Open with the ISS clip framing: astronauts on the International Space Station appear weightless, yet the station orbits only about 400 km above Earth's surface — roughly the driving distance from LA to San Francisco. Ask students to predict on a half-sheet: 'At the ISS altitude, gravity is about (a) zero, (b) 10% of surface gravity, (c) 50%, (d) 90%.' Take a hand vote. Reveal that gravity there is roughly 89% of surface gravity — astronauts float because they and the station are in continuous free-fall around Earth, not because gravity has vanished. Then pivot: 'Today we'll derive exactly how much gravity weakens with distance — and we'll find that electric forces between charges follow the same mathematical rule.' Collect the half-sheets to gauge the misconception baseline.

1. 9m

   Newton's Law of Universal Gravitation

   Content

   Newton's law of universal gravitation states that every point mass attracts every other point mass with a force F = Gm₁m₂/r², where m₁ and m₂ are the two masses in kilograms, r is the center-to-center distance in meters, and G = 6.67 × 10⁻¹¹ N·m²/kg² is the gravitational constant. The force is always attractive and acts along the line joining the two masses — equal in magnitude on each object (Newton's third law), opposite in direction. Worked example: find the gravitational force between two 70 kg students standing 0.50 m apart. F = (6.67 × 10⁻¹¹)(70)(70)/(0.50)² = (6.67 × 10⁻¹¹)(4900)/0.25 = 1.3 × 10⁻⁶ N. That's about a millionth of a newton — smaller than the weight of a grain of sand. The same formula applied to a 70 kg student and Earth (mass 5.97 × 10²⁴ kg, r = 6.37 × 10⁶ m) gives ≈ 686 N — the student's weight.

   Delivery

   Emphasize that G is tiny, so gravitational attraction between everyday objects is real but imperceptible — this heads off the misconception that gravity only acts near Earth. Ask students, 'Why don't you feel your neighbor pulling you?' and let them see the answer fall out of the number. Point at the slide's diagram of two masses with equal-and-opposite arrows and reinforce that the arrows are the same length on both objects regardless of which mass is bigger — a common stumbling block. Check for understanding by having students shout out the units on each factor to confirm F comes out in newtons.

2. 9m

   Coulomb's Law

   Content

   Coulomb's law gives the electric force between two point charges: F = kq₁q₂/r², where q₁ and q₂ are the charges in coulombs, r is the separation in meters, and k = 8.99 × 10⁹ N·m²/C². The force acts along the line joining the charges; like charges (both + or both −) repel, and unlike charges (+ and −) attract. Worked example: two small spheres carrying +2.0 × 10⁻⁶ C and −3.0 × 10⁻⁶ C are separated by 0.10 m. F = (8.99 × 10⁹)(2.0 × 10⁻⁶)(3.0 × 10⁻⁶)/(0.10)² = (8.99 × 10⁹)(6.0 × 10⁻¹²)/0.01 = 5.4 N, attractive. Notice: with charges a million times smaller than 1 C, at 10 cm, we already get several newtons — far larger than the gravitational force between the same objects. Sign convention: plug in magnitudes for the force size, then determine direction (attract or repel) from the signs of the charges.

   Delivery

   Draw the parallel structure explicitly — same mathematical shape as gravity, different constant, different 'source' quantity. Show the side-by-side charge diagram on the slide and have students call out 'attract' or 'repel' for each pair before you narrate. Pre-empt the misconception that gravity and electricity are 'the same force' — same math, different physics. Ask: 'A coulomb is a huge amount of charge — why?' Let them puzzle at how enormous k is compared to G (about 10²⁰ times larger) and connect that to why the electric force dominates at atomic scales.

3. 10m

   Inverse-Square Scaling — What 1/r² Really Means

   Content

   The 1/r² factor means force falls off much faster than most students expect. If r doubles (×2), force drops to (1/2)² = 1/4 of the original. If r triples, force drops to 1/9. If r is halved, force grows to 4×. This is the single biggest inverse-square misconception to defeat: doubling distance does NOT halve the force. Geometrically, the reason is that a source's influence spreads over a sphere whose surface area grows as 4πr² — so any 'flux' per unit area falls as 1/r². Worked example: two charges exert 36 N on each other at 1.0 m separation. What is the force at 3.0 m? Distance scaled by 3, force scaled by 1/9, so F = 36/9 = 4.0 N. At 0.5 m? Distance halved, force ×4, so F = 144 N. Now scale a different variable: if we double q₁ and triple q₂ but keep r fixed, force scales by 2 × 3 = 6, so 36 N → 216 N. Combining: double both charges AND double the distance → force scales by (2)(2)/(2)² = 4/4 = 1, unchanged.

