Spring Constant Formula and Sample Problems

Spring Constant Formula :

The spring constant formula F(N) in Newton and equal to minus of  the spring constant -k (Nm-1 ) in Newton meter-1 and multiply the object displacement of the spring from its equilibrium position x (Nm) in Newton meter. Hence the spring constant formula can be written as

F(N)=-k (Nm-1 )*x (Nm)

Where,

SI unit  Nm-1

F → restoring force of the spring directed toward the equilibrium in Newton

K → spring constant in Nm-1

X → displacement of the spring from its equilibrium position Nm

Sample Problems :

Example 1 :

Calculate the spring constant? In a spring with load 5Kg is stretched by 80cm.

Solution :

Given,

Mass m=5Kg

Displacement x=80cm

We know that

Force F =ma=5×0.8=4N

The spring  constant is given as

K=-F/x

=-4/0.8=-5N

Example 2 :

Calculate  the spring constant of the spring? In a  boy weighing 20 pounds stretches a spring by 80cm.

Solution :

Given,

Mass m=20Ibs=20/2.2=9.09kg

Displacement=80cm

The force F=ma=9×9.8=89.082N

The spring constant formula is given by

K=-F/x

=-89.082/0.8=-111.3525N/m

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