If the length of a #12 cm# spring increases to #20 cm# when a #10 kg# weight is hanging from it, what is the spring's constant?

1 Answer
Dec 9, 2015

Answer:

#1225 N/m#

Explanation:

A spring constant for a 'simple spring' is usually written as the #k# in:
#F= -kx#

For force of a #10 kg# weight is calculated using gravity:
#F = mg#

#F = 10*9.8 = 98 N#

The #x# in the equation above is relative to the relaxed length of the spring. If the length of the spring is #12 cm# without any mass attached, we call this position zero and we can see that the additional length with the mass attached is #8 cm# longer.

We now know #F# and #x# and we can solve for #k#. Notice that the direction of the force is opposite to the direction of gravity, so the sign has changed.

#F = -kx#

#-98 N = -k * 0.08 m#

#98/0.08 N/m = k = 1225 N/m#