A ball weighing 250 g hangs on a weightless thread 50 cm long. A horizontally flying bullet weighing 10 g gets

| January 7, 2021 | education

A ball weighing 250 g hangs on a weightless thread 50 cm long. A horizontally flying bullet weighing 10 g gets into it and gets stuck in it. What should be the modulus of the minimum speed of the bullet so that the ball with the bullet can make a full revolution in the vertical plane? Neglect air resistance.

mw = 250 g = 0.25 kg.
L = 50cm = 0.5m.
g = 9.8 m / s2.
mp = 10 g = 0.01 kg.
Vп -?
mp * Vp = (msh + mp) * V – the law of conservation of momentum, where V is the speed of the bullet from the balls immediately after the impact.
V = mp * Vp / (msh + mp).
When a bullet hits a ball, the kinetic energy of a bullet with a ball Ek transforms into the kinetic and potential energy of a bullet with a ball Еп, which rise to a height of 2 * L.
(msh + mp) * V ^ 2/2 = (msh + mp) * V1 ^ 2/2 + (msh + mp) * g * 2 * L, where V1 is the speed of the ball at the top point.
V12 = g * L.
(mш + mp) * V ^ 2/2 = (mш + mp) * g * L / 2 + (mш + mp) * g * 2 * L
V ^ 2 = (mw + mp) * g * L / (mw + mp) + (mw + mp) * g * 4 * L / (mw + mp).
V = √ (g * L + g * 4 * L) = √ (5 * g * L).
mp * Vp / (mw + mp) = √ (5 * g * L).
Vp = √ (5 * g * L) * (msh + mp) / mp.
Vp = √ (5 * 9.8 m / s2 * 0.5 m) * (0.25 kg + 0.01 kg) / 0.01 kg = 128.7 m / s.
Answer: the speed of the bullet before hitting the ball was Vp = 128.7 m / s.



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