Learn Fifty-nine original destinations implement motion, force/contact, energy/momentum, rotation/statics, elastic, fluid, thermal, oscillator and wave evidence in this distinct algebra-based college course. The finite six-module scope and final synthesis/project pair are authored; independent learner and practical evidence remain separate gates.
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: Algebraic equations and ratios, scientific notation, square roots, basic right-triangle trigonometry and graph reading. Calculus is not required. Every investigation distinguishes synthetic data from actual measurements and explains its reference convention.
Course outcome: Across the authored categories, reconstruct motion from bounded records, audit position/time calibration, resolve vector components and relative frames, test projectile assumptions using changed-case residuals, and distinguish admissible force/contact branches from failed constraints and calibration artifacts, then close staged work-energy and impulse-momentum accounts with explicit systems and measurement alternatives, including angular readouts, supported rotational constraints and elastic-domain limits, fluid pressure references, buoyant/capillary constraints and transport-regime audits, phase/second-law constraints and coupled oscillator-thermal inference.
All lessons are directly accessible. Reused foundation explanations are identified where relevant; completing a different course does not award this course's evidence. The 59 registered lessons keep separate predictions, captures, practice responses and reflections.
Use algebra to separate displacement from distance, measured records from hidden motion, frame changes from physical changes, and model mismatch from calibration error.
Compare scales 0.8,1.0,1.2 at offset 0.1 m, then change only offset. Retain anchor readings, raw and corrected speed and the stated raw interval. Propose an independent check for a nonlinear response that two anchors cannot exclude.
Hold second-leg length 4 m and compare headings 0°,90°,180°. Retain components, path distance and the undefined direction at cancellation. Then compare lengths 3 and 4 m near 180° and discuss sensitivity rather than claiming high directional precision.
Compare amplitudes 0,0.25,0.5 m at one sampling interval. Retain the identical recorded points and different generator distances. State which extra observation time would distinguish constant motion from the selected hidden oscillation without treating the revealed curve as measured data.
Compare a=1 at clock scales 0.8,1.0,1.2. Reconstruct one second difference and compare interval velocity with the fitted initial velocity. Then use a=0 to explain why a time-scale error cannot create curvature in this model.
Compare v0=3,4,5 m/s at b=1, then compare b=1 and 2 at v0=3. Retain the event time, interval classification and separately calculated distance/displacement. Explain why extrapolating after 4 s requires another model claim.
Compare B velocities 1,3,5 at observer velocities 0 and2. Retain one actual event and two missing-future classifications. Reconstruct the transformed meeting coordinate without altering the event time.
Compare current 0,1,2 at relative speed 2, retaining north-aimed drift and straight-across feasibility separately. Predict the equality boundary before checking. Explain which goal remains possible when current exceeds relative speed.
Compare vx=4 and12 at the same vy, then vy=−2, 0, 4 at vx=8. Retain the accepted root, endpoint and future maximum-height classification. State an observation that would challenge the no-horizontal-force assumption.
Compare a=0 and1 at offset 0.1 m, then change offset to −0.2 m. Retain raw, corrected and residual coordinates. Predict the second difference before checking and propose a separate timing/perspective test that the packet cannot supply.
Construct recipient-specific force inventories, solve algebraic contact branches, and test inferred dynamics against independently supplied measurements.
Compare H=−4,0,4 N while holding F=6 N. Retain component residuals and propose one independent acceleration or force check. Explain why a residual of zero at one setting does not establish every instrument calibration.
Compare F=8,0,−8 N at front mass 3 kg. Solve recipient equations and the pair equation independently. Retain the failed negative-contact candidate before replacing it with the separated branch.
Compare pulls of 10,20,30 N at 90°, then compare 0° and 30° at 15 N. Keep the conditional required normal and actual contact force separate. Explain what new event would require changing the assumed kinetic-friction direction.
Compare 15°,30°,45° at 2 kg and repeat one state at 1 and 3 kg. Retain actual friction separately from its maximum, and predict which outputs scale with mass.
Compare F=0,4,6,10 N at v0=2 m/s. Predict whether a stop exists and whether it lies in the 2 s interval. Retain the position and velocity at the event before evaluating the final state.
Compare support accelerations+2,−4,−10,−12 m/s² at one mass. Retain the conditional required normal and actual normal, then explain why the object cannot share the last prescribed acceleration.
Hold k fixed and compare masses 1,2,3 kg; then double k at one mass. Predict terminal-speed ratios before checking. Retain the force balance and a state above equilibrium, explicitly naming the graph’s horizontal variable.
Compare speeds 4,6,8 m/s at R=4 m. Draw the two actual interaction forces, then calculate the inward resultant. Keep failed required normal separate from actual force and state what is not predicted after separation.
Compare radii R,2R,3R at one test mass; retain field, force, speed and period ratios. Then change mass alone. Explain why equal periods need not imply equal instantaneous speeds at every point of a noncircular orbit.
