A box of mass m sliding with an initial speed of v_i on a rough horizontal surfa

Question

A box of mass m sliding with an initial speed of v_i on a rough horizontal surface runs into a fixed spring of elastic constant k, compressing it a distance x_i from its relaxed position while momentarily coming to rest. Which equation best represents the energy conversion during the process of the box compressing the spring? 1/2 mv_i^2 + 1/2 kx_^2 + W due to friction with surface = 0 1/2 mv_i^2 + W due to friction with surface = 1/2 mv_f^2 - 1/2 kx_1^2 1/2 mv_i^2 = 1/2 kx_1^2 W due to friction with surface = 1/2 kx_1^2 1/2 mv_i^2 + W due to friction with surface = 1/2 kx_1^2

Explanation / Answer

Initial energy of the system = KEblock,initial + PEspring, initial = KEblock = 0.5 mvi2 (since PEspring=0 initially)

Final energy = -Wdue to frictional forces + KEblock,final + PEspring,final

= -Wdue to frictional forces + 0.5 Kx12 (KE =0, since at rest)

By conservation of energy,

0.5 mvi2 + Wdue to frictional forces = 0.5 Kx12

Option-E

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