Question

A spring hangs at rest from a support. If you suspend a 0.46 kg mass from the spring it elongates 0.79m.

Answer 1

a. The restoring force in the spring has magnitude

F[spring] = k (0.79 m)

which counters the weight of the mass,

F[weight] = (0.46 kg) g = 4.508 N

so that by Newton's second law,

F[spring] - F[weight] = 0   ⇒   k = (4.508 N) / (0.79 m) ≈ 5.7 N/m

b. Using the same equation as before, we now have

F[weight] = (0.75 kg) g = 7.35 N

so that

(5.7 N/m) x - 7.35 N = 0   ⇒   x = (7.35 N) / (5.7 N/m) ≈ 1.3 m