Compare offsets−2,0,2 N at zero fault, then vary fault at one offset. Retain slope, intercept and held-out residual. Propose a changed acceleration that would test a curved force law rather than merely repeat one fitting point.
Select the system, interval and reference frame before applying work-energy or impulse-momentum; retain inaccessible states, conversion channels and calibration alternatives.
Compare a positive first segment with a resisting second, then reverse both force signs. Keep separate applied contributions, total work and intermediate kinetic energy. Explain how a perpendicular guide force can matter to momentum without adding energy.
Compare compressions0.5,0.8,1.0 m at a fixed target, then vary target at fixed compression. Retain the first inaccessible case and demonstrate algebraically that a common potential-energy offset cancels.
Compare requested distances1,2,4 m at friction 6 N, then double or halve friction where controls permit. Record requested versus actual distance and show both the point-only and object-plus-surface accounts without double-counting.
At T=2 s compare efficiencies0.4,0.8,1.0. Then keep one efficiency and change duration. Preserve energy and power units and explain why the two comparisons answer different questions.
Compare an η=0.8,s=1.1 packet with η=1,s=1 where available, then choose a state with apparent fraction above unity. Retain the product relationship and propose an independent measurement capable of separating its factors.
Compare two durations at zero baseline, then introduce one nonzero baseline. Retain true and indicated areas separately and propose a pre-/post-pulse baseline check without pretending those observations were already supplied.
At M=3 kg compare e=0,0.5,1. Retain both conservation and supplied-response equations and distinguish a predicted response from an empirical assumption. Then test the equal-mass elastic endpoint.
Compare an oblique packet, a head-on partial cancellation and exact zero momentum. Retain both components and kinetic-energy accounts. Explain why the displayed chain is a vector addition diagram rather than the collision trajectory.
Hold relative speed fixed and change U. Compare ground and center-frame velocities, momenta and kinetic energies. Then double u and predict the energy-source requirement before checking.
Compare incoming masses 0.5,1,2 kg at one speed and retain collision momentum, collision energy conversion and later rise separately. Identify which external interactions are neglected in each stage and which are not.
Audit angular representations, moment arms, contact equilibrium and inertia inference; reconcile rolling/coupling accounts and apply elastic relations only within their declared domains.
Compare a steady wrap, an interior reversal and a zero-velocity endpoint. Preserve raw wrapped samples, disclosed unwrapped coordinates, signed displacement and swept angle. Explain which conclusions rely on the known generator rather than the samples alone.
Hold radius fixed while comparing ω=−2,0,+2, then double radius at one rate. Retain inward and tangential components separately and explain which direction changes with ω and which does not.
Compare−90°,−30°,0°,30°,90° at one radius. Draw the force line and perpendicular pivot distance, then verify the same torque from rFy and F times signed moment arm. Keep all forces in the force balance even when their torque vanishes.
Compare a centered load, both zero-reaction boundaries and an outside state. At one feasible state vary the sensor offset and retain inferred position plus force residual. Propose an independent geometry or weight check rather than treating a fitted coordinate as a measurement of truth.
Compare radii0.25,0.5,1 m about the central axis, then shift the axis at fixed radius. Retain the bar, point-pair and axis-shift contributions separately. Explain why a center-of-mass location alone does not determine inertia.
Vary resistance with zero fault, then vary the one-reading fault at fixed resistance. Retain slope, intercept and held-out residual. Propose a third condition that would distinguish changing resistance from a shared acceleration scale error.
Compare β=0.5 and 1 at 30° and 40°. Derive required friction before evaluating the energy split. For one feasible state compare energy and constant-acceleration geometry, and explain why a failed state needs independent slip dynamics.
Compare same-direction, opposite-direction and exact-cancellation states. Retain each rotor’s angular impulse and the whole-pair total. Explain why the kinetic conversion cannot be found by subtracting angular-speed magnitudes alone.
Compare areas1,2,4 mm² at 20 N and compare20 with 40 N at 1 mm². Retain SI area, stress, conditional strain and whether the linear model is valid. Explain why a bounded elastic relation does not establish breaking strength.
Separate pressure references and calibration from density, test hydrostatic and buoyant constraints, and close flow mass/energy budgets only within declared capillary or viscous regimes.
Compare two offsets across three volumes. Save one-sample ratios and two-volume slope estimates, reserve the third volume as a check, and identify which calibration error the method cancels and which it does not.
Predict the interface and bottom pressures for two layer combinations with equal total depth. Preserve the continuous piecewise graph, gauge and absolute references, and explain why exchanging layer thickness changes the result.
Hold force fixed while doubling output area, then hold area fixed while changing input force. Retain pressure, displaced volume, both forces, strokes and works; explain why neither comparison creates energy.
