Two objects undergo a perfectly inelastic collision. Using conservation of momen

Question

Two objects undergo a perfectly inelastic collision. Using conservation of momentum, derive an expression for the velocity after collision, in terms of the masses and initial velocities (assume that, except collision forces, all other interactions are negligible). Using expression from part (a), calculate the final velocity, if the masses and initial velocities are as follows: m_1 = 3.2 kg, m_2 = 2.5 kg; v_1 = 1.1 m/s, v_2: = -0.85 m/s. Recalculate the final velocity, if v_2 = 0, i.e. the second object is motionless before collision.

Explanation / Answer

From law of ocnservation of linear momentum ,

Total linear momentum before collision = total linear momentum after collision

m1v1+m2v2 = (m1+m2) V

From this velocity after collision V = [m1v1+m2v2]/(m1+m2)

(b).m1 = 3.2 kg

    m2 = 2.5 kg

    v1 = 1.1 m/s

    v2 = -0.85 m/s

velocity after collision V = [(3.2x1.1)+(2.5x-0.85)] /(3.2+2.5)

                                  = 1.395 /(5.7)

                                 = 0.2447 m/s

(c).

velocity after collision V = [(3.2x1.1)+(2.5x0)] /(3.2+2.5)

                                  = 3.52 /(5.7)

                                 = 0.6175 m/s

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