Two masses A and B, each of mass M are fixed together by a massless spring. A force acts on the mass B as shown in figure. If the mass A starts moving away from mass B with acceleration a then the acceleration of mass B will be

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(4) (F-Ma)/M. Idea: the spring is the only thing touching A, so the spring force has magnitude Ma; by Newton's third law it acts on B with the same magnitude in the opposite sense, and that sense turns out to oppose F. Mass A. Its one and only horizontal force is the spring's, so F_spring=Ma. Which way does the spring pull? F drives B away from A, so the spring stretches. A stretched spring pulls its two ends towards each other: it drags A along after B, and it holds B back. The separation still grows, because B accelerates harder than A does — that is what 'moving away from B' records. Mass B. The applied force and the spring's pull act in opposite directions: F-F_spring=Ma_B a_B=(F-Ma)/M. Consistency check: the gap only opens if a_B>a, which needs F>2Ma — so the stem is quietly telling us the applied force is more than twice Ma.

Two masses A and B, each of mass M are fixed together by a massless spring. A force acts on the mass B as shown in figure. If the mass A starts moving away from mass B with acceleration a then the acceleration of mass B will be

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