Learn 68 original destinations cover all eight content units and two full-course synthesis investigations, with cumulative mixed assessment and a retained evidence portfolio. Authored coverage does not certify learner mastery, actual hands-on laboratory time or AP authorization.
This is the course outline. Open a unit to choose a lesson; every lesson opens on its own page. Explanations and experiments live inside those lesson pages.
Preparation: Algebra, right-triangle geometry, signed graph slopes and geometric areas. No calculus is required; use the supplied data or bounded CPU investigations before attempting supervised practical work.
Course outcome: Across mechanics and fluids, connect motion representations with system-specific force models, derive constraints, infer parameters and test assumptions using explicit evidence boundaries.
All lessons are directly accessible. Reused foundation explanations are identified where relevant; completing a different course does not award this course's evidence. The 68 registered lessons keep separate predictions, captures, practice responses and reflections.
Explain, predict and test motion using vectors, graphs, algebra and supplied-data investigations.
Keep observer velocity at 1 m/s and compare origins −2 and +2 m. Record initial and final positions and their difference. Next hold origin fixed and compare observer velocities 0 and 2 m/s. Explain why the first intervention translates the curve while the second changes its slope.
Compare (3,4), (−3,4) and (0,4). Sketch each route and direct displacement. Find when the route distance equals the displacement magnitude and explain the equality geometrically. Test the zero-vector case rather than assigning it a physical angle.
Hold acceleration at 1 m/s². Compare half-windows 1, 0.5 and 0.25 s; record the velocity estimate and worst-case bound. Explain why the exact midpoint velocity stays fixed while the measured estimate changes. Repeat with negative acceleration and retain the same error signs.
Compare (v₀,a)=(3,−1), (4,−1), and (−3,1). Calculate each area before checking the table. Locate any interior reversal and explain the boundary case where velocity reaches zero exactly at 4 s. Record both displacement and distance.
Choose total velocity change 8 m/s and elapsed time 4 s. Derive all three displacements from geometric areas before using the output. Then halve elapsed time while keeping the velocity change fixed. Distinguish the change in average acceleration from the change in displacement.
Hold upward velocity at 8 m/s and compare horizontal components 2,4 and 8 m/s. Then hold the horizontal component fixed and vary the vertical component. Use ratios to test the range, flight-time and height equations. State the condition needed for the return-time formula.
Fix ground horizontal velocity at 5 m/s and compare observer velocities −3,3 and 5 m/s. Then choose a ground horizontal velocity below the observer velocity to make relative motion negative. Check that apex height, return time and vertical landing velocity remain unchanged.
Compare sampling intervals 1,0.5 and 0.25 s at the same position bound. Record the number of selected observations, acceleration estimate, bound and held-out residual. Then change the error bound. Explain why passing a held-out check is conditional and why correlated calibration error is not eliminated by more points.
Choose a system, construct interaction diagrams, derive motion constraints and test force models with original evidence cases.
Compare equal masses, a heavier left mass and a heavier right mass. Calculate the weighted offsets for each case. Find two different mass pairs with the same center and explain the shared mass ratio. State which body-to-body forces become internal when both objects enter the system.
Compare pull angles 0°,30° and 60° at 20 N. Draw the three actual interaction arrows before using the ledger, then resolve components in equations. Check the vertical sum and the horizontal sum separately. Predict what would break if an unbounded pull lifted the cart off the track.
Compare equal masses and a 3:1 mass ratio. List each interaction force and the acceleration of its recipient. Multiply accelerations by their masses and verify cancellation for the whole system. Explain why this is not cancellation within either individual diagram.
Begin with equal forces and verify constant nonzero velocity. Increase only the leftward force, then only the rightward force. Predict whether the object initially speeds up or slows down and whether it reverses within 2 s. Explain the motion using signs rather than “positive force means forward motion.”
Hold mass fixed while varying offset; compare slopes using two well-separated data points. Then hold offset fixed and change mass. Explain which graph feature changes in each intervention. Write a calibration test that could distinguish a sensor offset from an actual constant opposing force.
Compare center distances 1,2 and 3 reference radii at fixed central mass. Then double central mass at fixed radius. Test the ratios without recalculating G. Record field and weight separately. Explain why the altitude column is always one less than the center-distance ratio.
At normal force 40 N, compare pushes 8,20 and 22 N. State the regime before calculating friction. Then hold the push at 22 N and increase normal force to 60 N. Explain why increasing the maximum allowed friction need not mean the actual friction reaches that maximum.
Compare positive, zero and negative extension at fixed k. Then compare two spring constants at the same extension. Fit a slope from two table values and distinguish the spring’s force from an external holding force. Explain why a line through total length would need a nonzero intercept.
