## 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.

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.