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One body of mass M = 1 kg at rest on one plane horizontal friction-free, is attached to a spring of elastic constant k, which in turn is attached to a fixed wall. A mass bullet m = 20 g and speed v hits the block and gets stuck there. Knowing that the period of oscillation is T = 0.21 s, and that the spring undergoes a maximum compression XM = 15 cm calculate the initial speed of the bullet and energy dissipated in the impact.

One body of mass M = 1 kg at rest on one plane horizontal friction-free, is attached to a spring of elastic constant k, which in turn is attached to a fixed wall. A mass bullet m = 20 g and speed v hits the block and gets stuck there. Knowing that the period of oscillation is T = 0.21 s, and that the spring undergoes a maximum compression XM = 15 cm calculate the initial speed of the bullet and energy dissipated in the impact.

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Answer step-wise with detailed explanations One body of mass M = 1 kg at rest on one plane horizontal friction-free, is attached to a spring of elastic constant k, which in turn is attached to a fixed wall. A mass bullet m = 20 g and speed v hits the block and gets stuck there. Knowing that the period of oscillation is T = 0.21 s, and that the spring undergoes a maximum compression XM = 15 cm calculate the initial speed of the bullet and energy dissipated in the impact. Two masses m₁ = 1 kg and m2 = 2 kg, are attached to two length ropes L. The ropes are hung at the same point to the ceiling. The mass m2 is in the equilibrium position, while the mass m₁ is moved at an angle 0 to the vertical and then left free. The mass m1 hits the mass m2 and remains attached to it; the two masses therefore describe small oscillations of period T = 4.92 s, with angular amplitude a = 12 th. Calculate the initial angle 8 and the energy lost in the impact.
Transcribed Image Text:Answer step-wise with detailed explanations One body of mass M = 1 kg at rest on one plane horizontal friction-free, is attached to a spring of elastic constant k, which in turn is attached to a fixed wall. A mass bullet m = 20 g and speed v hits the block and gets stuck there. Knowing that the period of oscillation is T = 0.21 s, and that the spring undergoes a maximum compression XM = 15 cm calculate the initial speed of the bullet and energy dissipated in the impact. Two masses m₁ = 1 kg and m2 = 2 kg, are attached to two length ropes L. The ropes are hung at the same point to the ceiling. The mass m2 is in the equilibrium position, while the mass m₁ is moved at an angle 0 to the vertical and then left free. The mass m1 hits the mass m2 and remains attached to it; the two masses therefore describe small oscillations of period T = 4.92 s, with angular amplitude a = 12 th. Calculate the initial angle 8 and the energy lost in the impact.
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