Daily lesson planning, accurate momentum and impulse calculations, force–time graph interpretation, safe investigations and a 20-point portfolio rubric.
Essential question, prerequisites and standard links
Why does interaction time matter during a collision? Students compare signed momentum changes, impulses, interaction times, average net force and peak values for explicitly specified force profiles. This week addresses quantitative modeling related to HS-PS2-2 and engineering reasoning connected to HS-PS2-3, but it does not alone demonstrate full mastery of those performance expectations.
Prerequisites: Weeks 06–08 vectors, net force, acceleration, positive/negative velocities and Newton's laws; Week 10 energy helps students distinguish work from impulse. Students may use the signed-unit worksheet and datasets rather than SVG.
Monday — Momentum and direction
Phenomenon (8 minutes): A model 2 kg cart travels at +3 m/s then −3 m/s. Is the momentum unchanged because speed is identical?
Reading (15 minutes): p=mv. Direction is specified by a signed axis. Units kg·m/s. Compare with K=½mv².
Worked answer (10 minutes): p_i=+6; p_f=−6 kg·m/s; Δp=−12 N·s. In both states K=9 J. Motion direction matters for momentum.
Investigation (12 minutes): signed value table and a sketch of one selected body with a labeled coordinate arrow. Exit: explain the difference between momentum and kinetic energy.
Starter: Identify the net force and duration required for a specified momentum change.
Equations: J_net=Δp=m(v_f−v_i)=F_meanΔt. For a 1.5 kg cart, +4 to 0 m/s gives −6 N·s. Over 0.20 s F_mean=−30 N; over 0.60 s F_mean=−10 N.
Misconception: N·s is the unit of impulse, N is force. Their numbers may coincide in special choices of time but the quantities are not interchangeable.
Exit: Write a complete sign-and-unit calculation for a matched pair of durations.
8-minute launch: Two mathematical pulses share area J=−12 N·s over 0.40 s. One is rectangular, the other a symmetric triangle.
Answer: Mean F=−30 N. Rectangular force is −30 N throughout; triangle peak −60 N, with area ½×0.40×(−60)=−12 N·s. Both change the body's momentum equally, but the triangle's peak magnitude is double.
Probe: If no pulse shape is known, impulse and duration determine mean but not maximum. A measured real collision may have a very different force curve.
Research question: How can longer interaction duration affect average force without changing total impulse?
Worked: m=2 kg, v_i=+3, v_f=−1 → J=−8 N·s. In 0.2 s, F_mean=−40 N; in 0.8 s, F_mean=−10 N. Separately, at 0.8 s the rectangular profile peak=−10 N but a triangular profile peak=−20 N.
Student work: Three Momentum Lab and three Pulse Studio trials; one controlled duration pair, one profile pair, formulas, signs and two limitations. Both journals can be exported as JSON, or the synthetic CSV can be used offline.
Claim: Under fixed Δp, increasing interaction duration lowers the magnitude of mean net force, with J=F_meanΔt. Peak force depends on the modeled time profile, not only the area.
Evidence: −8 N·s/0.2 s=−40 N and −8 N·s/0.8 s=−10 N; the 0.8-second triangle would peak at −20 N for the same −8 N·s.
Assessment: Friday draws ten randomized open-book questions from a published 20-question practice bank. Corrections target 80%. Official midterm/final exams and transcript signing remain separately supervised.
Correctly specifies a body, signed coordinate system, net impulse and interaction time.
Numerical evidence · 4
At least two accurate, clearly signed calculations with N, N·s and kg·m/s units.
Graph interpretation · 4
Uses signed area for impulse and distinguishes average force from peak for specified profiles.
Reasoning and controlled variables · 4
Explains impulse equality and duration comparison with sound physical reasoning.
Limitations, provenance and revisions · 4
Explicitly identifies synthetic data, missing safety evidence and corrects a misconception.
The teacher-reviewed target is 16/20. The separate open-book digital quiz is not an official assessment or credential.
Support and extension
Foundation: provide a number line, sign convention, formula card, rectangle area practice and datasets. Core: compute opposite-signed final velocities and triangular areas. Extension: compare two force profiles with equal area and write what sensors would be required to validate their real peak forces; Week 15 will extend this reasoning to an isolated two-body momentum conservation system.
Retain original khae_high_science_evidence_v1: Monday–Friday keys and all dormant STOS files. New supplemental browser-local work uses independent Week 14 namespaces and supports portable JSON export/import.