Compare one cord-feasible, one floating-feasible and one neutral case. Save weight, full-submersion buoyancy, required signed tension and branch flags. Never interpret a rejected conditional force as an actual instrument value.
Compare contact angles 0°, 90° and 120° at two radii. Retain signed height and signed vertical surface force, and explain why using the absolute value of cosine would destroy the physical distinction.
Compare two areas at the same prescribed split, then compare two splits at one area. Retain volume and mass residuals. State explicitly why continuity verifies an imposed split but does not predict a pressure-driven split.
Vary elevation while holding loss fixed, then vary loss at one elevation. Close the four-term power budget and distinguish reversible height or speed changes from the specified irreversible loss.
Predict the radius ratios for flow, speed and Reynolds number before changing radius. Retain at least one screened laminar and one rejected case, and explain which independent premises a Reynolds screen cannot establish.
Audit state and path quantities, phase and second-law limits, infer oscillator/wave parameters under calibration alternatives, and connect lost mechanical energy with a finite thermal receiver.
Compare an offset-only fault, a gain-only fault and both together. Retain raw anchors and held-out correction, then predict which fault biases an expansion inferred from a temperature difference.
Hold amount fixed and compare temperature changes with volume changes. Retain absolute pressure, internal energy and rms speed, then compare a hypothetical species with four times the molar mass at the same temperature.
Retain one partial-melting, one exact-boundary and one warmed-liquid case. Show the phase test before calculating temperature and close the energy ledger including the cup in every applicable term.
Compare equal and unequal thermal resistances, then alter only one layer. Retain both temperature drops and equal steady rates; identify a separate radiation or convection term that would invalidate a conduction-only inference.
Draw both routes and a closed clockwise cycle for two selected endpoints. Keep ΔU, W and Q distinct and explain why equal endpoint temperatures would not generally fix the work or heat.
Compare one entropy-increasing, one reversible-limit and one rejected proposal. Retain work, rejected heat and both reservoir entropy terms, then build a separate refrigerator energy account without reusing engine-efficiency terminology.
Compare two clock gains at one amplitude, then two amplitudes at one gain. Retain period-derived and independent static stiffness, quarter-cycle signs and energy partition. Explain why a shared instrument fault can survive repeated trials.
Fit the first and last generated records and retain the middle as a check. Vary length offset separately from time gain, then propose an independent length or time reference that distinguishes their effects.
Compare two damping values at the same drive, then sweep drive frequency with damping fixed. Keep free decay and steady response records separate and identify where energy enters and leaves each system.
Infer wavelength and period separately, then compare in-phase, intermediate-phase and opposite-phase sums. Sketch a separate fixed-end standing mode and label nodes without treating the traveling sum as a standing pattern.
Compare amplitude changes with capture-fraction changes. Retain the whole-system energy closure and receiver-only thermal account, then design an independent observation distinguishing a capture change from a temperature or heat-capacity error.
Combine motion, force, rotational, fluid and thermal accounts while preserving system boundaries, calibration alternatives and independently assessed transfer.
Predict the acceleration and tension from separate recipient diagrams before checking energy. Compare two heights and two capture fractions, preserve the two time intervals, and retain a rejected 10 N cord-capacity alternative. Explain what an independent timing or temperature calibration could challenge.
Retain input, fluid, height, kinetic, pipe and pump powers for contrasting settings. Infer efficiency from an independent hypothetical wattmeter record, then propose a new observation distinguishing an input-power bias from a thermal-capture error. Preserve original prediction, critique and revision in the course project.
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: Retain separate recipient diagrams, a component residual, pair-system balance and a held-out force-reading test. Distinguish an inferred missing interaction from an independently identified agent.
Boundary: Original synthetic forces and acceleration labels; no apparatus calibration, physical cart collisions or demonstrated practical competence.
Evidence to retain: Preserve conditional required force and admissible actual force, an exact or continuous boundary, a stop/lift-off event and the new branch. Compare maximum static capacity with actual friction.
Boundary: Virtual point/contact models only, not lifting, braking, lift operations or physical ramp instructions.
Evidence to retain: Compare a force-versus-speed equilibrium with a trajectory constraint, retain a rejected circular-contact state and derive a common-source orbital scaling without confusing radius and altitude.
Boundary: Assigned drag, spherical-source and point-contact assumptions; no real falling, driving, ride safety or orbital flight prediction.
Evidence to retain: Retain separate work contributions, an intermediate kinetic-energy check, a turning or stopping boundary and two different system-boundary accounts without counting thermal conversion twice.
Boundary: Virtual points, ideal guides and assigned friction; no real compressed springs, launches or stopping-distance safety certification.
Evidence to retain: Compare input/output energy and average/endpoint power, expose the loss-times-speed-scale product, and preserve true versus baseline-biased impulse over a declared recording window.
Boundary: Synthetic readouts and disclosed generator settings; no actual power measurement, force-sensor calibration or practical instrumentation claim.
