The blocks shown are released from rest with spring unstretched. Pulley & horizontal surface are frictionless. If k=400 N/m and M=4.5 kg, what is maximum extension of spring? http://s3.amazonaws.com/answer-board-image/20071222120396333222723984175004973.jpg

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The blocks shown are released from rest with spring unstretched. Pulley & horizontal surface are frictionless. If k=400 N/m and M=4.5 kg, what is maximum extension of spring? http://s3.amazonaws.com/answer-board-image/20071222120396333222723984175004973.jpg

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where are you stuck? during max extension, they are not moving. for M, \(\Sigma F_y= T-F_g=0\) \(T=F_g=4.5*9.8\) for 2M, \(\Sigma F_x= T-F_s=0\) \(F_s=T=4.5*9.8\) \(kx=4.5*9.8\) sub k and solve for x.
Hi! Careful: this assumption is not correct: "during max extension, they are not moving. for M, \(\Sigma F_y= T-F_g=0\)" Velocity is zero, but they are accelerating, so \(\Sigma F_y\) is not zero. Best way to solve this problem is to use conservation of mechanical energy.
ah. missed that. sorry. i was thinking that it was not SHM

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by the conservation of ME, since there is no potential energy, or kinetic energy, and setting that height of M as 0 at the very beginning, and that at the max extension, the velocities are zero, i.e. still no kinetic energy, \(0=\frac{1}{2} kx^2 + MgX\) sub it all in and this should do it.

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