Hooke's Law Formula

What is Hooke's Law?

Hooke's law is a rule of elasticity developed by the English scientist Robert Hooke in 1660, which asserts that the displacement or magnitude of deformation is exactly proportional to the deforming force or load for relatively minor deformations of an object. When the load is removed under these conditions, the item returns to its original shape and dimensions. The fact that minor displacements of their component molecules, atoms, or ions from normal locations are proportional to the force that generates the displacement explains the elastic behaviour of solids according to Hooke's law equation.


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Hooke’s Law Definition

The force which deforms an item can be applied to a solid item by stretching, compressing, squeezing, twisting, or bending the solid. When a metal wire is stretched by an applied force, the small increase in its length doubles every time the force applied to the metal wire is doubled, which is a Hooke's Law example of the action.


Hooke's Law Derivation

The following equation can be used to express Hooke’s law in mathematics terms is as follows,

F = kx

F is the force we apply, and it equals a constant in this equation. K denotes a constant equal to k times the displacement or change in the length of an object denoted by x.

Where, 

F = Applied force

k = Constant for displacement

x = Length of the object

The type of elastic material, its size, and its form all impact the amount of k. When a relatively large amount of force is exerted, the elastic material deforms several times more than the quantity indicated by Hooke's Law. The material, however, stays elastic and returns to its original size when the force is removed, and it preserves its form when the force is removed. Hooke's Law equation can be as follows at times:

Restoring force of a spring = - Spring constant x displacement of a spring

F = -kx

Where, 

F = Restoring force of a spring (Newtons, N)

k = Spring constant (N/m)

x = Displacement of the spring (m)


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Hooke's Law Example 

Ex.1. A spring is stretched by 22 cm and has a force constant of 6 cm /dyne. Determine the Force applied.

Solution:

Given parameters are

Force constant k is 6 cm/dyne,

Extension x = 22 cm.

The Hooke’s law formula is given by

F = – k x

= – 6 × 22 cm

= – 132 N


Ex.2. Determine the force constant if a force of 200 N is stretching a spring by 1.8 m.

Solution:

Given parameters are

Force F = 200 N,

Extension, x = 1.8 m.

The Hooke’s law formula is given by

k = – F / x

k = – 200 / 1.8

k = – 360 N/m.


Ex.3. A tough, shock-absorbing spring has been compressed a distance of 3.00 cm by exerting a force of 1500 N on the spring. What is the value of force constant k for this spring?

Solution:

The force exerted on the spring has a magnitude of 1200 N. This means that the spring is exerting an equal (magnitude) and opposite (sign) restoring force of -1200 N. The spring is compressed at a distance of 3.00 cm. To find the value of spring constant in units of N/m, the distance must be converted to meters:

x = 3.00 cm

x = (3.00)(1/100)

x = 0.03 m

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

F = -kx → k = -Fx

k = -(-1200 N)/0.03 m

k = 1200N/0.03 m

k = 40000 N/m

The value of spring constant of the shock-absorbing spring is 40,000 N/m.

FAQs (Frequently Asked Questions)

1. Why is There a Negative in F = -KX?

Answer: By convention, the minus or negative sign is present in F= -kx.

The restoring force F is proportional to the displacement x, according to Hooke's law. When the spring is compressed, the coordinate of displacement x is negative, zero when the spring is at its normal length, and positive when the spring is extended.

2. Does The Spring Constant Depend On How Far The Spring is Stretched?

Answer: In general, assuming we're talking about a spring of a specific material and thickness, the spring constant is inversely proportional to the length of the spring.

3. What is Hooke's Law Simple?

Answer: Hooke's Law is a scientific principle that states that the force required to extend or compress a spring is proportional to the distance covered. Hooke's Laws cover the behaviour of springs as well as many other situations in which an elastic body is deformed.