for a perfectly elastic collision, +=2+2, or alternatively. 2. If object 2 is initially at rest,...
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for a perfectly elastic collision, ₁+₁=2+2, or alternatively. 2. If object 2 is initially at rest, then u₂ = 0. Then U₁ - 1₂ = ₁ However, for a partially elastic collision the relative velocity after the collision will have a smaller magnitude than the relative velocity before the collision. We can express this mathematically as U₁-2=-₁, wherer (a number less than one) is called the coefficient of restitution. For some kinds of bodies, the coefficient r is a constant, independent of ₁ and ₂. Show that in this case the final kinetic energy of the motion relative to the center of mass is less than the initial kinetic energy of this motion by a factor of r². Furthermore, derive expressions for vi and 12 in terms of us and r. (6 marks) for a perfectly elastic collision, ₁+₁=2+2, or alternatively. 2. If object 2 is initially at rest, then u₂ = 0. Then U₁ - 1₂ = ₁ However, for a partially elastic collision the relative velocity after the collision will have a smaller magnitude than the relative velocity before the collision. We can express this mathematically as U₁-2=-₁, wherer (a number less than one) is called the coefficient of restitution. For some kinds of bodies, the coefficient r is a constant, independent of ₁ and ₂. Show that in this case the final kinetic energy of the motion relative to the center of mass is less than the initial kinetic energy of this motion by a factor of r². Furthermore, derive expressions for vi and 12 in terms of us and r. (6 marks)
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