Find a feasible and an infeasible setting pair. Predict the tension ratio after changing only speed, then only radius. Derive the maximum permitted speed symbolically and compare with the ledger. Explain why an outward force arrow would be inappropriate in the inertial-frame free-body diagram.
Compare(2,3) kg with(3,2) kg and retain both free-body diagrams. Then add mass only to the trailing cart and predict changes in acceleration and tension separately. Verify both individual equations and the combined equation numerically. State what independent observation could falsify the shared-acceleration assumption.
Build signed work and system-energy ledgers, test accessible states and compare energy transfer rates with explicit constraints.
Compare observer velocities−2,0,2 and 4 m/s at fixed mass. Predict the energy from relative velocity before checking. Then double the mass without changing either velocity. Explain the separate linear and quadratic dependencies.
Hold the force at 12 N and compare angles 0°,60°,90°,120° and 180°. Predict signed work, then final kinetic energy and speed. Explain why a backward component reduces energy even while the object still moves forward.
Compare endpoint pairs(8,−4),(4,−4) and(−8,−4) N. Sketch the line and signed areas first. Use both geometric splitting and the trapezoid expression. Check that the final kinetic energy equals 50 J plus the calculated work.
At initial radius ratio 1, compare outward increments 0.1,0.5 and 1 body radius. Compute exact and local-constant-field energy changes and their discrepancy. Repeat from initial radius ratio 3 and explain why the same absolute increment is a smaller relative change there.
Compare compressions 0.10,0.20 and 0.40 m at fixed spring constant. Record force, stored energy and release speed. Then double stiffness while holding compression fixed. Explain why speed scales with the square root of stiffness rather than stiffness itself.
Compare total energies 2,4 and 8 J. Locate turning points from the intersection condition before reading them. At E=2 J, test x=0 to produce a forbidden position; explain why the model withholds speed. Use graph slopes to identify force directions on both sides of the minimum.
Compare μ=0.2 and 0.5 for a requested 3 m, then request 5 m at μ=0.5. Reconstruct Kfinal+ΔEthermal and check it equals 36 J. Distinguish requested from actual travel, and explain why kinetic friction is not applied through a reversal after stopping.
Compare the same height over 1,2 and 4 s. Reconstruct useful and input energies separately from powers, then locate a schedule that fails the 250 W screen. Explain why satisfying this screen alone is not a validated real lifting design.
Construct impulse and vector-momentum ledgers, distinguish elastic and inelastic interactions, and assess conservation evidence with bounded measurement error.
Find two control pairs giving zero total momentum and compare their kinetic energies. Then choose equal velocities and verify the center has that same velocity. Explain why adding speeds instead of signed momenta would lose the system description.
Compare(8 N,0.5 s) with(4 N,1 s), then reverse the pulse sign. Calculate area, average force and final momentum before checking. Distinguish a zero final velocity from a zero force throughout the event. Sketch a momentum-time line rising from−2 to+2 kg m/s over2 s, then staying flat: the first segment has average net force+2 N and the flat segment zero, even though momentum remains+2 kg m/s.
Hold internal impulse at 3 N s and compare external impulses−2,0 and+2 N s. Verify the sum of individual momentum changes. Then hold external impulse fixed and change internal impulse; identify which system quantity stays the same.
Compare equal masses with(2,3) and(3,2) kg. Reconstruct total momentum and kinetic energy from the individual final velocities. Check the 5 m/s relative separation and explain why individual energies can differ from their initial values.
Find mass choices giving a small or zero final velocity. Reconstruct initial and final momenta and energies separately. Compare the same masses with the elastic model; identify which conserved quantity is common to both and which distinguishes them.
Compare inputs(3,4),(6,4) and(6,2) m/s. Sketch the component addition and predict direction changes before using output. Verify each component equation and distinguish a change in resultant direction from a change in total momentum magnitude.
Compare the three supplied packets at the smallest and largest error bounds. Compute momentum and energy differences before reading the classifications. Identify one resolved kinetic decrease and one unresolved change. Explain why a compatible zero does not establish exact conservation from measurements.
Connect angular representations, extended force diagrams and axis-specific inertia to equilibrium, rotational acceleration and coupled-motion inference.
Compare α=−1 and α=0 over 4 s. Sketch angular velocity before checking the plot, mark the reversal if present, and calculate signed and absolute areas. Then choose α=−2 over 5 s and explain why final orientation alone is insufficient.
Hold radius at 0.4 m and compare ω=2 with ω=4 rad/s. Draw the two perpendicular acceleration components at the rightmost point and compare their magnitudes. Then halve radius while retaining the angular quantities; distinguish an angular comparison from a linear one.
