Successive Impacts

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We can analyse the impact between two particles using the Law of Conservation of Momentum and Newton’s Law of Restitution. One of the particles may then go on to collide we another particle and we can again use the same laws. When th particles all lie in the same staright line, analysis becomes especially easy.

Suppose then that three particles A, B and C with masses 1 , 2 and 3 kg all lie in the same straight line. Initially particles A and B are moving to the right with speeds 5 and 3 m/s as shown below. Particle C is initially at rest. The coefficient of restitution be each particle is

The Law of Conservation of Momentum gives (1)

Newton’s Law of Restitution gives (2)

(1) +(2) gives

(1)-2*(2) gives

Now we analyse the collision between particles B and C. Initially particle C is at rest.

The Law of Conservation of Momentum gives (3)

Newton’s Law of Restitution gives (4)

(3)+2*(4) gives

(3)-3*(4) gives

Particles A and B will collide again if

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