Lesson 6: Hooke's Law & Simple Harmonic Motion (Extension)
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)) — the two period equations are extension only, beyond AS91171: Explanatory Note 4 limits assessment to “force and extension of a spring”.
Graph force vs extension to determine spring constant k and calculate stored elastic potential energy; as extension work, calculate oscillation periods and analyse the 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, and what the minus sign tells you about the direction of the restoring force.
- 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 (plus the SHM period calculations as extension).
⚡ 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 this data: (0.10 m, 2.0 N), (0.20 m, 4.0 N), (0.30 m, 6.1 N), (0.40 m, 8.0 N), (0.50 m, 10.1 N). Extract the spring constant from your gradient, and calculate the elastic potential energy stored at extensions of 0.25 m and 0.40 m. 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 0.40 kg mass oscillating on a spring of spring constant 20 N m⁻¹, and the period of a pendulum of length 0.99 m. 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: The Hooke's Law and elastic potential energy work in this lesson is direct preparation for Level 2 Physics (Demonstrate understanding of mechanics). The simple harmonic motion work is not — read the scope note below before planning assessment time against it. Emphasise linking mathematical working directly to physical concept explanations for Merit/Excellence grades.
Scope honesty (AS91171 v2, Explanatory Note 4): the standard assesses force and extension of a spring (F = −kx, as printed in the NZQA relationship list). Simple harmonic motion, the period equations and pendulums are not assessed in this standard — treat the oscillation work in this lesson as extension and Level 3 preparation, not exam preparation.