The block of mass m is attached to a frame by spring of force constant k, entire system moves horizontally without any frictions anywhere. The frame and block are at rest with x = x0, the relaxed length of spring. If frame is given a constant acceleration a0. Determine the maximum velocity of block relative to frame (in m/s). (Given: a0 = 2 m/s2, m = 4 kg, k = 4 N/m)
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answer is 2.
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Detailed Solution
Maximum velocity will be at elongation x=ma0k, mean position.Now, from work energy theorem,ma0ma0k−12kma0k2=12mv2−0m2a02k−m2a022k=+12mv2 and m2a022k=12mv2v=a0mk⇒v=244=2 ms−1