M/c)$
На самом деле пуль с такими скоростями не бывает, поэтому массу пули следовало бы все же уточнить...

Answer 2

Calculation of Bullet's Velocity

To determine the velocity of the bullet upon impact, we can use 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.

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

Initial momentum = Final momentum

The initial momentum is the momentum of the bullet before the collision, and the final momentum is the momentum of the bullet and the sandbag after the collision.

Let's denote the velocity of the bullet before the collision as v and the velocity of the bullet and sandbag after the collision as V. The mass of the bullet is 10 kg, and the mass of the sandbag is 5 kg.

The initial momentum is given by the product of the bullet's mass and velocity:

Initial momentum = 10 kg * v

The final momentum is given by the sum of the momenta of the bullet and the sandbag:

Final momentum = (10 kg + 5 kg) * V

Since the sandbag is at rest before the collision, its initial velocity is zero. Therefore, the final momentum can be simplified to:

Final momentum = 15 kg * V

According to the principle of conservation of momentum, the initial momentum is equal to the final momentum:

10 kg * v = 15 kg * V

To find the velocity of the bullet upon impact, we need to solve this equation for v.

Let's calculate the velocity of the bullet using the given information.