question_answer

Two ball bearings of mass m each moving in the opposite directions with equal speed \[\upsilon \] collide head on with each other. Predict the outcome of the collision, assuming it to be perfectly elastic.

Answer:

                Here \[{{m}_{1}}={{m}_{2}}=m,\]             \[{{u}_{1}}=\upsilon ,\] \[{{u}_{2}}=-\upsilon \]                 \[\therefore \]  \[{{\upsilon }_{1}}=\frac{({{m}_{1}}-{{m}_{2}}){{\upsilon }_{1}}+2{{m}_{2}}{{u}_{2}}}{{{m}_{1}}+{{m}_{2}}}\]                                 \[=\frac{(m-m)\upsilon +2m(-\upsilon )}{m+m}=-\upsilon \]                 and                 \[{{\upsilon }_{2}}=\frac{({{m}_{2}}-{{m}_{1}}){{\upsilon }_{2}}+2{{m}_{1}}{{u}_{1}}}{{{m}_{1}}+{{m}_{2}}}=\frac{(m-m)(-\upsilon )+2m\upsilon }{m+m}=\upsilon \]Hence after collision, the two ball bearings will move with same speeds but their directions of motion are reversed.