   Delivery

   Do proportional reasoning without plugging into a calculator — this is where honors students should be fluent. Cold-call: 'Distance ×4, force factor?' (1/16). 'Distance ÷2, force factor?' (×4). Reference the slide's 1/r² decay curve to reinforce that the curve is steep near the source and flattens far away but never touches zero — this is why gravity from distant stars still exists, just very weak. Explicitly name the wrong idea: 'Some of you will want to say doubling distance halves the force. That's linear thinking, and it's wrong here — the square makes distance dominate.'

4. 8m

   Compare & Contrast: Gravity vs. Coulomb

   Content

   Gravity and the electric force share the same mathematical form — both are inverse-square, both act along the line joining the two objects, both obey Newton's third law (equal and opposite pair). But the physics differs. Gravity's 'source' is mass (always positive), so gravity is always attractive; there is no negative mass and no gravitational repulsion. The electric force's source is charge (positive or negative), so it can attract OR repel. The constants differ enormously: k/G ≈ 1.35 × 10²⁰. For a proton and electron in a hydrogen atom, the electric attraction is about 10³⁹ times stronger than the gravitational attraction between them — which is why chemistry and materials are governed by electric forces, while gravity dominates at astronomical scales where huge masses accumulate but net charges cancel. Address 'no gravity in orbit': on the ISS, g ≈ 8.7 m/s² (about 89% of surface). Astronauts float because they are in continuous free-fall around Earth, and gravity is providing the centripetal force keeping them in that orbit.

   Delivery

   Build a two-column mental table with students calling out each row: source, sign, always/sometimes/never, strength, range. Push back hard on 'no gravity in space' — walk through the ISS numbers on the slide. Ask: 'If gravity were really zero at the ISS, what path would it follow?' (Straight line into space.) The fact that it orbits IS the evidence gravity is still acting. Close by naming today's target: students should be able to compute either force, and predict how each scales.

1. 35m

   Inverse-Square Light Intensity LabLab

   Students work in groups of 3 to measure light intensity vs. distance from a point source as a physical analog of inverse-square field behavior. Light spreads from a point over a sphere just like a gravitational or electric field, so intensity should follow I = P/(4πr²) — an inverse-square law they can measure directly. Setup: dim the room, clamp the light sensor at a fixed height pointing at the bulb, and position the bulb on the same axis. Zero-out background light by taking a reading with the bulb off and subtracting it from every measurement. Take intensity readings at r = 0.10, 0.15, 0.20, 0.30, 0.40, 0.60, 0.80, and 1.00 m from the bulb. Hand this to each group as their student handout: Inverse-Square Light Lab — Student Handout Purpose: Test whether light intensity from a point source follows an inverse-square law, and connect this to gravity and Coulomb's law. Part 1 — Data table. Record background reading (bulb off): ______ lux. Then with bulb on: - r = 0.10 m: I = ______ lux, corrected I = ______ - r = 0.15 m: I = ______ lux, corrected I = ______ - r = 0.20 m: I = ______ lux, corrected I = ______ - r = 0.30 m: I = ______ lux, corrected I = ______ - r = 0.40 m: I = ______ lux, corrected I = ______ - r = 0.60 m: I = ______ lux, corrected I = ______ - r = 0.80 m: I = ______ lux, corrected I = ______ - r = 1.00 m: I = ______ lux, corrected I = ______ Part 2 — Two graphs. 1. Plot corrected I vs. r. Sketch the curve. 2. Plot corrected I vs. 1/r². This should be linear. Part 3 — Analysis questions. 1. What is the shape of the I vs. r curve? Does it approach zero? 2. Is I vs. 1/r² linear? Find the slope and its units. 3. When you doubled r from 0.20 m to 0.40 m, by what factor did I change? Was it close to 1/4? Show numerically. 4. When you tripled r from 0.20 m to 0.60 m, by what factor did I change? Was it close to 1/9? 5. If your I vs. 1/r² graph isn't perfectly linear, list two physical reasons. (Hint: is your bulb truly a point? Is there room light?) Part 4 — Connect to fields. Answer in complete sentences: - Explain in one paragraph how this light experiment is a model for gravitational and electric forces. What plays the role of mass/charge? What plays the role of r? - Predict: if a certain gravitational force at 2.0 m is 8.0 N, what is the force at 6.0 m? Show your reasoning. Circulate and check that groups are subtracting background, measuring center-of-bulb to sensor face, and avoiding stray reflections. Watch for the frequent mistake of measuring bulb-to-table-edge rather than bulb-to-sensor. As groups finish plotting, ask a probe question: 'Your slope has units of lux·m². What physical quantity of your bulb does that slope estimate?' (Power output per 4π steradian.)

