Explosions - Higher tier only
An object being fired from a cannon is also a collision where momentum must be conserved. As the momentum before the collision is zero, the momentum after the collision is zero. In physics, this type of event is termed an explosion.
Consider a cannon ball of mass \({\text{m}}_{\text{B}}\) 4 kg fired at velocity \({\text{v}}_{\text{B}}\) 120 ms-1 from a cannon of mass \({\text{m}}_{\text{C}}\) 96 kg. This allows determination of the recoil The distance travelled in a fixed time period, usually one second. of the cannon \({\text{v}}_{\text{C}}\).
The total momentum before is zero, so by the law of conservation of momentum the momentum after the ball is fired is also zero.
\({\text{m}}_{\text{B}}{\text{v}}_{\text{B}}+ {\text{m}}_{\text{C}}{\text{v}}_{\text{C}}~=~{0}\)
Therefore
\((4\times 120) + (96 \times {\text{v}}_{\text{C}}) = 0\)
\({\text{v}}_{\text{C}}~=~\frac{{ - 480}}{{96}}\)
\(=~{-~5}{\text{ ms}}^{-1}\)
The negative sign means the cannon moves backwards to conserve the momentum in the explosion, this effect is known as Backwards movement produced by a force exerted on an object..