(4) Two blocks, A and B, are initially held together by a string as shown in the
ID: 1780561 • Letter: #
Question
(4) Two blocks, A and B, are initially held together by a string as shown in the figure; the mass of block A is of 2 kg and the mass of block B is 4 kg. The massless spring in between the two blocks has a spring constant of k-655 N/m and is initially compressed by 45 cm. The two blocks are initially moving together with a speed of 1 m/s. When the string is cut (i.e., when the blocks are released), the spring expands and pushes the two blocks apart. What is the speed (in m/s) of the block A? You may assume that the surface is horizontal and frictionless. HINT: As shown in the figure, va and v must be in opposite directions (i.e., have opposite sign).Explanation / Answer
applying momentum conservation,
(4 + 2) (1) = 4 vB - 2vA
3 + vA = 2 vB
Applying energy conservation,
PEi + KEi = PEf + KEF
665(0.45^2)/2 + (6 x 1^2 / 2) = 0 + 4 vB^2 / 2 + 2 vA^2 /2
138.6375 = (3 + vA)^2 + 2 vA^2
3 vA^2 + 6 vA - 129.64 = 0
vA = 5.65 m/s
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