question_answer

A body of mass m moving with speed \[\upsilon \]collides elastically head-on with another body of mass m initially at rest. Show that the moving body will come to a stop as a result of this collision.               

Answer:

                By conservation of momentum, \[m\times \upsilon +m\times 0=m{{\upsilon }_{1}}+m{{\upsilon }_{2}}\] or            \[\upsilon ={{\upsilon }_{1}}+{{\upsilon }_{2}}\] or            \[\upsilon -{{\upsilon }_{1}}={{\upsilon }_{2}}\] ?(1) By conservation of kinetic energy, \[\frac{1}{2}m{{\upsilon }^{2}}+0=\frac{1}{2}m\upsilon _{1}^{2}+\frac{1}{2}m\upsilon _{2}^{2}\] or            \[{{\upsilon }^{2}}=\upsilon _{1}^{2}+\upsilon _{2}^{2}\] or            \[(\upsilon +{{\upsilon }_{1}})(\upsilon -{{\upsilon }_{1}})=\upsilon _{2}^{2}\]    ?(2) Dividing (2) by (1), we get \[\upsilon +{{\upsilon }_{1}}={{\upsilon }_{2}}\]                                ?(3) Solving (1) and (3), \[{{\upsilon }_{1}}=0\] and \[{{\upsilon }_{2}}=\upsilon \] As a result of the collision, the moving body comes to a stop and the stationary body begins to move with the speed of the first body.