A10-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.? a) what is the spring constant k? b) how long is the spring when a 3.0 kg mass is suspended from it?

A) 392 N/m

The spring constant can be found by applying Hooke's Law:

F = kx

where

F is the force applied to the spring

k is the spring constant

x is the stretching of the spring

Here we have:

F is the weight of the block hanging from the spring, which is

The stretching of the spring is

Therefore its spring constant is

B) 17.5 cm

Now that we know the value of the spring constant, we can calculate the new stretching of the spring when a mass of m=3.0 kg is applied to it. In this case, the force applied on the spring is

Therefore the stretching of the spring is

And since the natural length of the spring is 10 cm, the new length will be

L = 10 cm + 7.5 cm = 17.5 cm