# If the length of a #21 cm# spring increases to #57 cm# when a #5 kg# weight is hanging from it, what is the spring's constant?

##### 1 Answer

Dec 26, 2015

*We should expect* *to be somewhere in the hundreds for typical springs.*

This is simply looking at the equation

#\mathbf(F = -kDeltay)#

...for when **an object is hanging off a spring**.

So, **the only force acting on the spring is the force** **due to gravity**

#F_g = -kDeltay#

#mg = -k(y_f - y_i)#

#(mg)/(y_i - y_f) = k#

#color(blue)(k) = (("5 kg")(-"9.80665" cancel"m""/s"^2))/("0.21" cancel"m" - "0.57" cancel"m")#

#= color(blue)("136.20 kg/s"^2)# or#color(blue)("N/m")#