   Materials

   • light sensor / lux meter (Vernier, PASCO, or smartphone lux app)
   • small bright bulb or LED flashlight (point-like source)
   • meter stick or tape measure
   • ring stand or clamp to hold sensor at fixed height
   • graph paper or laptop with spreadsheet
   • dark room or shaded lab bench

   Example outputs

   • Sample data: I(0.20 m) = 480 lux, I(0.40 m) = 122 lux. Ratio 480/122 ≈ 3.9, close to the predicted factor of 4 for doubling r. I vs. 1/r² plot yields a straight line with slope ≈ 19 lux·m² and small positive y-intercept from residual room light.
   • Part 4 prediction: force at 2.0 m is 8.0 N; at 6.0 m, distance triples so force scales by 1/9, giving F = 8.0/9 ≈ 0.89 N. Student paragraph identifies bulb power as analog of mass·mass or charge·charge product, and r as the same r.

   No-equipment fallback

   Provide pre-collected data in the same table format and have students do Parts 2-4 on paper.

2. 25m

   PhET Gravity Force Lab & Coulomb Problem Set

   Students work in pairs. First 10 minutes on the PhET simulation to build intuition; final 15 minutes on quantitative problems. Part A — PhET Gravity Force Lab (10 min). Direct students to this exact URL: https://phet.colorado.edu/sims/html/gravity-force-lab/latest/gravity-force-lab_en.html. They complete this student handout: Gravity Force Lab — Student Handout 1. Set m₁ = 200 kg, m₂ = 500 kg, r = 5.0 m. Record F = ______ N. 2. Double m₁ to 400 kg (keep m₂, r). Record F = ______ N. Factor change = ______ 3. Return m₁ to 200 kg. Double r to 10.0 m. Record F = ______ N. Factor change = ______ 4. Set r to 2.5 m (half of original). Record F = ______ N. Factor change = ______ 5. State the rule you observed for how F depends on each mass and on r. Part B — Coulomb Problem Set (15 min). Solve on paper. Show work with units. 1. Two point charges of +4.0 × 10⁻⁶ C and +6.0 × 10⁻⁶ C are separated by 0.20 m in air. Calculate the electric force between them. Is it attractive or repulsive? 2. A hydrogen atom has an electron (q = −1.6 × 10⁻¹⁹ C) orbiting a proton at r = 5.3 × 10⁻¹¹ m. Calculate the electric force. Then calculate the gravitational force between the proton (m = 1.67 × 10⁻²⁷ kg) and electron (m = 9.11 × 10⁻³¹ kg) at the same separation. What is the ratio of electric to gravitational force? 3. The gravitational force between two asteroids is 240 N when they are 100 m apart. What is the force when: - they are 200 m apart? ______ N - they are 50 m apart? ______ N - they are 300 m apart? ______ N - one asteroid's mass is tripled and the distance stays 100 m? ______ N 4. Trick question — think before computing. Sphere A has charge +3.0 μC and sphere B has +9.0 μC, separated by 0.30 m. They are identical conducting spheres. If you touch them together and then separate them back to 0.30 m, what is the new force between them? (Hint: when identical conductors touch, they share charge equally.) 5. Compare Newton's law of gravitation and Coulomb's law in a short paragraph. Address: (a) the mathematical form, (b) what plays the role of the 'source', (c) attractive vs. repulsive behavior, (d) which force dominates at the atomic scale and why. Circulate to check that students in problem 2 report the electric/gravitational ratio near 2 × 10³⁹, and that in problem 4 they compute new charge on each sphere = (3.0 + 9.0)/2 = 6.0 μC each.