Compare 0°, 30°, 90° and 150° at r=0.4 m. Sketch the force at the application point, extend its line of action and mark the perpendicular lever arm. Verify one calculation using Fℓ and another using rF sinφ.
Find three pairs that give zero net torque. Then hold the right force fixed and change only the left force. Draw all four forces, including weight and pivot reaction, and explain how net force stays zero while angular acceleration changes.
Compare (a,b)=(0.2,0.2) with (0.4,0.4), then with (0.4,0.2). Make a five-row mass-coordinate table and calculate every contribution before checking. Explain why only the first comparison gives an exact factor of four.
For mass 3 kg, compare offsets 0, 0.5, 1 and 2 m. Plot inertia against d² on paper using the ledger, identify the intercept and slope, and distinguish scaling the shift term from scaling the full sum.
With W=80 N compare x=1, 2 and 3 m. Draw all forces at their true locations. Compute both reactions and check net torque about both supports. Then change the load while keeping its location fixed and separate the beam-weight contribution from the added-load contribution.
Compare net torques 0 and +4 N m with inertia 2 kg m². Sketch angular velocity first, identify the moment of reversal, and compare signed graph area. Next double inertia at the same torque and predict how the reversal time changes.
Use at least three hanging masses while holding inertia fixed. Predict acceleration and tension, verify both Newton-law equations, and recover inertia from each synthetic acceleration. Then explain how a fixed opposing axle torque would alter the equation to a=(mg−τf/R)/(m+I/R²), and why treating it as zero could create mass-dependent inferred inertias.
Distinguish rotational energy and angular-momentum transfer, test rolling constraints and explain circular, elliptical and escape energy conditions.
Compare (vCM,ω)=(3,4) with (1,4), then with (3,0). Keep separate subtotals, predict a factor change before moving a control, and explain why no rolling relation is imposed on this free-body snapshot.
Compare start/end torques (4,−2), (2,−2) and (−4,−4). Compute each signed area and energy change. Sketch the cumulative work, identify where it reaches an extreme, and check that kinetic energy never reaches zero before the endpoint.
Compare offsets +1, 0 and −1 m at speed 3 m/s. Draw the actual horizontal paths separately from the angular-momentum plot. Explain the unchanged linear momentum, changing reference-dependent angular momentum and zero torque in each case.
Compare pulses (4 N m,1 s) and (2 N m,2 s), then reverse their signs. Reconstruct final angular momentum before checking. Sketch a separate L-time line rising from −2 to +2 over 2 s and then flat: its first average torque is +2 N m and its later torque is zero.
Compare inertia changes 4→2, 2→4 and 3→3. Calculate both angular speeds and kinetic energies. Then solve the separate two-rotor joining case from the explanation and identify why its internal energy change has the opposite sign from contraction.
Compare all three supplied shape factors at h=0.6 m. Verify energy subtotals and derive the friction requirement for each. For a separate assigned surface μs=0.15, decide which no-slip predictions are feasible rather than applying every displayed speed unconditionally.
Hold clockwise spin at 10 rad/s and compare center speeds 1, 2 and 3 m/s. Draw the center and rim contributions at contact, identify overspin/no-slip/underspin and predict the qualitative changes to translation and spin. Do not infer a transition time from this instantaneous snapshot.
At r=20 m compare speed ratios 0.75, 1 and 1.5 relative to circular speed. Identify the circular case and the sign of specific total energy. Then compare circular orbits at 10 and 40 m and derive speed, energy and angular-momentum ratios before checking the ledger.
Derive linear restoring models, coordinate phase and energy, infer periods with bounded evidence and separate capture from later oscillation.
Compare x=0.1 and 0.2 m first with b=0, then b=100. Calculate F/x away from zero. Save contrasting captures and distinguish linearity from restoring direction; predict the force at negative displacement before checking.
Choose two masses at one stiffness; predict the period ratio before capture. Then change stiffness to keep m/k fixed. Record T, f and ω separately, including their units. Explain which amplitude claim follows from the model rather than a measured spring.
Compare lengths 0.5 and 2 m at one amplitude, then compare 5° and 30° at fixed length. Explain why the displayed approximate period stays unchanged in the second comparison even though the approximation diagnostic worsens.
Capture phase fractions 0, 0.25, 0.5 and 0.75 for A=0.2 m. Predict signs before reading the ledger. Sketch separate labeled x–t, v–t and a–t graphs, and explain the slope relationships rather than copying a single curve into all three.
Compare position fractions 0, 0.5 and 1 for one amplitude; reconstruct the total from each pair of energy entries. Then double amplitude while keeping the same position fraction and predict the energy and speed factors before capture.
