If the length of a #32 cm# spring increases to #53 cm# when a #15 kg# weight is hanging from it, what is the spring's constant?
The calculation is based on Hooke's Law and is only applicable for simple springs where the deflection or compression is not excessive. In equation form it is expressed as F= ky.
Where F is the applied force in units of Newtons. K is the spring constant and y the deflection or compression in metres. As there is a mass attached to the spring there is a deflection of 0.21 m. The vertical force can be calculated using Newtons second Law as F = ma. Where m is the objects mass in kilograms and a the gravitational acceleration (9.8 m/s^2)
To confirm whether Hooke's law is valid, you could plot a graph of the applied force F against the deflection y for several weights. If the graph is linear you can safely assume Hookes law is valid. The slope of the graph will be the spring constant K.