Question

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?

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Answer 1

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.

Answer 2

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.

Answer 3

ah. missed that. sorry. i was thinking that it was not SHM

Answer 4

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.