At assigned timing error +0.1 s, compare N=1,5 and10. Save inferred periods and stiffness bounds. Check whether the true20 N/m is compatible, and explain which uncertainty sources the recipe deliberately excludes.
Compare center and endpoint capture for the same added mass. Write momentum and energy ledgers for the brief event, then a separate energy ledger for the later oscillation. Change added mass and predict whether amplitude and period both change in each case.
Connect microscopic fluid properties to density, pressure forces, buoyancy and ideal-flow conservation; test feasibility and infer parameters from bounded observations.
Compare tare 0 and0.10 kg at density1000, then density500 and1500 at fixed tare. Retain two sample points and the zero-volume point; derive the slope and intercept rather than reading one ratio. Explain why the dashed sample-only curve differs from the observed curve.
Compare the supplied force and area separately, then double both within the available settings. Write one-face pressure and explain what additional opposite-face pressure is needed for net force. Sketch normal-force directions on two differently oriented walls at equal pressure.
Compare oil thickness0.1 and0.5 m at water depth0.5 m. Then vary only water depth. Reconstruct both increments and the slope on each part of the graph. Explain why the graph uses absolute pressure and why its zero-depth value is not zero.
Compare area ratios2,4 and6 at input force60 N. Predict output displacement and work before capture. Then alter force at fixed ratio. Keep pressure, force and work in separate rows with their different units.
Hold mass3 kg and compare top depths0.1 and0.5 m, then compare masses1 and5 kg at fixed depth. Distinguish opposing pressure forces, their resultant, signed holding force and the ideal released acceleration. Explain which cases require downward rather than overhead restraint.
Compare payload4 and8 kg at fluid density1000. Record the required versus available displacement before accepting any draft. Then compare densities800 and1200 at fixed payload. Explain the special full-immersion equality case and the stability questions not answered.
At inlet speed1, compare branch fractions0.25,0.5 and0.75. Reconstruct eachQ from its own area and speed, then sum. Change inlet speed while fixing the split and predict all flow ratios before capture. State why the fraction requires independent information.
Compare outlet heights0 and5 m at inlet speed1, then compare inlet speeds0.5 and2 at fixed height. Reconstruct both three-term totals and use continuity before energy. Explain what a real pump or frictional loss would add to the boundary.
Vary head at fixed outlet height, then vary outlet height at fixed head. Reconstruct speed and flight time separately before calculating range. Use the assigned range error to bound inferred head; identify a loss mechanism that would bias inference even if repeated ranges were precise.
Select laws by system and interval, test physical feasibility, integrate representations and distinguish independent evidence from agreement caused by shared assumptions.
Compare the passing case (x=0.30,μ=0.10), a stopped case (0.10,0.20), and threshold (0.10,0.125). Retain a stage diagram and separate energy/momentum ledgers. Change launch compression and predict the feasibility boundary before capture. Explain why no downstream speed is displayed for a failed path.
Compare c=1 and1.05 with lagzero, then introduce lag0.05 at fixedc. Save both method estimates and the multiheight fall packet. Propose a genuinely independent calibration and predict how its evidence would differ under clock-scale versus fall-lag explanations. Specify how length error could confound the comparison.
Keep predictions before comparison, complete raw records and units, explain competing models and test a changed case. Supplied and simulated data are labeled in each lesson. A saved notebook is not proof of experimental technique or correct reasoning.
Evidence to retain: Keep separate diagrams for each recipient, compare whole-system and single-object statements, and predict which quantities change when mass or force components change.
Boundary: Ideal point-object models; horizontal component diagrams omit balanced vertical interactions only where explicitly stated.
Evidence to retain: Infer mass from a slope with a nonzero sensor offset; test friction regime, spring calibration and circular-force feasibility; use a mass-swap intervention to distinguish shared acceleration from internal tension.
Boundary: Supplied synthetic data and bounded models, not instrument calibration evidence or a validated real connector design.
Evidence to retain: Retain paired settings and reconstruct force-position areas, frame-dependent kinetic energies, exact versus local gravitational changes and spring-energy scaling.
Boundary: Original bounded models, not measured energy transfers; each approximation and zero choice is explicit.
Evidence to retain: Identify inaccessible positions, premature stopping and infeasible power schedules; explain a changed-case prediction before revealing results.
Boundary: A rejected state is not reported as an achieved trajectory; real thermal, material and practical constraints are not validated.
Evidence to retain: Compare equal-area force pulses, cancel internal impulses only at the combined-system level, and test signed total momentum against center-of-mass motion.
Boundary: Prescribed virtual interactions; no collision device or energetic-material procedure is required.
Evidence to retain: Reconstruct before/after momentum and kinetic energy, set up planar component equations, and distinguish a resolved difference from compatibility with zero under explicit bounds.
