The air-track carts in the figure are sliding to the right at1.0 m/s. The spring

Question

The air-track carts in the figure are sliding to the right at1.0 m/s. The spring between them has a spring constant of130 N/m and is compressed 4.2 cm. The carts slide past aflame that burns through the string holding them together. What isthe speed of the 100 g cart? The air-track carts in the figure are sliding to the right at1.0 m/s. The spring between them has a spring constant of130 N/m and is compressed 4.2 cm. The carts slide past aflame that burns through the string holding them together. What isthe speed of the 100 g cart?

Explanation / Answer

m = 0.100 kg, M = 0.300 kg, u = 1.0 m/s, k = 130 N/m, x = 4.2 cm,find speed v of m. initial momentum of the system = (m + M)u final momentum of the system = mv + MV (m + M)u = mv + MV, so MV = (m + M)u - mv = 0.4 - 0.1v energy conservation: (m + M)u2/2 + kx2/2 = mv2/2 +MV2/2 kx2 = mv2 + MV2 - (m +M)u2 130*0.0422 = 0.1v2 + (MV)2/M - 0.4= 0.1v2 + (0.4 - 0.1v)2/0.3 - 0.4 0.068796 = 0.03v2 + 0.16 - 0.08v + 0.01v2 -0.12 0.04v2 - 0.08v - 0.0288 = 0 v2 - 2v - 0.72 = 0 (v - 1)2 = 1.72 v = 1 ± 1.72 = -0.31 m/s, 2.31 m/s answer: 0.31 m/s

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