Evidence to retain: Solve momentum components and one supplied response rule, account for kinetic conversion or internal release, compare frames and choose separate conservation statements for collision and rise.
Boundary: Point collisions without retained rotation, negligible stated external impulse and ideal later guide; no physical impact, ballistic apparatus or explosive procedure.
Evidence to retain: Retain wrapped/unwrapped records, a reversal split, radian conversions, velocity/acceleration components and two equivalent moment-arm calculations. Distinguish a coordinate jump from a physical event.
Boundary: Disclosed fixed-axis generators, not unambiguously reconstructed sparse encoder data or real machinery.
Evidence to retain: Check unilateral support feasibility before inverting a reading; preserve force-closure residual, mass-distribution/axis contributions and a held-out torque-reading challenge.
Boundary: Synthetic sensors, provided uniform-bar inertia and ideal contacts; no measured load capacity or bearing certification.
Evidence to retain: Derive required friction and reject an unsupported rolling branch, compare energy with kinematics for a feasible state, then retain reciprocal rotor impulses and internal energy conversion at coupling.
Boundary: Ideal rigid bodies and negligible stated external angular impulse, not physical rolling or coupling trials.
Evidence to retain: Convert area units, retain stress/strain/extension and a rejected extrapolation; distinguish specimen stiffness from material modulus and compare supplied shear/bulk ratios.
Boundary: Hypothetical linear coefficients and imposed strain limit, not yield, fracture, safe working load or material testing.
Evidence to retain: Retain a two-volume density inference and unused volume check, continuous layered pressure graph, gauge/absolute conversion and paired hydraulic work accounts.
Boundary: Synthetic additive balance error and ideal static/quasistatic fluids; no physical pressure rig or instrument calibration claim.
Evidence to retain: Compare valid, rejected and neutral cord states, separate free-floating displacement from full immersion, and preserve capillary sign across 90 degrees at two radii.
Boundary: Ideal rigid object, prescribed contact angle and surface tension; no immersion, chemical handling, biological measurement or practical load rating.
Evidence to retain: Close branch volume/mass balances, distinguish imposed split from predicted split, reconcile pressure-work power with height/kinetic/loss terms, and reject a radius extrapolation that fails its laminar screen.
Boundary: Steady mathematical flow packets and approximate Reynolds guide; no pump, plumbing, exposure or clinical advice.
Evidence to retain: Retain affine temperature anchors and an unused check, absolute gas-state ratios and a partial/exact/complete melting comparison including receiver capacity.
Boundary: Disclosed ideal gases and simplified calorimetric constants; no physical heating, pressurization or measured material claims.
Evidence to retain: Close series conduction drops, compare endpoint energy with route heat/work, and retain an energy-balanced proposal rejected by reservoir entropy.
Boundary: Specified transport and equilibrium assumptions, not actual thermal machinery, emissions or safety certification.
Evidence to retain: Compare shared-clock and independent-static parameter evidence, retain a held-out pendulum record, and separate free decay from finite driven response.
Boundary: Small-amplitude ideal models; supplied finite-amplitude and viscous-response expressions are optional algebraic enrichment, not physical loading.
Evidence to retain: Infer wavelength and period from separate representations, compare coherent phase and standing-mode boundaries, then close a receiver-plus-environment endpoint energy account.
Boundary: Nondispersive linear waves and stipulated energy capture; no physical vibration, sound exposure or calorimetry.
Evidence to retain: Derive acceleration and tension from separate recipient diagrams, reconcile translation/rotation/axle energies and distinguish descent from terminal stopping. Retain a failed cord constraint and independent timing/temperature check.
Boundary: Fictional bounded mechanism; no physical rig, load, brake, heating or safe operating limit.
Evidence to retain: Close input/fluid/exported/loss powers, connect receiver warming to a stated capture boundary and compare actual rival wattmeter/flow/thermal calibration hypotheses.
Boundary: Specified virtual flow and receiver, not electrical installation, plumbing, clinical measurement or practical efficiency certification.
Evidence to retain: Freeze competing offset, scale, clock and hidden-motion explanations; retain contrasting recipes, raw records, corrected differences and one independently justified new observation.
Boundary: Synthetic affine sensors and disclosed smooth tracks, not observed apparatus. Exact reference anchors and time assumptions must not become unstated empirical claims.
Evidence to retain: Draw common axes, retain signed components and one undefined or infeasible event, compare two observer frames and identify which event quantity remains invariant.
Boundary: Flat low-speed mathematical geometry; no navigation, swimming, boating or traffic instruction.
Evidence to retain: Locate a reversal or ground event before evaluating endpoint claims, separate distance from displacement, then compare offset and curvature alternatives with changed numerical observations.
Boundary: No physical drops or launches; constant acceleration and known timing are hypotheses to examine, not guaranteed real-world behavior.
