PHY.2:4 - Solution

Choose the target consequence → propose physical mechanisms for it → connect their interactions → recover preparation and correspondence → derive or produce a consequence → use it and revise the construction.

PHY.2:4.1 - Choose what the source must help you obtain

State the target question in the terms of the work. You might need a response to an input, a possible mechanism for an observed change, a limit on a proposed behavior, or an arrangement that lets you manipulate an otherwise inaccessible relation. Say what is already known and what remains proposed about the target.

Follow the intended consequence to the relevant participants and interactions. A force on one body may change another through a stored deformation; a change at a boundary may propagate through transport. Recover the target relation that the source must help explain or use. B.5.FM and B.5.TU support this first account and its relation to a theory.

Keep the first construction as small as that question permits. For a question about coupling, two interacting parts can expose what a whole-device sketch leaves implicit. If the target mechanism is unknown, begin with an observed dependence and a proposed way it could arise. The proposal gives something to develop even before a complete target theory is available.

PHY.2:4.2 - Propose mechanisms by the physical effect they supply

Ask what the source must retain, transfer, resist, amplify, constrain or change. Then choose physical processes that can perform those contributions under known laws. These are prompts for selecting relevant effects, not a required inventory of every source.

For example, a mass retains motion while a force changes it; a deformable body stores energy under loading; a capacitor accumulates charge while current flows; a dissipative interaction converts organized motion into less accessible energy. A driven body can maintain motion by drawing on an energy supply. A stochastic transition account can express unresolved switching between physically different states. Choose among such mechanisms from the target relation and the proposed source conditions.

Write or explain the law of each chosen interaction, its participants and its regime. Include direction and sign: a coupling can restore a displacement or increase it. Identify what is being approximated when a law is linearized or treated as instantaneous. When no suitable law is available, retain the interaction as the physical contribution still to be found.

A source can combine contributions from several familiar arrangements. Derive the behavior of that combination. A chain of separately plausible resemblances can leave an unconstructed connection in the middle; locate the participants and interaction at that connection. Mathematical formulation through MMP.10 or MMP.11 makes the resulting conditions easier to solve.

PHY.2:4.3 - Construct the connection and its effect on the whole

For each connection that carries the target influence, identify what the connected parts share and what each can exchange. Write the interaction conditions together with the component laws. At an electrical junction, current conservation and common voltage connect the components; in a mechanical contact, the allowed motion and transmitted forces do that work. Other interactions need their own physical conditions.

Recover the state needed to continue the coupled behavior. The source may need a relative deformation, stored charge, field or direction of motion that neither isolated-component sketch retained. A.3.3.TR supplies the general state and joint-change construction. Here identify the physical means by which the additional state persists and affects the next change.

Check the physical restrictions that can defeat the construction. For an energy-carrying interaction, account for the relevant storage, exchange, dissipation and driving. A source that uses only passive dissipative elements cannot supply sustained amplification; an active source needs an identified supply. For a transport or switching mechanism, include the travel time, waiting law or constraint that changes the intended result. The useful restriction depends on the source, so follow it to the target consequence.

Use these restrictions to improve the construction. Add the missing coupling, replace an unsuitable element, change a boundary or keep a result limited to the regime the source can produce. If the target’s required relation conflicts with the source’s physical laws, choose another source or revise the hypothesis. This conflict is an informative result of construction.

PHY.2:4.4 - Recover preparation, interpretation and available range

Describe how the relevant source state starts and how it is driven. The initial deformation of a target spring, for example, can require stored current in an electrical source. Setting every source state to zero would solve a different initial-value problem. Likewise, the preparation of a distribution includes more than its mean when its later behavior depends on that distribution.

Connect each source quantity used in the result to what it represents about the target. Include units and scales: source voltage may represent target velocity through a dimensional conversion, and source time may run faster. Derive that correspondence by substituting the conversion into the laws and preparation. C.29.1 provides the general argument that a source result transfers to the intended mathematical target.

When proposing a material realization, determine whether its components can supply the required signs, ranges and rates together. Include the effect of observing or driving the source if it changes the relevant behavior. A nominally passive observation can load an electrical node; a finite switching time can matter when the requested event is short. C.29.3 supplies the preparation, action and readout relation for physical computation.

For a thought construction, state the physical idealizations on which its consequence depends. That conditional result can already direct a useful change or inquiry. Building an apparatus is a further choice, selected when its outcome would add a worthwhile contribution through C.11.DUA.

PHY.2:4.5 - Obtain a consequence and determine its reach

Manipulate the source according to its proposed laws. Start with a small input, a change of one interaction, or a limiting case that exposes how the construction works. Obtain the consequence by a derivation, a qualitative physical argument, a computation or an experiment. Use a known limiting case to find an omitted interaction or a sign error where it can discriminate between constructions.

Trace the obtained consequence back through its physical and mathematical premises. A computation can determine a property of the proposed source model. Interpreting an apparatus reading adds the account of the apparatus. Applying either result to a physical target adds the target correspondence and the physical premises used there. An existing explanation can supply those premises; no new evidence collection follows merely from enumerating them.

If the target mechanism remains proposed, use the result as a consequence of that hypothesis. Ask what change would make competing mechanisms disagree. This can reveal a useful intervention, a different observation interval or a parameter relation to examine. MMP.7 helps when the proposed distinction must be expressed through recorded data; C.11.DUA determines whether obtaining that distinction is worth the effort.

Different sources can contribute complementary results. One may expose an invariant or a bound, another the effect of noise or a difficult regime. Compare them for the usefulness, range and cost of the required contribution. G.5 distinguishes alternatives retained for later choice, non-dominated candidates and a set whose members contribute together. E.23 supports repeated improvement when a stated evaluation can judge the changed source.

PHY.2:4.6 - Return to the target and change the useful part

Use the result in the target work: choose a preparation, interpret an observation, propose a mechanism, reject a construction, or change the design of an experiment. Explain the physical route that makes the result relevant. EXD.3, in Explanation Design DPF, helps coordinate the words, diagram and equations another participant needs to recover that reasoning. C.2.8 characterizes the structure a recipient can extract with their available preparation and effort.

When a consequence fails or the question changes, locate the affected connection. Did the chosen source law fail, did connection change the source behavior, did computation or observation distort the result, or did the target correspondence omit an important difference? B.5.MPC.R supports this diagnosis. Revise the physical mechanism, state, preparation or correspondence that the failure implicates and retain the contributions that still work.

Keep a newly revealed question when pursuing it could open useful action. The next task can concern the target, the source or their connection. If the new construction changes what participants must produce or how their contributions join, ME.7 helps develop that proposed composition. ME.12 checks claims about the method and its description, and locates the contribution that needs correction.