A bullet weighing 15 g, flying horizontally, hits a ballistic pendulum with a length of 1 m and a mass of 1.5 kg and gets stuck in it. As a result, the pendulum deflected by an angle of 300. Determine the speed of the bullet
mp = 15 g = 0.015 kg.
L = 1 m.
g = 10 m / s2.
mm = 1.5 kg.
∠α = 30 °.
Let us write down the law of conservation of momentum: mp * Vp = (mp + mm) * V, where V is the speed of the bullet from the pendulums after hitting.
Vp = (mp + mm) * V / mp.
We find the speed of a bullet with a pendulum, according to the law of conservation of total mechanical energy:
(mp + mm) * V2 / 2 = (mp + mm) * g * h, where h is the height to which the pendulum with the bullet rose.
V2 / 2 = g * h.
h = L – L * cosα = L * (1 – cosα).
V = √ (2 * g * L * (1 – cosα)).
V = √ (2 * 10 m / s2 * 1 m * (1 – cos30 °)) = 1.6 m / s
Vp = (0.015 kg + 1.5 kg) * 1.6 m / s / 0.015 kg = 161.6 m / s.
Answer: the bullet was moving at a speed of Vp = 161.6 m / s.
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