Open the retained response and project workspaces. Practice, saved work and independently reviewed proficiency remain separate.
These 46 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.
A 3 kg point has independently supplied acceleration (2,−1) m/s² but listed forces total (4,−3) N. Infer the missing component. Separately a 2 kg rear cart and 4 kg front cart touch on a frictionless line; 12 N pushes the rear. Find acceleration and contact. Then apply −12 N only to the rear with no tether: give both accelerations and the pair center-of-mass acceleration.
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 point slides right while pulled with 10 N at 30° above horizontal; g=10 and μk=.2. Find N, friction and horizontal acceleration. Separately a 3 kg point begins at rest touching a support prescribed to accelerate downward12 m/s² for 1 s. Find actual normal, object acceleration and gap above support. Explain why neither calculation permits a negative actual normal.
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 point is initially at rest on a slope with sinθ=.3, cosθ=√.91, g=10 and μs=.5: find required static friction and test capacity. Separately a 2 kg slider starts rightward at 3 m/s under 6 N kinetic friction leftward and 2 N drive rightward. Static capacity is 10 N. Find stop time and displacement after 2 s, explaining the post-stop force.
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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 falling1.8 kg point has quadratic resistance k=.2 kg/m and g=10. Find terminal speed and signed downward acceleration at twice that speed. Separately a 3 kg point at a convex crest R5 m moves at 5 m/s: find normal. What changes at 10 m/s? Give actual instantaneous acceleration after failed contact, not the rejected circular value.
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An ideal spherical source has surface radius R. Compare exterior gravity at altitude R and altitude 3R. Compare circular speed and period at those locations for the same dominant source. Would doubling the negligible test mass change force, gravitational acceleration or circular speed? State where the center is in a general elliptical orbit.
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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.
At independently exact accelerations1 and 3 m/s², force readings are5 and 11 N. Infer mass and intercept. A held-out reading at 2 m/s² is 7.8 N: compute observed-minus-predicted residual. If each fitting force reading independently has a bounded±.1 N error, find the worst-case mass-error bound. Does this automatically cover acceleration-scale error or establish a unique cause of the residual?
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 3 kg point starts with K=6 J and receives works +12 and−4 J, with all other work zero. Find final K and speed. Separately a 1 kg point receives a fully relaxed spring’s energy with k=40 N/m and initial compression .5 m. Under g=10, can it reach .75 m above release level? Find the actual maximum height and K at .4 m. Explain what adding100 J to gravitational potential at both endpoints changes.
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 point starts with15 J kinetic energy and constant resisting friction3 N, with no drive. Compare requested paths4 and6 m: give actual distance, remaining K and object-plus-surface thermal gain. Separately a device delivers30 J useful energy in3 s at efficiency .6: find input energy and average input power. Can endpoint power be found from just those three numbers?
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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 height-to-speed generator has true kinetic fraction .75 and speed readout scale1.1. What apparent fraction is inferred? Can three exact height points separate these parameters? Separately a 2 kg point begins at−2 m/s and receives a triangular true net force pulse of peak12 N over1 s. A readout baseline+.2 N affects the full record. Find true and indicated impulses and true versus inferred final velocities.
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A 2 kg point at4 m/s hits a stationary3 kg point with negligible external impulse. Using the supplied optional recovery relation v2−v1=.5(4−0), find both final velocities and kinetic-energy conversion. Compare the same masses in a sticking collision and explain why momentum alone does not choose either response.
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A 2 kg point at(3,0) m/s sticks to a 1 kg point at(0,3) m/s without external impulse or retained rotation. Find common velocity, speed and kinetic conversion. Separately masses1 and3 kg initially share ground velocity2 m/s and release with final relative speed4 m/s and no external impulse: find final velocities and the kinetic increase. Compare that increase in the center-of-mass frame.
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A 1 kg point at6 m/s sticks to a stationary2 kg point in a short horizontal collision with negligible external horizontal impulse. The combined point then rises without mechanical loss on a guide under g=10. Find immediate common speed, collision kinetic conversion and maximum rise. Explain why neither initial kinetic energy nor total point momentum can be carried unchanged through both stages.
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A fixed-axis body starts with omega2 rad/s and constant alpha−1 rad/s² for3 s. Find signed angular displacement, swept angle and final omega. At the final instant, a point is .5 m from the axis: find speed, inward acceleration magnitude, signed tangential acceleration and total acceleration magnitude. Could wrapped endpoint angles alone establish the swept angle?
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A10 N force acts at radius .4 m at30° above an outward horizontal lever. Find signed torque and explain why work is not yet determined. Separately use the taught12 N beam plus24 N load with supports x1 and3. True load coordinate2 m; right readout has+1 N bias and left readout is unbiased. Find actual reactions, indicated right force, inferred coordinate and force-closure residual. What if the actual load coordinate is0?