   Materials

   • laptop or Chromebook per pair
   • printed problem set (below)
   • calculator

   Example outputs

   • Problem 1: F = (8.99 × 10⁹)(4.0 × 10⁻⁶)(6.0 × 10⁻⁶)/(0.20)² = 0.216/0.04 = 5.4 N, repulsive (both +).
   • Problem 3: at 200 m force = 240 × (1/4) = 60 N; at 50 m force = 240 × 4 = 960 N; at 300 m force = 240 × (1/9) ≈ 26.7 N; triple one mass at same r → 720 N.
   • Problem 4: new charge on each sphere = 6.0 μC; F = (8.99 × 10⁹)(6.0 × 10⁻⁶)² / (0.30)² = (8.99 × 10⁹)(3.6 × 10⁻¹¹)/0.09 = 3.6 N repulsive.

   No-equipment fallback

   Skip Part A; provide the PhET data in a printed table and run Part B as-is.

1. Two 0.50 kg lead spheres are placed 0.10 m apart (center to center). Calculate the gravitational force between them. Give your answer in newtons with the correct number of significant figures.

   calculationF = Gm₁m₂/r² = (6.67 × 10⁻¹¹)(0.50)(0.50)/(0.10)² = (6.67 × 10⁻¹¹)(0.25)/0.01 = 1.7 × 10⁻⁹ N, attractive.

2. The electric force between two charged spheres is 100 N when they are 2.0 m apart. What is the force when they are moved to 8.0 m apart?

   multiple choice6.25 N. Distance scaled by 4, so force scales by 1/16. F = 100/16 = 6.25 N. (A common wrong answer of 25 N corresponds to the misconception that force scales as 1/r rather than 1/r².)

3. An astronaut on the ISS (400 km altitude) says, 'There's no gravity up here — that's why I'm floating.' Explain in 2-3 sentences why this statement is wrong and what is actually happening.

   short answerGravity at ISS altitude is about 89% of Earth's surface gravity (g ≈ 8.7 m/s²), not zero. The astronaut floats because they and the station are in continuous free-fall around Earth — gravity is providing the centripetal force keeping them in orbit. If gravity were truly zero, the station would fly off in a straight line into space.

4. List two similarities and two differences between Newton's law of universal gravitation and Coulomb's law.

   short answerSimilarities (any two): both are inverse-square laws (F ∝ 1/r²); both act along the line joining the two objects; both produce equal-and-opposite (Newton's third law) force pairs; both are proportional to the product of the source quantities. Differences (any two): gravity's source is mass (always positive), Coulomb's is charge (can be + or −); gravity is always attractive, Coulomb's can be attractive OR repulsive; the constants differ by ~10²⁰ so the electric force is vastly stronger for comparable source magnitudes; gravity dominates at astronomical scales where charges cancel, while the electric force dominates at atomic scales.

5. Two point charges exert a force of 12 N on each other. If q₁ is doubled, q₂ is tripled, and the distance is doubled, what is the new force?

   calculationNew force scales by (2)(3)/(2)² = 6/4 = 1.5. F = 12 × 1.5 = 18 N.

• ☐Light sensor / lux meter (one per group of 3) — or smartphone lux app
• ☐Small bright bulb or LED flashlight approximating a point source
• ☐Meter sticks / tape measures
• ☐Ring stands and clamps
• ☐Extension cord and power strip for bulbs
• ☐Laptops or Chromebooks (one per pair) with internet access to phet.colorado.edu
• ☐Printed Inverse-Square Light Lab handout (one per student)
• ☐Printed PhET Gravity Force Lab handout and Coulomb Problem Set (one per student)
• ☐Printed formative assessment (one per student)
• ☐Scientific calculators
• ☐Graph paper (if not using spreadsheet)
• ☐Half-sheets for hook prediction