What is Hooke’s law? Illustrate its applications. Also, define and calculate the spring constant.

Hooke’s Law states that the force required to stretch or compress a spring is directly proportional to the displacement (change in length) of the spring from its equilibrium position. Mathematically, it is expressed as:

F=k⋅x

Where:

• F is the force applied to the spring (in newtons, N),
• $k$ is the spring constant (in newtons per meter, N/m),
• $x$ is the displacement from the equilibrium position (in meters, m).

Illustration of Hooke’s Law Applications:

1. Stretching a Spring:

   • When a force is applied to a spring, it stretches by a certain amount. Hooke’s Law helps predict how much the spring will stretch for a given force.
   • Example: A spring with a spring constant k=100 N/m is stretched by 0.2 meters. The force required to stretch it is: F=k⋅x=100 N/m×0.2 m=20 N

2. Compression of a Spring:

   • When a compressive force is applied to a spring, it compresses. Hooke’s Law also applies to compression, predicting the force required to compress the spring by a certain distance.

3. Mechanical Systems:

   • Springs in mechanical systems, such as in suspension systems of cars, are designed based on Hooke’s Law to provide stability and damping.

Spring Constant:

The spring constant k is a measure of a spring’s stiffness. A higher value of $k$ means the spring is stiffer and requires more force to stretch or compress it by a given amount.

To calculate the spring constant k, rearrange Hooke’s Law:

k=F/x​

Where:

• $F$ is the applied force,
• $x$ is the displacement.

Example Calculation of Spring Constant:

If a spring is stretched by 0.5 meters using a force of 50 N, the spring constant $k$ is:

$$=100\text{N/m}$$

Thus, the spring constant $k$ is 100 N/m.