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The taught2 kg,2 m bar carries two1 kg points at±.5 m. Find central inertia and inertia about a parallel axis .5 m away, then net torque for alpha2 rad/s² about that axis. Separately drive torques3 and9 N m correspond to exact angular accelerations1 and4 rad/s² under constant opposing torque. Infer inertia and resistance; predict an independent reading at alpha2.
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An ideal rolling body has beta=1, mass2 kg, radius .5 m, available mu_s=.30 and g10. Compare slopes30° and40°. Calculate required coefficient and classify no-slip feasibility. For the feasible case, find speed squared and translation/rotation energies after a .6 m vertical drop. Explain why simply clipping friction at .30N in the failed branch does not preserve the no-slip acceleration.
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Coaxial rotors I1=2,omega1=3 and I2=1,omega2=−2 lock with negligible external angular impulse. Find total L, common final rate, initial/final kinetic energy, internal conversion and the angular impulse on each rotor. Explain what changes if the pair receives an unmodeled external angular impulse.
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A hypothetical linear specimen has E=10^10 Pa,L1 m,A2 mm² and tension10 N, valid only through strain .001. Find stress,strain and extension in mm. Repeat with area1 and .5 mm²: identify supported and unsupported predictions. Separately supplied shear modulus4e9 Pa under shear stress2e6 Pa and bulk modulus2e9 Pa under pressure increase1e6 Pa: find the corresponding dimensionless shear strain and signed volume fraction change.
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An unknown liquid gives mass indications 66 g at 80 cm³ and 146 g at 180 cm³ under a common additive balance offset and exact volumes. Infer density and offset; predict a held-out reading at 130 cm³. Separately oil density 800 kg/m³ occupies 0.3 m above 0.2 m water density 1000. With g=10 and atmospheric pressure 100000 Pa, find interface gauge, bottom gauge and bottom absolute pressure.
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Ideal equal-elevation pistons have areas 3 cm² and 15 cm². Input force is 12 N over 0.2 m. Find pressure increase, balanced output force, output displacement and both works. What changes in the argument if the pistons have different elevations or fluid leaks?
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A rigid 200 cm³ object has mass 120 g in liquid density 800 kg/m³, g=10. Find full-submersion buoyancy and required overhead-cord tension. Is the stipulated static state feasible? In a separate free-floating configuration find displaced volume and submerged fraction. Repeat feasibility at mass 200 g, with the same volume and liquid.
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Use supplied capillary law h=2γcosθ/(ρgr) with γ=0.05 N/m, ρ=1000, g=10, r=1 mm. Compare θ=0,90,120 degrees. What happens if radius halves? Separately use supplied drop and two-surface bubble laws 2γ/R and 4γ/R at γ=0.03 N/m,R=2 mm.
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Steady incompressible flow of density 900 kg/m³ enters at 6 L/min and one outlet carries 3 L/min; second outlet area is 2 cm². Find its mean speed and mass flow. Separately use the taught water-flow packet Q=.002 m³/s, inlet/outlet speeds 1/2 m/s, inlet gauge pressure 30000 Pa, g=10, outlet elevation 2 m and prescribed loss 10000 Pa. Find outlet gauge/absolute pressure under atmosphere 100000 Pa and reconcile the pressure-work power decrease.
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For the taught liquid and tube at radius 1 mm and pressure drop 1000 Pa, a report proposes Q=π×10⁻⁷/8 m³/s. Audit this proposed number independently using Q=πr⁴Δp/(8ηL), η=.001,L=1. Then find mean speed and Reynolds number with ρ=1000. Double radius at unchanged pressure and classify the new conditional regime. Separately with supplied xrms=√(2Dt), what happens to typical displacement when time quadruples?
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An affine thermometer reads 3 °C at true 0 °C and 87 °C at true 80 °C. A new sample reads 45 °C. Infer true Celsius and kelvin temperature. A separate fixed-volume ideal gas starts at 250 K and ends at 400 K; find its pressure ratio. Compare molecular rms speeds at the same temperature for two species with molar masses M and 4M. A 2 m rod with supplied alpha 1.5e−5/K warms by 20 K: find expansion.
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Use the taught .5 kg liquid, 100 J/K cup, c 4000 J/(kg K), latent heat 300000 J/kg and .14 kg ice initially 0 °C. Compare initial warm-liquid/cup temperatures 10, 20, 30 °C. Find melted mass, remaining ice and final temperature in each; explain what omitting the cup changes.
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Two series layers have resistances .3 and .5 K/W between hot 330 K and cold 306 K, with no side loss or interface storage. Find heat rate and interface temperature when the .3 layer touches the hot boundary. Separately a supplied gray surface has epsilon.5, A 1 m², T 300 K, surroundings 290 K and sigma 5.67e−8 SI. Find net outward radiative power; what changes at equal temperatures?
