Property is Described by Hooke’s Law

The stress-strain curve gives a relationship between the stress and strain experienced by an object under an externally applied force. Hooke’s law can also obtain this relationship; this law was proposed by Robert Hooke and explained that under force, the stress is directly proportional to the strain experienced by the body. Hooke’s law can mathematically be derived, which helps calculate the elasticity coefficient for different materials. The following article explains Hooke’s law, and what property is described by Hooke’s law with the help of examples.

Stress and Strain

When an object experiences an external force, the object’s shape undergoes certain deformations. When such a force is applied to an object, it exerts a restraining force in response to the external force. This equal and opposite restoring force applied by the object is known as stress. The change that is experienced by the object in its shape is known as the strain.

Hooke’s law

The English physicist Robert Hooke presented Hooke’s Law in 1660. Hooke’s law is one of the fundamental principles in understanding the physics and elasticity of different materials. So, what property is described by Hooke’s law?

Hooke’s law asserts that the displacement or the change in the position of the spring from its rest position is directly proportional to the amount of force applied to the spring. When the applied force is removed, the spring returns to its original form and dimensions. In terms of stress and strain, Hooke’s law gives a relationship between the two properties.

According to Hooke’s law, when an object undergoes a condition of stress and strain under the influence of an external force, the amount of total stress experienced by the object is directly proportional to the amount of strain experienced by the same object.

stress ∝ strain

Stress = k.strain

Derivation of Hooke’s law

To understand Hooke’s law and derive a mathematical solution for it, the following expression has been given,

F = k.x

In the above equation, F is the force applied to the spring, the applied force in the given equation is constant. k is defined as a constant the value of the constant is equal to k times the displacement or change in the length of the spring; this length is denoted by x.

Where, 

F = force applied to the spring.

k = constant for displacement in spring

x = total displacement in spring

The constant of displacement or elastic displacement (k) is dependent on the material of the spring, the size, and the form of the spring. When a large force is applied to the spring, the deformation experienced by the spring is much more than anticipated by Hooke’s law. However, the spring material still keeps its elastic properties and returns to its original size when the force is removed.

The Restoring force applied by the spring is equal to the spring constant multiplied by the total deformation experienced by the spring from its normal position,

F = -k.x

Where, 

F = Restoring force of the spring,

k = Spring constant of elasticity,

x = displacement of the spring,

Solved Examples

Let us understand the concept with, what property is described by Hooke’s law? 

Example1. A spring is stretched by 25 cm and has a 10 cm /dyne force constant. Find the total force applied to the spring.

Solution:

Given parameters are,

Force constant, 

k = 10 cm/dyne,

The displacement of spring,

x = 25 cm

By Hooke’s law,

F = – k x

= – 10 × 25 cm

= – 250 N

Example 2. Determine the force constant, (k) if a force of 100 N is displacing a spring by 2 m.

Solution:

Given values are,

Force F = 100 N,

Displacement, x = 2 m.

The Hooke’s law gives,

k = – F/x

k = – 100 / 2

k = – 50 N/m.

Example 3. A shock-absorbing spring has been compressed a distance of 5 cm by applying a force of 2000 N on the given spring. Find the value of force constant k for the given shock-absorbing spring?

Solution:

The amount of force applied to the spring has a magnitude of 2000 N. 

The spring is applying an equal and opposite restoring force of -2000 N magnitude. 

The spring undergoes a displacement of 5.00 cm. 

x = 5 cm

Or,

x = (5.00)(1/100)

x = 0.05 m

The value of force constant can be found by rearranging the Hooke’s law formula,

F = -kx,

k = -F/x

k = -(-2000 N)/0.05 m

k = 2000N/0.05 m

k = 40,000 N/m

The spring constant( k) value of the shock-absorbing spring will be 40,000 N/m.

Conclusion

Hooke’s law gives an expression for the coefficient of elasticity for different materials; the law states that the stress and strain experienced by an object under the influence of an external force are in direct proportion. The relationship can be given as follows,

stress ∝ strain

The derivation for Hooke’s law gives an expression for the value of the constant of displacement for an object; in the above article, spring is considered. The solved examples explain the various practical applications of the law. Do we also look into what property is described by Hooke’s law? Questions, and what property is described by Hooke’s law? Importance. Hooke’s law doesn’t apply to all the materials, and its properties differ for different materials.