Reading Time: < 1 minute
Springs and Elastic Potential Energy: Exploring Hooke’s Law and Energy Storage
What Is Hooke’s Law?
Hooke’s Law describes the relationship between the force applied to a spring and its extension:
\[ F = kx \]
Where:
- \( F \): Force (N)
- \( k \): Spring constant (N/m)
- \( x \): Extension or compression (m)
Elastic Potential Energy (\( E_{\text{elastic}} \))
The energy stored in a spring is given by:
\[ E_{\text{elastic}} = \frac{1}{2}kx^2 \]
Factors Affecting Spring Behavior
Spring Constant (\( k \))
Determines the stiffness of the spring.
Elastic Limit
If stretched beyond its elastic limit, a spring will not return to its original shape.
Applications of Springs and Elastic Potential Energy
Engineering
Springs are used in shock absorbers and suspension systems.
Sports Equipment
Elastic energy enhances performance in archery and gymnastics.
Medical Devices
Prosthetics and medical instruments use springs for flexibility and energy storage.
Example Problem
A spring with \( k = 200 \, \text{N/m} \) is stretched by \( 0.1 \, \text{m} \). Calculate the force and elastic potential energy.
- Force (\( F \)):
\[ F = kx = 200 \times 0.1 = 20 \, \text{N} \] - Elastic Potential Energy (\( E_{\text{elastic}} \)):
\[ E_{\text{elastic}} = \frac{1}{2}kx^2 = \frac{1}{2} \times 200 \times (0.1)^2 = 1 \, \text{J} \]
Common Mistakes in Spring Calculations
- Exceeding the elastic limit and applying Hooke’s Law incorrectly
- Mixing up force and energy formulas
- Using inconsistent units for spring constant and displacement
Practice Questions
- A spring with \( k = 150 \, \text{N/m} \) is compressed by \( 0.05 \, \text{m} \). Calculate the force and elastic potential energy.
- Explain the significance of the elastic limit in engineering applications.
- Describe one application of elastic potential energy in sports.