Exercise 5. The coefficient of restitution, denoted by e, is defined as the rati

Question

Exercise 5. The coefficient of restitution, denoted by e, is defined as the ratio of final to initial relative velocity of the two sliders before and after the collision. Mathematically, u1-142 Determine the coefficient of restitution for elastic collision using the obtained results in Exercise 3 and completely inelastic collision. Exercise 3. For an elastic collision between two sliders, m1 and m2, let u1 and u2 be the velocities before collision, v1 and v2 the velocities after collision. Determine the velocities vi after collision in terms of the masses, mi, and the velocities before collision, ui. By the conservation of momentum we have mlul + m2u2 : m1v1 + m2v2-_-(1) Velocity of approach = velocity of recess v2-v1 = ul-u2--(2) multiply (2) by m1 and adding we have (m1 + m2)v2 2mlul + m2u2-m1u2 v2 (2mlu1+m2u2 -mlu2)/ (m1+m2) multiply by m2 and subtracting we have v1 (m1m2) 2m2u2+ m2u1mlu1 v1 (2m2u2 + m2u1mlul)/ (m1+ m2)

Explanation / Answer

e = (v2-v1)/(u1-u2)

v2-v1 = ((2m1u1+m2u2-m1u2) - (2m2u2+m2u1+m1u1)]/(m1+m2) = (m1+m2(u1-u2)/(m1+m2) = u1-u2

e = (v2-v1)/(u1-u2)

So e= 1 (ans)

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