A bullet flying at a horizontal speed of 400 m / s hits a bag filled with foam rubber, weighing M = 4 kg, hanging on a long string. The height to which the bag rises if the bullet gets stuck in it is 5cm. what is the mass of a bullet?
Given: V (horizontal velocity of the bullet) = 400 m / s; mm (bag weight) = 4 kg; h (height of the bag with foam rubber after being hit by a bullet) = 5 cm (in SI h = 0.05 m); a bag on a long string is a mathematical pendulum.
Constants: g (acceleration due to gravity) ≈ 10 m / s2.
To determine the mass of a given bullet, we apply the law of conservation of energy: mp * Vp ^ 2/2 = mm * g * h, whence mp = 2 * mm * g * h / Vp ^ 2.
Calculation: mp = 2 * mm * g * h / Vp ^ 2 = 2 * 4 * 10 * 0.05 / 400 ^ 2 = 0.000025 kg or 25 mg.
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