question_answer

When a sphere of mass 5 kg strikes a wall with a velocity of 5 m/s, it rebounds with the same velocity: (a) What is the momentum of the sphere before striking and after rebounding? (b) Also find the change in momentum of the sphere?

Answer:

Given, Mass of the sphere, m = 5 kg Velocity of the ball before striking = 5 m/s (a) Momentum of the sphere striking the wall= mass of the sphere × velocity of the sphere before striking. \[=5\times 5=25\,\,kg-m/s\] ..............(1) Momentum of the sphere after rebouncing = mass of the sphere × velocity of the sphere after rebouncing \[=5\times (-5)=-25\,\,kg\,\,m/s\] ............(2) (Negative sign indicates the motion of ball in opp. direction) (b) Change in momentum of the sphere = Final Momentum - Initial Momentum = (Momentum of the sphere after rebounding) - (Momentum of the sphere before striking the wall) - (3) Substituting the values from eq. (1) and eq. (2), in (3) we get \[\Rightarrow \] Change in momentum of the ball = (-25) - (25) \[=-50\,kg-m/s\]