#F_(el) = k*x#

#F_(el)# is the force upon the spring, the "elastic" force;

#k# is the spring constant;

#x# is the deformity of the spring;

#F_w# is the force from the weight;

#g# is gravity;

#m# is mass.

Since the length of the spring is #25cm#, the deformity is #67 - 25#, or #42cm#. Using the International Sistem (or S.I.), the deformity must be measured in meters, since the constant(#k#) is measured in Newtons/meter. So # x =0.42# #meters#.

The force applied to the spring is the weight force from the weight hanging from the spring. So #F_w = F_(el)#. Now, we apply the math:

#m*g = k*x#

#15 * 10 = k * 0.42#

#k = 150/(42/100)#

#k = 150/1 * 100/42#

#k = 15000/42 = 7500/21 = 2500/7 ("Newtons")/(meters)# or

#k = 357.14# #"Newtons"/"meter"#