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A monatomic ideal gas goes from 100 kPa, 1 L to 150 kPa, 2 L. Compare pressure-first then expansion with expansion-first then pressure increase. Compute DeltaU, W, Q for each. Separately a cyclic engine takes 600 J from 400 K and proposes 180 J work while rejecting the remainder to 300 K. Audit both laws. For a reversible refrigerator between the same temperatures with 20 J work, find removed and delivered heats.
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An ideal spring oscillator has m 2 kg, k 18 N/m, A.2 m and starts at positive amplitude at rest. Find angular frequency, period, maximum speed, total energy and velocity after a true quarter period. If the clock reads 1.1 times true time, what stiffness is inferred from the uncorrected period? Separately a small-angle pendulum period-squared fit has slope 4pi²×1.1²/10 and an inferred length offset.05 m; does correcting the length offset alone recover g 10?
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Using the supplied optional models, take m 1 kg, k 4 N/m, drive amplitude.2 N and damping c.8 kg/s. Find the steady amplitude at Omega 2 rad/s and the free-envelope ratio after 4 s. Compute the displacement resonance frequency sqrt(k/m−c²/(2m²)). Why are the three results not one free-motion trajectory?
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A nondispersive string has speed 6 m/s and frequency 3 Hz. Find wavelength and period. Two same-direction waves each have amplitude.01 m and phase difference 120 degrees: find resultant amplitude and intensity ratio to one wave at the same medium/frequency. Separately a 3 m fixed-end string has the same speed: which harmonic is 3 Hz? What beat frequency comes from 4 and 4.5 Hz?
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Use m 2 kg, k 200 N/m, A.2 m, receiver capacity 20 J/K and initial receiver temperature 300 K. At capture fraction.8 find energy partition, temperature rise and undamped period. A later packet at the same nominal amplitude gives rise.10 K: infer fraction conditionally, then name two rival causes other than a real capture change. What happens to rise and ideal period if amplitude doubles at fixed fraction/capacity?
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A position sensor obeys xread=1.1x+0.2 m and reads 0.2, 1.3, 3.5 m at exact times 0, 1, 2 s. Recover actual positions and interval-average velocities; can these samples alone determine total distance if reversals may occur between frames? Separately two consecutive displacements are(3, 4) m and(−1, 2) m. Find resultant and magnitude. If two objects have velocities 3 and 1 m/s along the same axis, does changing to an observer moving at−2 m/s change their relative velocity?
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A hypothetical 2 kg block on a level surface has g 10, mu_s.4, mu_k.3. Compare rightward applied forces 5 and 10 N from rest: classify motion and find friction/acceleration. Once moving right, the drive is removed: find deceleration and stopping distance from 2 m/s under the same kinetic model. Why cannot the block–surface reciprocal friction pair be canceled in the block-only force diagram?
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A 2 kg cart starts at rest and receives constant net force 6 N over 3 m on a horizontal track. It then sticks to a stationary 1 kg cart with negligible external impulse. Find incoming speed, common speed and kinetic energy converted during sticking. The combined cart then compresses an ideal spring k 12 N/m on a frictionless track. Find maximum compression. State which conservation law applies in each interval and whether the pair’s kinetic energy was conserved in the collision.
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Use the taught beam weight 12 N atx 2, load 24 N atx 2 and supportsx 1/x 3. Right sensor reads 19 N, left 18 N. Infer load coordinate if the right sensor is wrongly assumed exact and calculate force residual. Separately rotors I 1=2, omega 1=3 and I 2=1, omega 2=−2 lock without external angular impulse: find final omega and energy conversion. A specimen E 1e 10 Pa, L 1 m, A.5 mm² under 10 N is stipulated linear only through strain.001: is the linear extension prediction admissible?
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Oil density 800 occupies.2 m above.3 m water density 1000, with g 10 and atmosphere 100000 Pa. Find bottom gauge/absolute pressure. A 200 cm³ object of mass 150 g is separately fully submerged in water with only an overhead cord: find required tension and classify feasibility. For another straight tube whose conditional laminar Reynolds number is 250 at radiusr, double radius at fixed pressure drop, viscosity, density and length. Find the new conditional Reynolds number and explain the resulting limitation.
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Use the taught .5 kg warm liquid plus 100 J/K cup at 20 °C, .14 kg ice at 0 °C, c 4000 and latent 300000. Find the final phase/temperature. Separately an adiabatic gas does 80 J work: find DeltaU under work-by-gas convention. A cyclic engine absorbs 800 J from 400 K and proposes 320 J work, rejecting the remainder to 300 K. Audit energy and total reservoir entropy; does correct energy arithmetic establish admissibility?
