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 (nu_i = 0). (Figure 1) After the collision, block 1 moves with speed u_f, while block 2 moves with speed nu_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. This collision is elastic. What quantities, if any are conserved in this collision? kinetic energy only momentum only kinetic energy and momentum What is the final speed u_f of block 1? Express u_f in terms of m_1, m_2, and u_i. What is the final speed nu_f of block 2? Express nu_f in terms of m_1, m_2, and u_i.

Explanation / Answer

We know m1v1i+m2v2 i = m1v1 f + m2v2f

a) Kinetic energy and momentum both are conserved

b)

m1v1i+m2v2 i = m1v1 f + m2v2f

m1ui+m2v i = m1u f + m2vf

u f = ((m1-m2)/(m1+m2)) x (ui)

c)

m1ui+m2v i = m1u f + m2vf

vf = ((2m1)/(m1+m2)) x (ui)

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