Object (A) of mass 0.2kg strikes a second object (B), of mass 0.35kg that is ini

Question

Object (A) of mass 0.2kg strikes a second object (B), of mass 0.35kg that is initially at rest. Mass A has an initial velocity of +3 m/s. A) Assume that collision is entirely inelastic. Calculate the final state for these objects. Calculate the total energy of the system before and after the collision. Is mechanical energy conserved? If not, account for discrepancy. B) Now assume the collision is entirely elastic . Calculate and describe the final velocities for the two objects. Assume everything is 1 dimensional

Explanation / Answer

entirely inelastic --> body stick together by conservation of momentum m_A(v_a) = (m_a+m_b)v ---> 0.2*3= (0.35+0.2) v ---> v = 0.6/(0.55) = 1.09 m/s The 2 bodies will stick together and move at 1.09 m/s in the positive direction. No mechanical energy is not conserved in inelastic collison. Some of the energy is transfered to heat and sound. Totally elastic collision --> kinetic energy is conserved m_A(u_a)^2= m_A(v_a)^2 + (m_b)v_b^2 -->0.2*3^2 = 0.2 v_a^2 + 0.35 v_b^2 -----(1) momentum is still conserved -->m_A(u_a) = (m_a)v_a+(m_b)v_b -->0.2*3= 0.2v_a + 0.35v_b ----(2) solving the simultaenous equation: v_a=-0.818m/s v_b=2.181 m/s

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