Block 1, of mass m_1, moves across a frictionless surface with speed u_i. It col

Question

Block 1, of mass m_1, moves across a frictionless surface with speed u_i. It collides elastically with block 2, of mass m_2, which is at rest (v_i = 0) After the collision, block 1 moves with speed u_f, while block 2 moves with speed v_f Assume that m_1 > m_ 2, so that after the collision, the two objects move off in the direction of the first object before the collision. What is the final speed u_f of block 1? Express a u_f in terms of m_1, m_2, and u_i. u_f = _____ What is the final speed v_f of block 2? Express v n terms of m_1, m_2, and u_i. v_f = _____

Explanation / Answer

Part a) apply momentum conservation we get

m1ui = m1uf +m2vf

apply energy conservation we get 1/2m1u2i = 1/2m1u2f +1/2m2vf2

uf = ui(m1 - m2)/m1 +m2   

vf = 2m1ui/m1+m2

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