Lesson 6: Hooke's Law & Simple Harmonic Motion (SHM)
Demonstrating understanding of mechanical principles, motion, forces, and energy for NCEA Level 2 Physics.
🎯 Ngā Whāinga Akoranga | Learning Intentions
Hooke's Law (F = -kx), elastic potential energy (E_ep = 0.5kx^2), period of a mass-spring system (T = 2 pi sqrt(m/k)) and pendulum (T = 2 pi sqrt(l/g)).
Graph force vs extension to determine spring constant k, calculate SHM oscillation periods, and analyse energy interchange during oscillation.
🎥 Media Anchor & Pedagogical Scaffold
Hooke's Law & Simple Harmonic Motion
Video Clip: Introduction to springs and Hooke's law — Khan Academy Physics (Runtime: 10m 05s).
🧠 1. Before Viewing (Activate & Predict)
What restores a stretched spring or swinging pendulum back to equilibrium, creating continuous periodic oscillation?
👁️ 2. During Viewing (Watch With a Job)
- State Hooke's Law: write the equation F = kx, explaining what each variable means and its unit.
- Proportionality: what does the spring constant k tell you about a spring? Would a stiffer spring have a larger or smaller k? Why?
- Elastic limit: what does the video say happens when you stretch a spring beyond its elastic limit? How does this relate to the graph shape?
🗣️ 3. After Viewing & Kaiako Move (Process & Apply)
Kaiako Move: Conduct spring extension lab to plot F vs x line of best fit and measure spring constant k.
Immediate Task: Complete Section 6 of your Mechanics Portfolio: Hooke's Law Spring Constant Lab & SHM Period Calculations.
⚡ Whakaoho | Do Now: Physics Mechanics Recall (10 mins)
A heavier child does not swing more slowly. Put a small child and an adult on the same swing and time them.
Two minutes: predict first, then look at T = 2π√(l/g). Say which quantities set the period and which — surprisingly — do not appear at all. Then predict what would change it, and check whether the same is true of a mass on a spring.
📖 Activity 1: Mechanical Investigation & Vector Problem Solving (25 mins)
Find k from a graph (15 min). Plot force against extension for the data provided. Extract the spring constant from your gradient, and calculate the elastic potential energy stored at two extensions. State the range over which Hooke's Law held, and what the graph looks like beyond it.
Two oscillators (10 min). Calculate the period of a mass-spring system and a pendulum. Then answer the Do Now properly: explain why mass appears in one period equation and not the other, in terms of what supplies the restoring force in each.
📝 Activity 2: Level 2 Physics Portfolio Task & Merit/Excellence Scaffolding (20 mins)
Portfolio — Section 6. Submit: (1) your force-extension graph with k extracted from the gradient and the elastic limit marked; (2) both period calculations; (3) a paragraph explaining why pendulum period is independent of mass but spring period is not.
🏫 Kaiako Planning & Pedagogy Notes
NCEA Level 2 Alignment: Direct preparation for Level 2 Physics (Demonstrate understanding of mechanics). Emphasise linking mathematical working directly to physical concept explanations for Merit/Excellence grades.