Two blocks of masses m and 3m are placed on a frictionless, horizontal surface.

Question

Two blocks of masses m and 3m are placed on a frictionless, horizontal surface. A light spring is attached to the more massive block, and the blocks are pushed together with the spring between them as shown in the figure below. A cord initially holding the blocks together is burned; after that happens, the block of mass 3m moves to the right with a speed of varrowbold3m = 1.65 m/s. Find the system's original elastic potential energy, taking m = 0.370 kg. Explain your answer to part (c) Is the momentum of the system conserved in the bursting-apart process? Explain how that is possible considering there are large forces acting. Explain how that is possible considering there is no motion beforehand and plenty of motion afterward?

Explanation / Answer

(a)   By the law of momentum conservation
=>m1u1 + m2u2 = 0
=>3M x 1.65 + M x u2 = 0
=>u2 = -4.95 m/s

(b)   PE = 1/2m1u1^2 + 1/2m2u2^2
=>PE = 1/2M[3u1^2 + u2^2]
=>PE = 1/2 x (0.370)[3 x (1.65)^2 + (4.95)^2]

=>PE= 0.185 x 32.67
=>PE = 6.04 J

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