Question

A unstretched spring hangs from the ceiling with a length of 0.31 m. a 9.1-kg block is hung from the spring and the spring stretches to be 0.50 m long. how long will the spring be if a 3.3-kg block is hung from the spring? for both cases, all vibrations of the spring are allowed to settle down before any measurements are made.

Answer 1

As we know that spring force is given by

$F = kx$

here we know that for the equilibrium of the mass suspended with the spring we have

$mg = kx$

so now we have

$9.1(9.81) = k(0.50 -0.31)$

now we have

$k = 469.8 N/m$

now we have another mass

m = 3.3 kg

again from above equation we have

$3.3 (9.81) = 469.8(L - 0.31)$

$L = 0.38 m$

so final length of the spring will be 0.38 m