Question

Derive an equation for coefficient of restitution

Answer 1

Answer:

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Explanation:

Newton's famous experimental collision-formula given in text-books [1,2] relates these with the equation vr/ur = - e or (v1-v2)/(u1-u2) = - e , where e is said to be coefficient of restitution ( normally, 0 < e < 1; but for perfect-elastic-collision e = 1 and for perfect-plastic-collision e = 0).

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Answer 2

Answer:

This cant be fully derived but a part of it can be.

In an elastic collision kinetic energy is conserved, so

12m1u21+12m2u22=12m1v21+12m2v22

m1u21+m2u22=m1v21+m2v22

m1u21−m2v21=m2v22−m2u22

m1(u1+v1)(u1−v1)=m2(v2+u2)(v2−u2)(1)

Now, according to conservation of linear momentum,

m1u1+m2u2=m1v1+m2v2

m1(u1−v1)=m2(v2−u2)(2)

Dividing equation 1 by 2 we get,

u1+v1=u2+v2

u1−u2=v2−v1

v2−v1u1−u2=1

Thus, we get an equation which is the coefficient of restitution equals to 1. This proves that if collision is elastic this will be equal to 1. Moreover, of it approaches 1 both the equations will be satisfied approximately, which will contribute to the fact that kinetic energy is conserved which in turn Will increase the fact that collision happens in a elastic plane. Thus it’s a measure of elastic collision.

Explanation:

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