Five-day teaching plan, explicit demonstrations, full worked calculations, student misconceptions and human-reviewed evidence rubric.
Purpose, prerequisite skills and safety
Essential question: Why do curved paths require inward net force? Students connect Week 07 Newton's second law to uniform circular motion and determine when an idealized friction mechanism can supply the necessary radial net force. Supports quantitative representations of force and acceleration relevant to HS-PS2-1; this week alone does not fulfill the entire performance expectation.
Prerequisites: vector direction, distinction between speed and velocity, net external force on one body, m, kg, s and N units, signed values, square and square root, position on a circle, and the normal reaction for a horizontal support.
Monday · A Turn at Constant Speed
Starter (8 min): Sketch two velocity arrows along a circle separated by one-quarter turn. Ask whether equal arrow length means equal velocity.
Direct reading (15 min): Velocity is a vector. Constant speed can coexist with changing velocity direction. Derive a_c=v²/r inward, distinguish inward force from tangent velocity.
Investigation (15 min): Circle Studio: m=2 kg, v=4 m/s, r=8 m, gives a_c=2 m/s² and F=4 N. Rotate the phase: magnitudes stay constant but Cartesian components change.
Evidence and exit (12 min): Diagram at two locations plus paragraph distinguishing changing direction and changing speed. Model limits acknowledged.
Starter (8 min): Ask what inward force acts on a puck attached to a taut connector versus a car on a flat road.
Reading (15 min): Tension or contact friction can supply radial net force. A centripetal force is the net inward component, not an extra interaction to draw.
Worked answer: m=5 kg, v=3 m/s, r=3 m → F=5×9/3=15 N inward. If only a horizontal tether pulls inward, the tension magnitude is 15 N.
Investigation and exit (22 min): Students draw two force diagrams with agents, axes and net radial component, and correct the double-counting misconception.
Starter (8 min): Show a block initially at rest with a small horizontal push. Ask why static friction need not reach its maximum.
Reading and math (18 min): Under level contact N=mg. Static friction is at most μ_sN; if the push is within that bound and no other horizontal force acts, f_s equals the push magnitude and opposes it. Once the threshold is exceeded, our model switches to f_k=μ_kN opposite initial sliding direction.
Numerical answer: m=5 kg, μ_s=0.4, μ_k=0.3, N=49 N, static max=19.6 N. +12 N applied yields friction −12 N, net 0 and a=0. +25 N applied exceeds max; initial kinetic approximation −14.7 N yields net +10.3 N and a=+2.06 m/s².
Investigation and exit (19 min): Explore a matched force sweep and locate the model threshold. Explicitly avoid claiming all actual friction equals μN.
Experimental design: Require one hypothesis and a controlled pair of runs. First m=2 kg, r=8 m, v=4 m/s gives F_required=4 N. Double speed to 8 m/s, fixed radius/mass: required force becomes 16 N. Double radius to 16 m while restoring v=4 m/s: F becomes 2 N.
Constraint: Ideal flat lateral contact requirement mv²/r ≤ μ_s mg. On the specified ideal surface, μ_s=0.4, m=2 kg implies capacity=7.84 N. The baseline 4 N is within and the 16 N case exceeds the boundary. This is not a real-world road limit.
Lab evidence: Three circle trials and two friction trials, numerical source statements, model limits and one error correction. Use downloaded CSV if slider or SVG interaction is inaccessible.
Claim: Uniform circular motion requires an inward net force, even at steady speed. Its magnitude mv²/r grows with speed squared and decreases with larger radius. The source can be tension, friction or gravity, depending on system.
Sample evidence: m=2 kg, v=4 m/s, r=8 m → 4 N; v=8 m/s → 16 N. For friction, a +12 N push needs −12 N static opposition when the threshold is 19.6 N. Explain why a maximum is a limit rather than a fixed always-on force.
Public practice: Ten randomized questions from a 20-question bank, with shuffled choices and 80% correction target. Student-written CER is human-reviewed separately; these public tests do not provide secure midterms, finals or official grading.
Precisely states inward acceleration and distinguishes speed from vector velocity.
Numerical evidence · 4
At least two meaningful calculations with formulas, units and data provenance.
Interaction diagrams · 4
Correct tangent velocity and inward resultant, with actual force agents identified and no double-counting.
Reasoning · 4
Justifies v²/r and relates friction required to available static limit correctly.
Limitations & revisions · 4
Explicitly identifies idealization and corrects at least one misconception.
16/20 is the teacher-reviewed 80% target. Formal examination questions and access controls must live in a distinct supervised assessment system.
Support and enrichment
Foundation: labeled velocity and acceleration arrows, supplied formula card, preset CSV values, table instead of SVG. Teach N=mg and the meaning of 'at most' with familiar inequalities.
Core: independent calculation and three comparable simulations; two different interaction mechanisms.
Extension: derive v_limit=√(μ_sgr) algebraically for ideal flat-road contact and explain why mass cancels, while questioning weather, surface condition, banking and real load distribution.
Keep khae_high_science_evidence_v1: Monday–Friday records unchanged. The new notebooks have independent schemas and JSON portability, not cloud sync. Leave STOS files dormant and unmodified.