The spring constant (k) is the physical measure of the spring stiffness. It gives the magnitude of force to be applied in stretching and compressing the spring through a unit length. A high spring constant, therefore, corresponds to a stiffer spring.

Formula

The spring constant is obtained from Hooke's Law. This states that:

Variables in the Formula

F = Force applied in the spring (in Newtons)
k = Spring constant (in Newtons per meter, N/m)
x = Displacement from the equilibrium position in meters

This can be expressed as an increase in force with the displacement of the spring from its rest position.

Spring Constant Dimensional Formula

We know that,

F=-kx

Therefore,

Dimension of F=[MLT-2]

Dimension of x= [L]

Hence, the dimension of k,

The Spring Constant Formula is given as,

where,

F = Force applied,
x = displacement by the spring

The negative sign shows that the restoring force is opposite to the displacement

It is expressed in Newton per meter (N/m)

Solved Examples

Example 1: A spring with a load of 5 Kg is stretched by 40 cm. Determine its spring constant.

Solution:

Given,

Mass m = 5 Kg

Displacement x = 40 cm

We know that,

Force F = m a = 5 × 0.4 = 2 N

The spring constant is given as:

= – 2 / 0.4= – 5 N/m

Example 2: A boy weighing 20 pounds stretches a spring by 50 cm. Determine the spring constant of the spring.

Solution:

Given,

Mass m = 20 lbs = 20 / 2.2 = 9.09 Kg

Displacement x = 50 cm

Force F = ma = 9.09 × 9.8 = 89.082 N

Formula of spring constant is as below:

= – 89.082 / 0.5

= – 178.164 N/m.

Conclusion

The understanding of a spring constant and its relation to force and displacement is significant in physics and engineering. Students will have to grasp the concepts and formulas underlying this principle, which might be applied to various scientific and practical contexts.

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Spring Constant Formula

Definition

Formula

The spring constant is obtained from Hooke's Law. This states that:

Variables in the Formula

F = Force applied in the spring (in Newtons)
k = Spring constant (in Newtons per meter, N/m)
x = Displacement from the equilibrium position in meters

This can be expressed as an increase in force with the displacement of the spring from its rest position.

Spring Constant Dimensional Formula

We know that,

F=-kx

Therefore,

Dimension of F=[MLT-2]

Dimension of x= [L]

Hence, the dimension of k,

The Spring Constant Formula is given as,

where,

F = Force applied,
x = displacement by the spring

The negative sign shows that the restoring force is opposite to the displacement

It is expressed in Newton per meter (N/m)

Solved Examples

Example 1: A spring with a load of 5 Kg is stretched by 40 cm. Determine its spring constant.

Solution:

Given,

Mass m = 5 Kg

Displacement x = 40 cm

We know that,

Force F = m a = 5 × 0.4 = 2 N

The spring constant is given as:

= – 2 / 0.4= – 5 N/m

Example 2: A boy weighing 20 pounds stretches a spring by 50 cm. Determine the spring constant of the spring.

Solution:

Given,

Mass m = 20 lbs = 20 / 2.2 = 9.09 Kg

Displacement x = 50 cm

Force F = ma = 9.09 × 9.8 = 89.082 N

Formula of spring constant is as below:

= – 89.082 / 0.5

= – 178.164 N/m.

Conclusion

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List of Physics Formulas

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Frequently Asked Questions

Ptolemy’s Theorem

Formula: Ptolemy’s Theorem relates the sides and diagonals of a cyclic quadrilateral. For a cyclic quadrilateral ABCD with diagonals AC and BD, the theorem states:

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