AP Physics 1 Lesson on Hooke's Law & Elastic Potential Energy

Hooke's Law and Elastic Potential Energy

Introduction to Springs

• Springs provide conservative forces, useful in conservation of energy equations.

• Introduction to forces that vary over time.

Key Concepts

• Kinetic Energy & Gravitational Potential Energy: Previous topics learned.

• Elastic Potential Energy: Work done on a spring stores energy.

Understanding Springs

• Ideal Spring: No weight, behaves perfectly under force.

• Stretching a Spring:

  • Force applied causes spring to stretch.

  • Stretch denoted as (x), representing change in length (delta (l)).

Force and Distance Relationship

• Linear Relationship: More force results in more stretch.

  • Doubling the force doubles the stretch length.

• Can represent as:

  • (F = kx) (where (F) is the force, (k) is spring constant, (x) is displacement from equilibrium).

Hooke's Law

• Definition: Spring force (F_s = -kx)

  • Negative sign indicates a restoring force (forces are in opposite directions).

  • Examples:

    • Pull down on the spring, it pulls up.

Spring Constant (k)

• Measures stiffness of a spring.

• Calculated as (k = \frac{F}{x}) = force per unit stretch.

  • Higher (k) = stiffer spring.

• Units: Newtons per meter (N/m).

Experimenting with Springs

• Measure force and displacement to determine spring constant:

  • Graphical method: Slope of the force versus displacement graph yields (k).

  • Single data point method: Use mass hanging to find stretching distance for (k).

Important Points

• Ideal springs obey Hooke's Law until limits are reached (non-linear behavior occurs when overstretched).

  • Real-world springs may not behave perfectly and have limits to elasticity.

Example Problem

• A 50-kg person stretches a 50 cm long spring to a new length—it can be analyzed using Hooke's Law.