A spring is 28 cm long. It has a force constant of 100 N/m. If we exert 25 N to it, what is the length of the spring then?

Answer 1

Spring force = spring constant x extension (or compression) Assuming the spring acts linearly over the extent of the length change.

A 28 cm spring = 0.28 m long (simple conversion)

If we know length and spring force, we can rearrange the formula to solve for length change.

F = k x L change OR L change = F / k = 25N / 100 N/m = 0.25 m = 25 cm.

Final spring length = original length + L change = 28 cm + 25 cm = 53 cm

Answer 2

This is actually a Physics problem.

The equilibrium, unstrained length of a spring is yo = 0.28 m. The spring constant of the spring is 100 N/m. We now exert a force of F = 25 N on the spring. According to Hooke's law, if a force F is exerted on a spring of spring constant k, it will stretch or compress, whichever if appropriate, a displacement y according to F = ky.

So, y = F/k = 25N / 100 N/m = 0.25 m = 25 cm. Given that the original spring is only 28 cm long and that the displacement will be 25 cm, I assume that the spring is being stretched, otherwise it will be extremely compressed. So, the new spring length will be 28 cm + 25 cm = 53 cm.