Open by asking students to estimate the efficiency of three real-world devices they used this morning: an incandescent light bulb, an EV regenerative braking system, and a gasoline car engine. Take quick verbal guesses (write class predictions on the board). Then reveal the real numbers: incandescent ≈ 5% (95% waste heat), EV regen ≈ 60-70%, gasoline engine ≈ 20-25%. Ask: 'Where does the missing energy GO? It didn't disappear.' Elicit that energy is conserved but degraded — mostly to thermal energy. Frame the day: they will engineer a rubber-band car, measure exactly where the input energy goes, and iterate to raise efficiency within fixed constraints. Emphasize that this is real engineering — the same design cycle Tesla uses on drivetrains and SpaceX uses on rockets.

1. 10m

   Energy Conversion and Conservation

   Content

   Every device on Earth is an energy converter — it takes energy in one form and transforms it into another. A rubber-band car converts elastic potential energy (stored in the stretched band) into kinetic energy (the moving car), with unavoidable losses to thermal energy from axle friction, rolling friction, and air drag. The First Law of Thermodynamics guarantees total energy is conserved: PEₑ (input) = KE (useful output) + Q (thermal losses) + other losses. A device NEVER creates energy — it only transforms and redirects it. For a stretched rubber band calibrated as approximately linear over its working range, the stored elastic PE is PEₑ = ½kx², where k is the effective spring constant (N/m) measured with a force probe and x is the stretch distance (m). The kinetic energy of the moving car is KE = ½mv², where m is the total mass of the car (kg) and v is its speed just after the band has released fully (m/s), measured with a photogate.

   Delivery

   Emphasize that 'conversion' does NOT mean 'creation' — this is the misconception students bring from everyday language ('the generator makes electricity'). Ask: 'If I doubled the stretch, would I double the input energy?' (No — quadruple it, because of the x² term.) Walk through the energy accounting equation and connect each term to something physical students will actually feel or hear during the lab: warm axles = Q from friction, buzzing sound = acoustic loss. Pre-empt: some students will insist a 'perfect' design could reach 100% — remind them that even superconductors and near-frictionless magnetic bearings lose SOMETHING.

2. 10m

   Efficiency: Definition and Calculation

   Content

   Efficiency η is the ratio of useful output energy to total input energy, expressed as a percent: η = (useful output / input) × 100%. For today's car, η = (½mv² / ½kx²) × 100%. Efficiency is ALWAYS less than 100% for a real device — the Second Law of Thermodynamics guarantees some energy always degrades to thermal form. Work an example on the fly: suppose the rubber band has k = 40 N/m, stretched x = 0.15 m, so PEₑ = ½(40)(0.15)² = 0.45 J. The car has mass m = 0.20 kg and photogate measures v = 1.2 m/s, so KE = ½(0.20)(1.2)² = 0.144 J. Efficiency η = (0.144 / 0.45) × 100% = 32%. Where did the other 68% go? Mostly thermal energy at the axles and wheel-floor contact, plus a small amount to sound and to internal heating of the rubber band itself (rubber bands are notoriously lossy — squeeze one after stretching, it's warm). 'Higher efficiency' does NOT mean more total energy — a 32% efficient car with 0.45 J input produces less KE than a 20% efficient car with 5 J input. Efficiency is a RATIO.

   Delivery

   Work the example numbers slowly on the board, showing units cancel to give a dimensionless ratio. Ask students to predict what typical efficiencies will be for their cars — most will guess 70-90%; reality will be 15-40%. This gap is the learning moment. Head off the ratio-vs-total misconception directly: 'If team A gets 40% efficiency with a small band and team B gets 25% with a giant band, which car goes farther?' (Depends on total input — bigger band could still win.) Efficiency measures QUALITY of conversion, not QUANTITY of output.

3. 10m

   The Engineering Design Cycle: Constraints, Criteria, Iteration

   Content

   Engineering is not one-shot design — it is an iterative cycle. Every real product (a Tesla battery pack, an iPhone antenna, a wind turbine blade) went through dozens or hundreds of design cycles. The cycle: (1) define criteria and constraints, (2) design v1, (3) build v1, (4) test and measure, (5) analyze losses, (6) refine → v2, and repeat. Criteria are what you're trying to MAXIMIZE or MINIMIZE — today, maximize efficiency. Constraints are fixed LIMITS you cannot violate — today: one rubber band from the supply bin, chassis footprint no larger than 20 cm × 10 cm, only materials on the supply table, and total build time 45 minutes for v1 and 20 minutes for v2. Constraints force trade-offs: bigger wheels reduce rolling friction (good) but reduce torque delivered by the band (bad), so v1 might crawl or spin the wheels. Adding mass reduces wheel-spin at launch (good) but reduces final v for the same input energy (bad). Every design decision has an opposing consequence — the engineer's job is to find the balance that best satisfies criteria within constraints. More energy input is NOT always the answer: with a fixed band you cannot 'just add more input' — you must convert what you have more effectively.

