Particle 1 of mass 230 g and speed3.60 m/s undergoes a one-dimensionalcollision

Question

Particle 1 of mass 230 g and speed3.60 m/s undergoes a one-dimensionalcollision with stationary particle 2 of mass 400 g.
(a) What is the magnitude of the impulse onparticle 1 if the collision is elastic?
1 kg·m/s

(b) What is the magnitude of the impulse on particle 1 if thecollision is completely inelastic?
2 kg·m/s (a) What is the magnitude of the impulse onparticle 1 if the collision is elastic?
1 kg·m/s

(b) What is the magnitude of the impulse on particle 1 if thecollision is completely inelastic?
2 kg·m/s

Explanation / Answer

Given m = 230 g = 0.23 kg            u= 3.6 m / s          m ' =400 g = 0.4 kg          u ' =0 from law of conservation momentum , mu + m' u ' = mv +m'v'                                                      0.828 + 0 = 0.23 v + 0.4 v '    ---( 1) for elastic collision v ' - v = u - u '                             v' - v = 3.6                                    v ' = v + 3.6 ---( 2) from eq( 1 ) and ( 2 ) , 0.828 = 0.23 v + 0.4( v + 3.6 )                                             = 0.23 v + 0.4 v + 1.44                                          v = - 0.9714 m / s Magnitude of impulse = m ( u - v )                                 = 1.051 kg m / s (b). from law of conservation momentum , mu + m' u ' = ( m + m' ) v                                                               0.828+0 = 0.63 v                                                                          v = 1.314 m / s magnitude of impulse = m ( u - v )                                 =  0.52578kg m / s

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