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ELASTIC AND INELASTIC COLLISION ELASTIC COLLISION 	www.citycollegiate.com An elastic collision is that in which the momentum of the system as well as kinetic energy of the system   before and after collision is conserved. INELASTIC COLLISION An inelastic collision is that in which the momentum of the system before and after collision is conserved   but the kinetic energy before and after collision is not conserved. ELASTIC COLLISION IN ONE DIMENSION	www.citycollegiate.com Consider two non-rotating spheres of mass m1 and m2 moving initially along the line joining their centers   with velocities u1 and u2 in the same direction. Let u1 is greater than u2. They collide with one another   and after having an elastic collision start moving with velocities v1 and v2 in the same directions on the    same line. Momentum of the system before collision = m1u1 + m2u2 Momentum of the system after collision = m1v1 + m2v2 According to the law of conservation of momentum: m1u1 + m2u2 = m1v1 + m2v2 m1v1 – m1u1 = m2u2 – m2v2 m1(v1 – u1) = m2(u2 – v2) ---(1) Similarly                                             www.citycollegiate.com K.E of the system before collision = ½ m1u12 + ½ m2u22 K.E of the system after collision = ½ m1v12 + ½ m2v22 Since the collision is elastic, so the K.E of the system before and after collision is conserved. For latest information, free computer courses and high impact notes visit : www.citycollegiate.com Thus ½ m1v12 + ½ m2v22 = ½ m1u12 + ½ m2u22 ½ (m1v12 + m2v22) = ½ (m1u12 + ½ m2u22 m1v12-m1u12=m2u22-m2v22 m1(v12-u12) = m2(u22-v22) m1(v1+u1) (v1-u1) = m2(u2+v2) (u2-v2) --- (2)		  Dividing equation (2) by equation (1) 		V1+U1 = U2+V2 		   From the above equation		V1=U2 +V2 -U1_________(a) V2=V1+U1 -U2_________(b)		   Putting the value of V2 in equation (1)		m1 (v1-u1) =m2 (u2-v2) m1 (v1-u1) =m2{u2-(v1+u1-u2)} m1(v1-u1)=m2{u2-v1-u1+u2} m1(v1-u1)=m2{2u2-v1-u1} m1v1-m1u1=2m2u2-m2v1-m2u1 m1v1+m2v1=m1u1-m2u1+2m2u2 v1(m1+m2)=(m1-m2)u1-2m2u2		   In order to obtain V2 putting the value of V1 from equation (a) in equation (i) 		m1 (v1-u1) = m2(u2-v2) 		m1(u2+v2-u1-u1)=m2(u2-v2) m1(u2+v2-2u1)=m2(u2-v2) m1u2+m1v2-2m1u1=m2u2-m2v2 m1v2+m2v2=2m1u1+m2u2-m1u2 v2(m1+m2)=2m1u1+(m2-m1)u2 		For latest information, free computer courses and high impact notes visit : www.citycollegiate.com	ELASTIC AND INELASTIC COLLISION