A horizontally flying bullet with a mass of m2 = 4 g hits a wooden ball with a mass of m1 = 8 kg

| February 3, 2021 | education

A horizontally flying bullet with a mass of m2 = 4 g hits a wooden ball with a mass of m1 = 8 kg, suspended by a thread l = 1.8 m long. At what speed did the bullet fly if the thread with the ball and the bullet stuck in it deviated from the vertical by an angle a = 30? Disregard the size of the ball. The bullet blow is considered direct, central.

Problem data: m1 (mass of a wooden ball) = 8 kg; l (thread length) = 1.8 m; m2 (bullet weight) = 4 g = 0.004 kg; α (angle of deflection of the ball with a bullet) = 3º.

Constants: g (acceleration due to gravity) = 9.81 m / s2.

1) The speed of a wooden ball with a stuck bullet: V = V2 * m2 / (m1 + m2).

2) Kinetic energy of a wooden ball and a bullet: Ek = (m1 + m2) * V ^ 2/2 = m1 * (V ^ 2 * m2 / (m1 + m2)) ^ 2/2 = (m1 + m2) * V2 ^ 2 * m2 ^ 2 / (2 * (m1 + m2) ^ 2) = V2 ^ 2 * m2 ^ 2 / (2 * (m1 + m2)).

3) Potential energy at a deviation of 30º: Ep = m * g * l * (1 – cosα) = (m1 + m2) * g * l * (1 – cosα).

4) Bullet speed: Ek = Ep; V2 ^ 2 * m2 ^ 2 / (2 * (m1 + m2)) = (m1 + m2) * g * l * (1 – cosα) and V ^ 2 = √ ((m1 + m2) * g * l * (1 – cosα) * 2 * (m1 + m2) / m2 ^ 2) = √ ((m1 + m2) ^ 2 * g * l * (1 – cosα) * 2 / m2 ^ 2) = √ ((8 + 0.004) 2 * 9.81 * 1.8 * (1 – cos 3º) * 2 / 0.0042) = 440.2 m / s.

Answer: The bullet flew at a speed of 440.2 m / s.



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