Spring Force Formula

What is Spring Force?

Spring force is the force exerted on a spring that is stretched or compressed from its unstretched or uncompressed position. In essence, you compress or stretch a spring which, in turn, will try to regain its original shape and develop a restoring force that opposes the applied force. It is because of this property that springs are ubiquitous in most everyday objects and mechanical systems-from mattresses to toys.

Formula 

This force, by Hooke's Law, is proportional to the displacement of the spring from its natural length. The expression for spring force is given as:

F = k(x – x0)

Where

• xo is the spring force is F

• x  is  equilibrium position displacement of the spring from its position at equilibrium 

• k is the spring constant

• The negative sign indicates that the visualized spring force is a restoring force that acts in the opposite direction.

Solved Problems

Problem 1: A spring has length 22 cm/s. If it is loaded with 2 kg, it gets stretched by 38 cm/s. Find  its spring constant.

Solution: 

(Mass) m = 2 kg

(initial length) xo = 22 cm

(displacement) x = 38 cm

Final displacement = x – xo = 38 cm – 22 cm = 16 cm = 0.16 m

The spring force is articulated as,

F = ma

F = 2 kg × 0.16 m

F = 0.32 N

The spring constant is articulated as,

Hence, the spring constant is -2 N/m.

Problem 2: With force 100 N, if a body is stretched by 2m Calculate its spring constant.

Solution:

Given,

(Displacement) x = 2m

(force) F = 100 N

The spring constant is articulated as,

 

Hence, the spring constant is -50 N

 

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