## Inspired 2 years ago 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

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.

2. Vincent-Lyon.Fr

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

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.