Boundary: Synthetic packets and exact masses do not establish actual collision measurements, calibration or secure independent assessment.
Evidence to retain: Retain actual force locations, compare two pivots, reconstruct five-particle inertia, and test a reaction-force prediction under a changed load position.
Boundary: Original virtual geometries; no structural rating, load-bearing construction or physical suspended-weight activity.
Evidence to retain: Predict before controls; keep raw synthetic accelerations for several masses, derive both Newton-law equations and the no-slip constraint, propagate an assigned interval, and challenge friction/radius assumptions.
Boundary: Supplied/model-generated observations do not establish instrument calibration, independently measured inertia, laboratory time or supervised practical proficiency.
Evidence to retain: Contrast torque-angle and torque-time areas, preserve the same axis, compare initial/final energy and angular momentum under redistribution or joining, and evaluate a bounded residual.
Boundary: Virtual pulses and endpoint states only; no high-speed rotor, clutch, human spinning or stored-energy apparatus.
Evidence to retain: Check the static-friction requirement before accepting a rolling prediction; diagnose slipping qualitatively; reconstruct circular and elliptical conservation ledgers and an escape threshold.
Boundary: No quantitative slipping-time requirement, rolling-resistance model, physical incline experiment or launch activity. Synthetic outputs are not independent measurements.
Evidence to retain: Compare force-to-displacement ratios, spring mass/stiffness scaling and pendulum approximation diagnostics; predict phase signs and retain contrasting settings.
Boundary: Virtual idealized systems only; no spring loading, overhead suspension or physical pendulum construction. A restoring-force discrepancy is not an exact pendulum period correction.
Evidence to retain: Carry total-time bounds into period and stiffness; evaluate a T² fit and residuals; compare center and endpoint capture with separate momentum and energy ledgers.
Boundary: Assigned timing errors and idealized attachment, not observed measurements or a secure independent assessment. No physical capture apparatus.
Evidence to retain: Infer density and tare from a mass-volume graph; distinguish force components and pressure references; predict layered pressure and hydraulic displacement/work.
Boundary: Synthetic readings and ideal static systems, not immersion of unknown materials, pressurization or load-bearing equipment.
Evidence to retain: Reconstruct opposing pressure forces, infer displaced-fluid weight, distinguish support from acceleration and reject a required displacement exceeding the available volume.
Boundary: No underwater activity, physical load test or vessel stability/safety claim. Drag, added-fluid inertia and flooding are not modeled.
Evidence to retain: Close branch volume/mass flows, combine continuity with three-term energy conservation and infer head from range with a stated error bound. Identify an observation that could falsify an ideal assumption.
Boundary: Steady full-pipe idealization and supplied jet records only; no actual jet construction, machinery operation or independently measured flow.
Evidence to retain: Retain passing, stopped and threshold cases; account for every energy transfer and choose momentum intervals. Compare two gravity methods under shared and method-specific bias, then design an independent test that discriminates alternatives.
Boundary: Original supplied-data models only. No physical spring launch, collision, drop or suspension; practical execution needs qualified local supervision and a separately reviewed safe design.
Evidence to retain: Predict before changing settings; retain paired settings, signed quantities, plotted representations and an explanation of which observations are frame-dependent.
Boundary: Prescribed synthetic motion, not calibrated physical measurement.
Evidence to retain: Derive areas for three histories; vary one launch component or observer speed while holding other quantities fixed; explain a new case.
Boundary: Uniform gravity and no drag; do not build or launch projectiles for this activity.
Evidence to retain: Choose sampling interval, retain raw selected coordinates, fit acceleration, state bounded error, test held-out evidence and propose an independent calibration check.
Boundary: Synthetic supplied data; does not establish laboratory time, instrument competence or independent practical review.
Open the retained response and project workspaces. Practice, saved work and independently reviewed proficiency remain separate.
These 42 course-specific public tasks are practice, not a secure examination. Each retains up to three immutable written responses, known feedback exposure before each response, and human rubric critiques. Drafts remain editable. No text-length check or self-reported review certifies correctness, independence, laboratory skill or mastery.
