# Spring Constant Formula

Springs have their own natural "spring constants" that define how stiff they are. The letter k is used for the spring constant, and it has the units N/m. By Newton's Third Law of Motion, as a spring is pulled, it pulls back with a restoring force. This force follows Hooke's Law, which relates the force of the spring to the spring constant, and the displacement of the spring from its original position.

*force of the spring = -(spring constant k)(displacement)*

*F = -kx*

*F* = restoring force of the spring (directed toward equilibrium)

*k* = spring constant (units N/m)

*x* = displacement of the spring from its equilibrium position

Spring Constant Formula Questions:

1) Find the spring constant of a spring if it requires a 9000 N force to pull it 30.0 cm from equilibrium.

Answer: The formula can be rearranged to solve for the spring constant, k:

In this question, a 9000 N force is pulling on a spring. That means that the spring pulls back with an equal and opposite force of -9000 N. The displacement is 30.0 cm = 0.30 m.

*k* = 30 000 N/m

The spring constant of this spring is 30 000 N/m.

2) A 3500 N force is applied to a spring that has a spring constant of k = 14 000 N/m. How far from equilibrium will the spring be displaced?

Answer: The displacement can be found by rearranging the formula:

In this question, a 3500 N force is pulling on a spring. That means that the spring pulls back with an equal and opposite force of -3500 N.

x = 0.250 m

x = 25.0 cm

The spring is displaced by 0.250 m, which is equal to 25.0 cm.

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