How long is the spring when a 3.0 kg mass is suspended from it?

Question

A 10-cm-long spring is attached to the ceiling. When a 2.0 kg mass is hung from it, the spring stretches to a length of 15 cm.

Answer 1

17.5 cm

Hooke's law says that the amount of stretch is proportional to the load. If you increase the load by 50% you increase the stretch from 5 cm o 7.5 cm. So the total length is 17.5 cm.

Answer 2

When a 2 kg mass is hung, then the spring stretches by 15 cm - 10 cm = 5 cm

Therefore, force constant of the spring = force/elongation = 2 kg-wt/5 cm = 0.4 kg-wt/cm

When 3.0 kg mass is attached, then elongation = force/force constant = 3/0.4 cm = 7.5 cm

New length = 10 cm + 7.5 cm = 17.5 cm

Ans: 17.5 cm

Answer 3

Surely the length it stretches to depends on the resistance of the material that the spring is made from.