Find the center of mass for 1 kg at (0,0), 2 kg at (6,0) and 3 kg at (0,4). Separately derive the frictionless bank angle condition for radius 20 m and speed 10 m/s with g=10 m/s². Compare periods for circular orbits whose radii differ by a factor of 4 around the same dominant mass.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
A 4 kg block on a horizontal track is pulled by 20 N at 30° above horizontal. Use g=10 m/s², μs=0.5 and μk=0.3. The block starts at rest. Determine normal force, whether rest is possible, and initial horizontal acceleration if it slides. Name the third-law partner of the normal force.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
The leading cart has mass 2 kg and trailing cart 3 kg. A 20 N pull acts on the leader and a constant 4 N opposing horizontal force acts on the trailer. Derive acceleration and string tension. Then remove the opposing force and swap the masses: identify which quantities change.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
A 2 kg object is moved from a spherical body’s surface to center distance 2R; surface g=10 N/kg. Separately, an ideal spring with k=50 N/m is compressed by 0.10 m. Finally a 2 kg object requires a horizontal circle of radius 1 m at 4 m/s with a connector limit 20 N. Find weight, signed spring force for negative compression, and circle feasibility. Explain why the same force formula cannot be used for all three.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
A 2 kg object begins with 20 J kinetic energy. A net horizontal force varies linearly from 6 N to −2 N over a 4 m positive displacement. Find net work and final speed. Explain why adding area magnitudes or using force-time area would answer different questions.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
Three equal masses occupy an equilateral triangle of side r. Write their total gravitational potential energy using zero at infinite separation. Separately, a 2 kg particle has E=4 J in U=2|x−2| J: find turning points, speed at x=1, and force direction on each side of x=2.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
A 1 kg cart starts at rest against an ideal spring k=100 N/m compressed 0.20 m. After release to equilibrium it enters a horizontal rough track with constant friction 0.5 N. Find entry speed and stopping distance. Give separate consistent ledgers for cart alone and cart+spring+surface.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
Lift 10 kg through 4 m in 2 s at constant speed with g=10 m/s² and 80% efficiency. Compute useful work, input energy and required input power. A second schedule takes 1 s: which quantities change, and does either exceed a 250 W input limit?
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
A virtual 0.5 kg object moves at +4 m/s before contact. Compare stopping with rebound at −4 m/s. Find impulses. If the rebound pulse is triangular and lasts 0.20 s, find its signed average and peak force. What changes if duration doubles with the same impulse and pulse shape?
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
Masses 2 and 3 kg approach at +4 and −1 m/s with negligible external impulse. Compare their elastic final velocities with the shared sticking velocity; calculate kinetic-energy change for each model.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
A 2 kg object at 3 m/s east sticks to a 3 kg object at 4 m/s north. Set up the component equations and infer shared components. Separately, four velocity observations of two exact 1 kg objects each have error at most 0.02 m/s; observed total momentum change is 0.06 kg m/s. Is zero change compatible, and is it proven?
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
In a supplied virtual case, a 0.2 kg object moving at 10 m/s is caught by a stationary 1.8 kg carrier. They stick with negligible horizontal external impulse during the brief catch, then rise without further mechanical-energy loss. Use g=10 m/s². Find immediate shared speed and rise height; explain why one energy-conservation equation cannot be applied across the entire event.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
A rigid rotor starts at +3 rad/s with constant α=−1 rad/s² for 6 s. Find angular displacement, angular travel and final angular velocity. At t=2 s, compare speeds and inward accelerations of points at radii 0.2 and 0.4 m. Give their tangential acceleration magnitudes.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
A uniform 4 m beam weighs 40 N. A 60 N downward point load is at x=1 m from the left support. Find both upward support reactions and check torque balance about each support. Explain why force balance alone is insufficient and why this is not a construction safety rating.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
Four 1 kg particles lie at (±0.3,±0.4) m and a fifth 2 kg particle at the origin. Find inertia about the perpendicular center axis, then about a parallel axis 0.5 m away. A net +5 N m torque acts about the shifted fixed axis; find angular acceleration. Explain why the 2 kg particle has zero contribution about the first axis but not the second.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
A supplied virtual pulley case uses m=1 kg, R=0.10 m and g=10 m/s². Acceleration is reported as 3.2–3.4 m/s² with other quantities exact. Infer the inertia interval under no slip and negligible bearing friction. Then explain how a positive opposing bearing torque biases an inference that omits it, and propose a discriminating comparison.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
A fixed-axis rotor has I=2 kg m² and begins with rotational energy 20 J. Its net torque falls linearly from +4 to −2 N m across +2 rad. Find work and final angular speed, assuming no reversal. Separately, a triangular +4 N m torque pulse lasts 1 s. Find its angular impulse and explain why the first graph does not give that impulse.
Include calculations with units, source or dataset provenance, assumptions, competing explanations and limitations as relevant. The draft is saved but is not a locked response until submitted.
0/3 responses retained. No recorded feedback exposure for this task version. Earlier versions may already be familiar. Public inspectability still prevents certification of unfamiliarity.
Two coaxial rotors have inertias 2 and 1 kg m² and initial angular velocities +4 and −2 rad/s. They join through internal friction with negligible external axle torque. Find shared final speed, total angular momentum and kinetic-energy change. Then a separate isolated system with L=6 kg m²/s contracts from I=4 to I=2 kg m²; compare its energy change.
