Consider a one dimensional elastic collision between a given incoming body A andbody B, initially at rest. How would you choose the mass of B in compariosn to the mass of A in order that B should recoil with (a) greaterst speed (b) greatest momentum ?

Consider a one dimensional elastic collision between a given incoming

1.	Consider a one dimensional elastic collision between a given incoming body A andbody B, initially at rest. How would you choose the mass of B in compariosn to the mass of A in order that B should recoil with (a) greaterst speed (b) greatest momentum ?
Answer» Solution :As in a COLLISION, monentum is always conserved `m_(A)u = m_(A)v_(A) + m_(B) v_(B)` `u=v_(A)+kv_(B)("with" k=m_(B)//m_(A))` `v_(A) = u - kv_(B) "".....(1)` Now as collision is elastic `(1)/(2)m_(A)u^(2)=(1)/(2)m_(A)v_(A)^(2)+(1)/(2)m_(B)v_(B)^(2)` `u^(2)=v_(A)^(2) + kv_(B)^(2)` Subsituting the value of `v_(A)` from Eqn. (1) in (2) `u^(2)=(u-kv_(B))^(2)+kv_(B)^(2)` Which on SOLVING GIVES `v_(B) = (2u)/(i+k) "" .......(3)` (a) So for `v_(B)` to be maximum, k must be MINIMUM, `i.e., k=(m_(B))/(m_(A))rarr0orm_(B)ltltm_(A)` (b) Now `P_(B) = m_(B)v_(B)` In PERFECT elastic collisions, when masses are equal, the total momentum of A is completely transfered to B. i.e., `m_(A) = m_(B)`.