   Delivery

   Emphasize that iteration is REQUIRED, not optional — v1 will disappoint and that is expected and correct. Data from v1 tells you WHERE the losses are, and that tells you what to change in v2. Coach: 'If your car's axle is warm after a run, that's thermal loss you can attack — try a smoother axle, or lubricate the bushing.' Pre-empt the misconception that adding more input is the fix — with the one-band constraint, students must convert more efficiently, not push more energy in. Ask each team to name their target efficiency for v2 BEFORE they iterate, so they can test whether their change actually helped.

1. 50m

   Build & Measure Rubber-Band Car v1Lab

   Students work in teams of 3-4. Distribute the handout below on paper or project it. The teacher circulates, checks force-probe calibration, and verifies photogate placement is 20-30 cm past the launch line so the band has fully released before the photogate reads. Student handout: Part 1 — Define your design (5 min) You will build a rubber-band car that converts elastic PE into KE. Constraints: - Exactly ONE rubber band, chosen from the supply bin - Chassis footprint ≤ 20 cm × 10 cm - Only materials on the supply table - Must roll — no sliding, no rockets, no external push Sketch your v1 design in the box below. Label: chassis, wheels, axles, and how the rubber band attaches and releases. Part 2 — Calibrate the rubber band (8 min) You must know the elastic PE your band stores. Assume it behaves approximately linearly over your working stretch (this is an approximation — real rubber bands are non-Hookean, but good enough for today). 1. Anchor one end of the band. Hook the force probe to the other end. 2. Stretch to x = 0.05 m and record force F. Repeat at 0.10 m and 0.15 m. 3. Compute the effective spring constant: k = F / x for each, then AVERAGE. Data table: - x = 0.05 m → F = ______ N → k = ______ N/m - x = 0.10 m → F = ______ N → k = ______ N/m - x = 0.15 m → F = ______ N → k = ______ N/m - Average k = ______ N/m Part 3 — Build v1 (20 min) Build your car. Keep a running list of every material used and its mass so you can find the total mass m. Total car mass m = ______ kg Part 4 — Test run (12 min) 1. Choose a launch stretch x (record it — use the SAME x for all runs) 2. Position car at launch line, band stretched to x 3. Photogate placed 30 cm downrange, with fence flag (width w, measured with calipers) attached to car 4. Release cleanly (no shove) 5. Photogate gives time Δt for flag to pass → v = w / Δt 6. Repeat for 3 trials Data: - Launch stretch x = ______ m - Flag width w = ______ m - Trial 1: Δt = ______ s → v = ______ m/s - Trial 2: Δt = ______ s → v = ______ m/s - Trial 3: Δt = ______ s → v = ______ m/s - Average v = ______ m/s Part 5 — Calculate efficiency (5 min) - PEₑ = ½kx² = ______ J - KE = ½mv² = ______ J - Efficiency η = (KE / PEₑ) × 100% = ______ % Where did the missing energy go? Feel the axles and wheel-floor contact points. Listen for sound. Watch for wheel spin at launch. List your TOP TWO suspected loss sources — you will attack them in v2. Suspected loss #1: ______ Suspected loss #2: ______

   Materials

   • Rubber bands (assorted, ~40-80 N/m range)
   • Cardboard, foam board, or corrugated plastic for chassis
   • Wooden skewers or metal rods for axles
   • Plastic bottle caps, CDs, or wooden wheels
   • Hot glue guns, tape, scissors
   • Digital force probe (Vernier or PASCO) OR spring scale
   • Meter stick
   • Photogate + timer (Vernier or PASCO) with fence flag on car
   • Digital balance (0.1 g resolution)
   • Smooth floor lane, 3-5 m long, marked with tape

   Example outputs

   • Team A: k = 52 N/m, x = 0.12 m → PEₑ = 0.374 J. m = 0.145 kg, v = 1.35 m/s → KE = 0.132 J. η = 35%. Suspected losses: wheels spinning at launch (visible), warm rear axle after run.
   • Team B: k = 38 N/m, x = 0.15 m → PEₑ = 0.428 J. m = 0.220 kg, v = 0.95 m/s → KE = 0.099 J. η = 23%. Suspected losses: axle rubbing against chassis (heard scraping), rubber band snagged briefly on chassis edge.
2. 25m

   Iterate to v2 and CompareLab

   Teams now REDESIGN. They may not swap rubber bands (must use the same band as v1, same stretch x) so the input PEₑ is fixed. This forces them to attack LOSSES rather than 'add more input' — reinforcing the constraint-and-trade-off lesson. Student handout: Part 6 — Predict and redesign (5 min) Based on your v1 loss analysis, choose ONE targeted change. Examples: - Replace wooden skewer axles with metal rods through plastic-straw bushings (reduce axle friction) - Add mass to the drive wheels to reduce launch wheel-spin - Change wheel diameter (trade-off: bigger wheels ↓ friction but ↓ torque) - Reroute the rubber band so it does not snag - Reduce total car mass You may not change the rubber band or the launch stretch x. Input PEₑ is fixed. Write your prediction as a testable statement: 'Our change is: ______. We predict η will increase from ______ % (v1) to ______ % (v2) because ______.' Part 7 — Build v2 and test (15 min) Make the change. Re-run 3 trials with the SAME x and SAME photogate placement. - Trial 1: v = ______ m/s - Trial 2: v = ______ m/s - Trial 3: v = ______ m/s - Average v(v2) = ______ m/s - New total mass m(v2) = ______ kg - KE(v2) = ½mv² = ______ J - η(v2) = KE(v2) / PEₑ × 100% = ______ % Part 8 — Compare (5 min) Build an iteration table: - v1: m = ______ kg, v = ______ m/s, KE = ______ J, η = ______ % - v2: m = ______ kg, v = ______ m/s, KE = ______ J, η = ______ % - Δη = ______ percentage points Did your prediction match reality? If η went UP, explain the physics of why your change reduced losses. If η went DOWN or stayed the same, explain what went wrong — was the change too small, did it introduce a new loss, or was your loss diagnosis in v1 incorrect?