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A uniform disk with I=½mR² is released on a 30° incline. Use g=10 m/s². Derive the minimum static coefficient needed for no-slip rolling and test an assigned μs=0.15. Separately, a disk moving right has contact slipping left due to overspin: predict friction direction and qualitative changes in translation, clockwise spin and total mechanical energy.
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For an ideal central parameter GM=100 m³/s², a satellite has closest and farthest radii 10 and 30 m. At those points velocity is perpendicular to radius. Use angular momentum and energy conservation to check vp=√15 m/s and va=√15/3 m/s. Find specific total energy and compare escape speed at 10 m.
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Before and after angular momenta are independently bounded within 0.04 kg m²/s each, and the observed difference is +0.06 kg m²/s. Is zero change compatible? A separate straight-line 2 kg particle moves right at 3 m/s on y=1 m: find signed angular momentum about the origin, counterclockwise tendency positive, and explain why it stays constant.
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A vertical ideal spring has k=40 N/m and supports m=2 kg; use g=10 m/s². Find equilibrium extension. At 0.10 m below that equilibrium find net force and acceleration. Compare the period with the same mass and spring oscillating horizontally without friction.
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An ideal oscillator has m=2 kg,k=20 N/m,A=0.20 m. At x=+0.10 m find acceleration, potential energy, kinetic energy and speed. Can velocity direction be deduced? Predict all quantities at the negative endpoint.
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Two ideal small-angle pendulums are at the same gravity: lengths0.5 and2 m, with different bob masses. Compare approximate periods. Then the longer pendulum amplitude rises from5° to30°. Explain why an unchanged displayed small-angle prediction is not proof that actual period stays constant, and why the endpoint sinθ/θ discrepancy is not a period error.
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Five complete cycles take7.00±0.20 s, with exact mass1 kg. Find period bounds and stiffness bounds under the ideal spring model. Separately, a T²-versus-m fit is T²=2m+0.20 in SI units. Infer stiffness from slope and explain what the intercept does and does not establish.
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A1 kg horizontal oscillator with k=20 N/m and amplitude0.20 m captures1 kg initially at rest horizontally. Compare capture at equilibrium with capture at the positive endpoint. Find new amplitude, period and horizontal mechanical energy in each case; identify the short-impulse approximation.
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Observed masses are 0.30 and 0.70 kg at exact volumes 0.0002 and 0.0006 m³. Each mass has an assigned error bound ±0.01 kg. Infer density, intercept and worst-case density interval. Explain why one raw mass/volume ratio is not the same result.
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Oil density800 kg/m³ occupies0.30 m above water. A point is0.50 m below the interface. Use g=10 and surface pressure100000 Pa. Find its absolute and gauge pressures. A small horizontal plate at that point has area0.002 m² and opposite-face pressure100000 Pa; assuming uniform pressure on each face, find net force magnitude.
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Small and large piston areas are0.001 and0.004 m². Applied force above ambient is60 N. At equal heights find output force and displacement for input travel0.10 m, then compare work. Separately, if the output piston is1 m higher in fluidρ1000 withg10, find the pressure-corrected output force at a static instant.
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A fully immersed object has mass4 kg and volume0.003 m³ in fluidρ800 withg10. Find buoyancy and upward holding force. Separately, a sealed box of total mass12 kg has maximum displaced volume0.010 m³ in waterρ1000. Evaluate a claimed floating equilibrium and identify what remains unknown even if vertical balance were feasible.
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An inlet area0.004 m² carries water at1 m/s. A supplied split sends25% to a0.001 m² branch and75% to a0.002 m² branch. Find both branch speeds. In a separate unbranched ideal pipe, area halves, inlet speed1 m/s, inlet pressure200000 Pa and outlet rises2 m; find outlet pressure forρ1000,g10.
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A supplied horizontal-jet range is1.20±0.02 m and outlet height0.60 m is exact. Under a large-open-tank, negligible-drag model infer head and its interval. Identify two systematic effects that the range interval does not cover, and distinguish outlet height from head.
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A 3 kg cart begins at x=2 m with v=4 m/s. Its net horizontal force is −6 N for3 s, with no controller stopping it at reversal. Find final position, displacement, distance and final momentum. An observer moves at+1 m/s: compare the cart’s displacement and acceleration in that frame.
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Use the synthesis cart assumptions. First compression0.30 m and friction coefficient0.10: find arrival energy, shared capture speed and final compression. Then compression0.10 m with coefficient0.20: determine whether capture occurs and explain why a negative proposed kinetic energy is not a physical result.
