Question

a 4.60 kg mass is placed on top of a vertical spring, which compresses a distance of 2.31 cm. calculate the force constant (in n/m) of the spring.

Answer 1

The restoring force of the spring cancels the weight of the mass, so by Newton's second law

∑ F = F[spring] - mg = 0 ⇒ F[spring] ≈ 45.1 N

where m = 4.60 kg and g = 9.80 m/s². Then the spring constant is k such that by Hooke's law,

F[spring] = k x

where x = 0.0231 m. Then the spring constant is

k = F[spring]/x ≈ 1950 N/m