   Materials

   • All v1 materials
   • Additional axle materials: metal rods, plastic straws for bushings
   • Small amount of light lubricant (graphite powder or silicone spray)
   • Same photogate/force-probe setup

   Example outputs

   • Team A replaced wooden skewers with metal rods in straw bushings. v1: η = 35%. v2: v = 1.58 m/s, KE = 0.181 J, η = 48%. Δη = +13. Explanation: metal-in-plastic sliding friction is much lower than wood-on-cardboard, so less input energy became thermal at the axle.
   • Team B lightened chassis by replacing cardboard with foam. v1: η = 23%. v2: m dropped to 0.140 kg but v only rose to 1.05 m/s → KE = 0.077 J, η = 18%. Δη = −5. Explanation: v1 loss was axle scraping, not mass — team attacked the wrong loss. New plan: fix axle alignment for v3.

1. A team's hand-crank generator receives 24 J of mechanical work per crank cycle and lights an LED that dissipates 6.0 J of light and electrical energy per cycle. Calculate the efficiency of the generator, and identify the dominant form the 'lost' energy took.

   calculationη = (useful output ÷ input) × 100% = (6.0 J ÷ 24 J) × 100% = 25%. The 'lost' 18 J was converted mostly to thermal energy — heating of the motor coil (I²R resistive heating), friction in the gears and bearings, and a small amount of sound. The energy is NOT destroyed; it is degraded to a less-useful form (low-grade heat).

2. Team A's car has efficiency 40% with input PEₑ = 0.30 J. Team B's car has efficiency 25% with input PEₑ = 0.80 J. Which car has more kinetic energy at launch? Show work and explain why 'higher efficiency' does not always mean 'more useful output.'

   calculationTeam A KE = 0.40 × 0.30 J = 0.12 J. Team B KE = 0.25 × 0.80 J = 0.20 J. Team B has more KE (0.20 J > 0.12 J) despite lower efficiency, because efficiency is a RATIO of output to input — not a total. Team B started with more input energy, so even a smaller fraction of it produced more useful output. Efficiency measures the QUALITY of the conversion; total useful output depends on BOTH efficiency AND input.

3. A student claims: 'If I use a bigger rubber band, my car will be more efficient because it has more energy to work with.' Is the student correct? Explain in 2-3 sentences using the definition of efficiency.

   short answerThe student is incorrect. Efficiency is the RATIO of useful output to input — using a bigger band increases the INPUT (PEₑ = ½kx²) but does not by itself change the RATIO. The car will go faster (more KE), but efficiency depends on the losses (friction, air drag, sound), which are properties of the car's design, not the size of the band. To increase efficiency, the student must reduce losses (smoother axles, less wheel-spin), not add more input.

4. In your v1-to-v2 iteration today, name the specific change you made, the change in efficiency you observed (Δη), and one physics reason (in terms of energy forms) why that change did or did not work.

   short answerAnswers vary by team. A strong response names a specific change (e.g., 'replaced wooden skewer with metal rod in plastic straw bushing'), gives a numerical Δη (e.g., '+13 percentage points, from 35% to 48%'), and explains in energy-form language (e.g., 'the metal-in-plastic bushing has lower kinetic friction than wood-on-cardboard, so less kinetic energy of the axle was converted to thermal energy during the run, leaving more useful KE in the car'). Weak responses give only 'we made it better' with no numbers or no energy-form reasoning.

• ☐Assorted rubber bands (spring constants roughly 40-80 N/m)
• ☐Cardboard, foam board, and corrugated plastic sheets
• ☐Wooden skewers, metal rods (2-3 mm dia.), plastic drinking straws for bushings
• ☐Plastic bottle caps, spare CDs, small wooden wheels
• ☐Hot glue guns with glue sticks
• ☐Scissors, box cutters, masking tape, ruler
• ☐Digital force probe (Vernier/PASCO) or 5 N spring scales — 1 per team
• ☐Photogate + timer — 1 per team
• ☐Digital balance (0.1 g) — 1-2 for the class
• ☐Meter sticks and calipers
• ☐Small container of graphite powder or silicone lubricant
• ☐3-5 m of smooth floor lane marked with tape
• ☐Student handouts (Parts 1-8 printed) and calculator per student