Lecture on Springs and Hooke's Law

Introduction to Springs

• A spring is a mechanical device that can be compressed or extended by applying a force.
• Springs are often encountered in everyday objects like sofas and beds.
• Natural state: The position where the spring is neither compressed nor extended.

Force and Displacement

• When a force is applied to a spring, it compresses or stretches.
• Example: A 5 Newton force compresses a spring to a certain length. If increased to 10 Newtons, the spring compresses more.
• Key Question: How much will a spring compress or extend when different forces are applied?

Relationship Between Force and Displacement

• The relationship is linear within reasonable limits, meaning the force applied is directly proportional to the displacement.
• Works both ways: can compress or elongate the spring.

Hooke's Law

• Formula: Restoring force (F) = -k * x
  • k: Spring constant, a property of the spring material.
  • x: Displacement from the natural state.
• The negative sign indicates the restoring force acts in the opposite direction of displacement.*

Calculating the Spring Constant (K)

• Example: A displacement of 10 meters with a force of 5 Newtons.
  • Restorative force = 5 Newtons
  • Using Hooke’s Law: 5 = 10k
  • Solving: k = 1/2

Applying Hooke's Law

• If a force is applied in the opposite direction, displacement will also be in the opposite direction.
• Example: Applying 10 Newtons leftward results in a 20-meter displacement.

Additional Problem Example

• If a spring is stretched 1 meter by a 2 Newton force:
  • Restorative force = -k * 1 meter
  • Solving for k gives k = -2.
• To find the force for a 2-meter displacement: 2 * 2 = 4 Newtons needed.

Conclusion

• Hooke's Law helps in understanding the force needed to compress or elongate a spring and how the restoring force works.
• Important in physics and engineering applications.
• Negative sign in Hooke’s Law indicates the spring’s tendency to revert to its natural state.