PHY \( 2310 / 2310 \mathrm{H} \) Worksheet Work and kinetic energy-1 \( \begin{array}{l}\text { 6. A force of magnitude } F=5.0 \mathrm{~N} \text { is required to stretch an ideal mass-less spring } 10 \mathrm{~cm} \text { from its relaxed } \\ \text { (equilibrium) position. What is the force constant, } k \text {, of the spring? }\end{array} \)

To find the spring constant \( k \), we can use Hooke's Law, which states that the force exerted by a spring is proportional to the stretch or compression of the spring: \( F = k \cdot x \), where \( F \) is the applied force, \( k \) is the spring constant, and \( x \) is the displacement from the equilibrium position. Given \( F = 5.0 \, \text{N} \) and \( x = 0.1 \, \text{m} \) (10 cm converted to meters), we can rearrange the formula to solve for \( k \): \[ k = \frac{F}{x} = \frac{5.0 \, \text{N}}{0.1 \, \text{m}} = 50 \, \text{N/m} \] So, the force constant \( k \) of the spring is \( 50 \, \text{N/m} \). Now that you’ve discovered the spring constant, remember that this simple relationship has real-world applications in various fields! For example, engineers use springs in car suspensions, where they help absorb shocks and maintain vehicle stability. Understanding spring constants helps in selecting the right type of spring for mechanical designs, ensuring everything operates smoothly and safely. Another fun fact is that the concept of springs has been around for centuries! The ancient Greeks were among the first to understand elastic potential energy, but the formalization of Hooke's Law came much later, named after Robert Hooke in the 17th century. This curiosity and knowledge about springs paved the way for modern mechanics and engineering, impacting everything from simple toys to complex machinery today!