A new rapid-fire machine gun is being tested, giving 100 rounds per second. The bullet speed is 1000 m / s

A new rapid-fire machine gun is being tested, giving 100 rounds per second. The bullet speed is 1000 m / s, and its mass is 10 g. The target is a vertically suspended box of sand, the mass of which is 1000 kg. Assuming that the bullets get stuck in the box, determine the maximum angle of deflection of the box from the vertical after the start of firing.

according to the rule impulse of force = change in impulse: F * t = n * m * v or F = n * m * v / t – force that acts on the box where n * m * v impulses from n bullets arrive in t = 1 second … A “restoring” force F₀ = M * g * t * g * α acts on a box with sand deflected at an angle α The box will stop deflecting when F = F₀ M * g * t * g * α = n * m * v / tt * g * α = n * m * v / (M * g * t) = 100 * 0.01 * 1000 / (1000 * 10 * 1) = 0.1 So, α = arctan (0. 1) ≈ 6 ° answer: α = arctg (0. 1) ≈ 6 °