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
Paul N.
Dec 9, 2015

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

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