Question

prove that bodies of identical masses exchange their velocities after head on elastic collision

Answer 1

in elastic collision,

v2 - v1 =  u1 - u2

so....... v2 = u1 - u2 + v1......(1)

from coservation of linear momentum,

m1u1 +  m2u2 = m1v1 + m2v2

but since masses are equal,

mu1 + mu2 = mv1 + mv2

substituting the value for v2 from (1)

m(u1 + u2) = m(v1 + u1 - u2 +v1)

mu1 + mu2 =  2mv1 +  mu1 - mu2

2mu2 = 2mv1

u2 = v1

substituting this value of v1 in (1) we get,

v2 = u1 - u2 + u2

v2 = u1

as u can see, the initial velocity of one body has now become the final velocity of second body after collision and

initial velocity of the second body has becum the final velocity of the first.

Answer 2

Answer:

Explanation:

in elastic collision,

v2 - v1 =  u1 - u2

so....... v2 = u1 - u2 + v1......(1)

from coservation of linear momentum,

m1u1 +  m2u2 = m1v1 + m2v2

but since masses are equal,

mu1 + mu2 = mv1 + mv2

substituting the value for v2 from (1)

m(u1 + u2) = m(v1 + u1 - u2 +v1)

mu1 + mu2 =  2mv1 +  mu1 - mu2

2mu2 = 2mv1

u2 = v1

substituting this value of v1 in (1) we get,

v2 = u1 - u2 + u2

v2 = u1

as u can see, the initial velocity of one body has now become the final velocity of second body after collision and

initial velocity of the second body has becum the final velocity of the first.