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An ideal spring m 2 kg, k 8 N/m, A.1 m is recorded by a clock reading 1.1 times true time. Find true/indicated periods, uncorrected inferred stiffness and true maximum speed. Separately a nondispersive wave speed 6 m/s at 3 Hz combines with an equal same-direction wave of phase difference 120 degrees. Find wavelength, resultant amplitude for individual amplitude.01 m, and intensity ratio to one wave at that same frequency. Why is this not a standing-wave construction?
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For the taught drum packet take h 2 m and terminal receiver capture .5, with an idealized negligible-displacement terminal stop (no additional gravitational work). Find acceleration, tension, speed, translational/rotational/axle energies and receiver rise. For the taught pump packet take Q.2 L/s and eta.6. Find input power, pipe/pump heat powers and receiver rise after 60 s. If the pump receiver instead warms 2.0 K with all other readings unchanged, name two alternative explanations rather than declaring efficiency uniquely known.
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True position anchors 0 and3 m read 0.2 and3.8 m. A target indicated displacement 2.4 m takes a displayed 2 s. Infer the position-corrected average velocity if clock readings are exact. Then suppose displayed elapsed time is 1.25 times true elapsed time: revise velocity. Explain why the two position anchors cannot resolve the clock scale.
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A record gives positions 0,2,4 m at times 0,1,2 s. What average velocity is established, and why is traveled distance not uniquely established? Separately x=4t−t² m over 0–3 s: find final displacement and traveled distance, retaining the reversal time.
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A route goes 6 m east then 8 m north: find displacement magnitude, direction from east and distance. Separately A starts 0 at 4 m/s and B starts 5 m ahead at 1.5 m/s. Find meeting time and ground coordinate; transform the event to an observer moving −2 m/s whose origin matches at t=0.
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A virtual channel is 12 m wide with current 3 m/s eastward. Relative-water speed is 5 m/s. Compare north-aimed relative motion with a directly opposite ground path: give times, drift for the first and heading for the second. Explain what changes if relative speed becomes 3 m/s. This is only a vector model, not practical route advice.
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An ideal virtual projectile starts 5 m above ground with horizontal velocity 6 m/s and vertical velocity 0, under g=10. Find ground time, range and impact velocity components. Compare horizontal velocity 12 m/s. Would vertical velocity zero at the start imply zero vertical acceleration? State one assumption needing independent evidence.
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At exact times 0,0.2,0.4 s, indicated horizontal positions are0.1,0.88,1.62 m. Infer signed acceleration under a constant-acceleration model and initial velocity after removing the origin. Would a different constant origin remove the acceleration? Does the result establish a drag coefficient?
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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.
Submit a cumulative first report using these fixed packets: motion readouts 0.2, 1.3, 3.5 m at 0, 1, 2 s under xread=1.1x+.2; the 2 kg drive 6 N over 3 m then sticking 1 kg and spring k 12 packet; the taught drum at h 2 m, capture .5, with its idealized negligible-displacement terminal stop and no additional gravitational work; the taught pump at Q.2 L/s, eta.6; and an independent spring m 2, k 8 with indicated period 1.1pi s. Explain everyday motion/flow/thermal models without pretending synthetic records are observations of real equipment. Complete all six module evidence clusters and the separate cumulative mixed assessment.
Record raw and corrected motion, unresolved between-frame distance, force diagrams and fixed unit/reference conventions. List which parameters are supplied, which are inferred and which observations genuinely test a prediction.
Evidence to retain: Versioned first report, raw/calibrated table, recipient/system diagrams and exposure/assistance record.
Carry drive work through the sticking collision and spring endpoint. Derive drum force/torque and interval energy accounts. Include a rejected contact, friction or material-domain alternative from the retained course investigations.
Evidence to retain: Independent motion/work/momentum/rotation calculations, stage boundaries and a failed-branch explanation.
Close pump/fluid/exported/receiver powers and drum receiver energy. Contrast shared-clock oscillator inference with independent static evidence. Include one phase/entropy constraint and one wave-coherence or standing-mode comparison from the actual course tasks.
Evidence to retain: Thermal and flow ledgers, calibration rival table, phase/second-law test and explicit wave model conditions.
A human reviewer cites concrete criteria and report passages, including one numerical or domain error or an explicitly justified no-error finding. Preserve the first report and critique before revision; identify every changed claim.
Evidence to retain: Reviewer relationship and expertise limits, criterion-linked critique, first/revised reports and change rationale.
The reviewer supplies actual new numerical observations spanning at least two modules, with a different calibration or physical-boundary issue and allowed resources. Freeze those details before the response and disclose public-key exposure or assistance.
Evidence to retain: Immutable unfamiliar packet, response, independence declaration, criterion review and unresolved limitations.
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.
The human-frozen packet must include actual new numbers and at least two of mechanics/rotation, fluids/thermal, oscillator/waves plus a meaningful calibration or domain change. The public cumulative cases and a generic request to change a number are not independent transfer evidence. No physical apparatus is requested; authentic practical participation requires separately supervised opportunities.
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:college-physics1.
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