Vasiliy Znamenskiy

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A point mass m₁ initially moving at speed v₀ collides with an originally stationary point mass m₂: m₂= αm₂, where α < 1. The collision is completely elastic. After the collision, the mass m₁ moves at speeds v₁ and the mass m₂ moves at speed v₂. Assume that the collision is one dimensional and that the mass m₁ cannot pass through the mass m₂. Find the speed ratio r₂ = v₂/v₀.

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As shown in the figure, a solid uniform sphere with mass m with initial horizontal velocity v and angular velocity ω comes into contact with the ground. Friction is not negligible, so both the velocity and angular velocity of the solid sphere changes. What is the critical velocity v₀ such that the solid sphere will stop and remain stopped?

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Two blocks are suspended by two massless springs to the ceiling as shown in the figure. The masses of the lower and upper block are m₁ and m₂ respectively. If the upper spring is suddenly cut just above the top block what are the accelerations of the lower and upper block at the moment when the top block begins to fall?

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Two blocks are suspended by two massless springs to the ceiling as shown in the figure. The masses of the lower and upper block are m₁ and m₂ respectively. If the upper spring is suddenly cut just above the top block what are the accelerations of the lower and upper block at the moment when the top block begins to fall?

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