Question

derive an expression for final velocities of two bodies moving in same direction after collision​

Answer 1

Consider two bodies with masses m1 and m2

Let the masses be travelling with velocities v1 and v2

Let their initial (i.e., before collision) velocities be v1i and v2i respectively

Similarly, let their final (i.e., after collision) velocities be v1f and v2f respectively

According to the law of conservation of linear momentum,

Total momentum Pi before collision = Total momentum Pf after collision

In a two body collision, this implies,

p1i + p2i = p1f + p2f

∵ the collision is one-dimensional (along x-axis), the vectors of the equation become unidirectional

∴ substituting p = mv in the above equation becomes,

m1v1i + m2v2i = m1v1f +m2v2f

Now, in terms of parameters before collision, the equation becomes,

m1v1i +m1v1f = m2v2i + m2v2f

m1 (v1i + v1f) = m2 (v2i + v2f)

Special Case: If the one of the bodies, say the second body, is at rest before collision, then

v2i = 0

Then the equation becomes, m1 (v1i + v1f) = m2v2f

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