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A fixed-axis rotor has I=2 kg m² and initial angular velocity+1 rad/s. A triangular net torque pulse peaks at+6 N m over2 s. Find final angular momentum and angular velocity. Is its rotational-energy gain equal to the numerical torque-time area? Separately, infer work from a constant3 N m torque over2 rad.
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A uniform disk withβ=0.5 rolls from rest through vertical drop0.60 m on a30° stationary incline withg10. Derive its no-slip speed and test μs=0.15. Separately, a gravity-only satellite has GM=100,closest radius10 and speed√15 at that point; decide whether the local circular-speed equation applies and calculate specific total energy.
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An ideal horizontal oscillator has m=2 kg,k=20 N/m,A=0.20 m. Atx=−0.10 m find acceleration, kinetic energy and possible velocity signs. If another2 kg with zero horizontal velocity is captured at the positive endpoint instead, predict the new amplitude and period ratio.
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A sealed object has total mass6 kg and maximum external volume0.005 m³ in waterρ1000,g10. Can it float? If fully immersed, find buoyancy and the upward support needed. Explain whether moving the rigid object deeper in uniform water changes buoyancy.
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In an unbranched ideal pipe, inlet area0.004 m²,speed1 m/s,pressure200000 Pa; outlet area0.002 m² and elevation2 m higher. Useρ1000,g10 to find outlet speed/pressure. Separately a horizontal open-tank jet has range1.20±0.02 m at outlet height0.60 m. Infer head and interval without equating head with outlet height.
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Two supplied gravity methods use the same clock with scale1.05 and no added method-specific lag. True gravity in the teaching generator is10 m/s². Calculate both estimates and propose an observation that can distinguish shared timing bias from a true change in gravity. Explain why repeated agreement is insufficient.
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A cart begins at x=3 m with v=4 m/s and constant a=−2 m/s². For 0–3 s find final position, displacement, distance, average velocity and average speed. A second observer moves at +1 m/s from the original origin: find the cart’s displacement in that frame. Explain all signs.
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Two carts start at rest and reach 6 m/s in 4 s. One accelerates uniformly. The other waits 2 s then accelerates uniformly for the remaining time. Compare average acceleration, displacement and the evidence needed to distinguish them. Retry with the acceleration concentrated in the first half instead.
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Reviewer identity and role are declarations, not authenticated credentials. Unsaved review fields below are lost on navigation. Review every criterion with an exact quotation, calculation or evidence citation and a next step.
Assemble original predictions, replayable virtual evidence and changed-case explanations across all eight content units. This is an authored learning workflow, not a claim that a learner has completed supervised practical work or an authorized AP course.
Select a novel mechanics or fluid claim, identify the system/frame/interval and represent it with a diagram, graph and symbolic relationships.
Evidence to retain: First prediction retained before feedback; units, signs and a prerequisite explanation.
Use force, energy, linear/angular momentum or mass-flow balances as appropriate. Test a constraint before applying a shortcut.
Evidence to retain: At least two contrasting captures and a rejected or threshold case, with replayable settings and an independent calculation.
Develop a supplied-data inference with a bounded error calculation, an alternative explanation and an observation that could discriminate it. Address shared calibration explicitly.
Evidence to retain: Data table, graph/fit or interval, uncertainty assumptions and an independent-reference plan.
Complete cumulative cases across kinematics/forces, energy/momentum, rotation/orbits, oscillations and fluid statics/dynamics without merely repeating worked solutions.
Evidence to retain: Versioned task attempts, disclosure of viewed answers and reviewer comments; public answer access is not a secure examination.
Prepare a locally supervised practical proposal with risk assessment, variables, instrument calibration, repeat design and review criteria. Record actual execution only if it genuinely occurs under appropriate supervision.
Evidence to retain: Proposed versus performed work explicitly distinguished; actual raw observations, supervision and independent review must be supplied externally, never synthesized by the app.
Retain raw-data identifiers, provenance, units, prior predictions, methods, calculations, competing explanations and safety boundaries. State explicitly when data are simulated, supplied or genuinely observed. This saved text cannot verify a real experiment; do not invent measurements or completed supervised work. Maximum 12,000 characters; retain larger evidence files separately and cite them.
A nonempty report is only a saved submission. First and revised reports remain separate and cannot be overwritten. A critique of the first report is required before retaining one revision.
Compare a new multi-stage mechanism and a new fluid/evidence problem. Defend each system boundary and explain how your conclusion would change if one essential assumption failed.
A human must supply the actual new task, evidence and conditions before the learner responds. The transfer-direction text is not itself an unseen assessment. Use the retained assignment form after the first project; exposed public task identifier: expanded-public:ap-physics1.
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