Complete, curriculum-linked lesson plans using PHYSIX. Each includes objectives, activity instructions, discussion questions, and assessment ideas.
Learning objectives: Students will (1) verify that all objects fall at the same rate in vacuum, (2) explain why air resistance changes this, and (3) relate their observations to the kinematic equation y = ½gt².
Ask: "Which falls faster — a feather or a bowling ball?" Take a class vote. Record predictions.
Load 🪶 Feather vs Ball preset. Press Play with atmosphere ON. Observe. Then toggle atmosphere OFF using the Display toggle. Press Reset and Play again. Discuss the result.
Students pair up. Task: find the relationship between drop height and fall time. They adjust the y-position, press Play, and record the time t shown in the topbar when the ball hits the ground. Plot h vs t².
Plot h vs t² together. The slope should equal ½g ≈ 4.9 m/s². Relate to the BINAS kinematic formula.
Exit ticket: "If you drop a 10 kg ball from 20 m in vacuum, how long before it hits the ground? Show your working."
Learning objectives: Students will verify p = mv is conserved in elastic collisions and explain why Newton's Cradle behaves as it does.
Load ⚫ Newton's Cradle preset. Play at 0.5× speed. Ask: "What's being transferred? Is it energy or momentum?"
Click each ball. Read its velocity from the properties panel at the moment of collision. Calculate p = mv for each ball before and after. Is total momentum conserved?
Challenge: change one ball's restitution to 0.5 (inelastic). What happens? Why doesn't the original pattern hold? Discuss real-world cradles and energy loss.
"Why does pulling two balls release two balls at the other end, not one ball at double speed?" Guide students to discover that both p and E must be conserved simultaneously.
Learning objectives: Students will derive T² ∝ a³ empirically by measuring orbital periods of planets at different distances from a star.
Students follow the Solar System tutorial to put a planet in circular orbit. Assign each group a different orbital radius (0.5 AU, 1 AU, 2 AU, 4 AU, etc.).
Set speed to 10×. Use the simulation clock to time one complete orbit (when the trail makes a full loop). Record T in Earth years.
Collect all (a, T) pairs. Plot T² vs a³. Does the line pass through the origin? What is the slope? Compare to 4π²/GM.
Derive Kepler's Third Law from Newton's gravity: set mg = mv²/r, substitute v = 2πr/T, solve for T². Show it matches the empirical result.
Learning objectives: Students will describe the Lorentz force and explain how a magnetic field causes circular motion of charged particles.
Load 🧲 Cyclotron. Play at −2× (slow). Watch the proton spiral. Ask: "What determines the radius of the circle?"
F_Lorentz = qvB provides centripetal force. Set qvB = mv²/r. Solve: r = mv/qB. This is the cyclotron radius formula.
Read v from the proton's properties panel. Calculate predicted r. Measure actual r using the ruler tool. Do they match?
Double the proton's initial speed. What happens to the radius? Double the B field strength. What happens? Students record predictions then test them.
Learning objectives: Students will demonstrate sensitive dependence on initial conditions and distinguish deterministic chaos from randomness.
Discuss: "Can a system be both perfectly deterministic AND unpredictable?" Most students will say no. Use the double pendulum to challenge this assumption.
Each student opens PHYSIX in two tabs. Load the double pendulum in both. In one tab, change the outer bob's x position by 0.001 m. Press Play in both simultaneously. How long before they diverge?
Introduce the Lyapunov exponent λ. If two trajectories diverge as e^(λt), and they look noticeably different after ~30 s, estimate λ ≈ 0.1–0.2 s⁻¹.
"If chaos is not random, can we predict the weather?" "Why do weather forecasters give probabilities instead of certainties?" Connect to real-world applications of chaos theory.