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State total linear momentum is conserved in all collisions. |
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Answer» SOLUTION :(i) Linear momentum is conserved in all collision processes. When two bodies collide, the mutual implusive force acting between them during the collision time `(Delta t)` produces a change in their respective momenta. (ii) That is, the FIRST body exerts a force `VEC(F)_(12)` on the second body. From Newton's third law, the second body exerts a force `vec(F)_(21)` on the first body. This causes a change in momentum `Delta vec(p)_(1)` and `Delta vec(p)_(2)` of the first body and second body respectively. Now, the relations could be written as, `Delta vec(p)_(1)=vec(F)_(12)Delta t ""`.....(1) `Delta vec(p)_(2)=vec(F)_(21)Delta t ""`...(2) (III) Adding equation (1) and equation (2), we get `Delta vec(p)_(1)+Delta vec(p)_(2)=vec(F)_(12)Delta t + vec(F)_(21)Delta t=(vec(F)_(12)+vec(F)_(21))Delta t` According to Newton's third law `vec(F)_(12)=-vec(F)_(21)` `Delta vec(p)_(1)+Delta vec(p)_(2)=0 "" Delta (vec(p)_(1)+vec(p)_(2))=0` (iv) Dividing both sides by `Delta t` and taking linit `Delta t to 0` we get `lim_(Delta t to 0)(Delta (vec(p)_(1)+vec(p)_(2)))/(Delta t)=(d(vec(p)_(1)+vec(p)_(2)))/(dt)=0` `THEREFORE p_(1)+p_(2) =` constant. (v) The above expression implies that the total linear momentum is a conserved quantity. |
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