Distinguish between mathematical and physical models
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Physical models
Physical models are three-dimensional representations of reality. Two types of physical models exists: mock-ups and prototypes. The first type of physical model is designed to show people how a product or structure will look. This type of model is an appearance model or Conceptual, Physical, and Mathematical Models mock-up. It is used to evaluate the styling, balance, color, or other aesthetic feature of a technology artifact. Mock-ups are generally constructed of materials that are easy to work with. Commonly these materials include wood, clay, Styrofoam, paper, and various kinds of cardboard.
The second type of physical model is a prototype. A prototype is a working model of a system, assembly, or a product. Prototypes are built to test the operation, maintenance, and/or safety of the item. They are generally built of the same material as the final product. It would be impractical to make a prototype of a skyscraper to full scale. Prototypes and other models should be used to test and evaluate the solutions.
Mathematical models
Mathematical models show relationships in terms of formulas. For example, the relationship among voltage, amperage, and resistance in an electrical circuit is shown by the formula E = IR, where E = electromotive force measured in volts, I = electrical current in amperes, and R = electrical resistance measured in ohms. In a similar way, the relationship between the force needed to move an object and the distance it is lifted is shown in the formula for work: Work = Force x Distance. The examples given so far are for simple mathematical models. Individuals use more complex models with thousands of formulas to predict the results of complex relationships.
For example, these formulas can be part of economic models that predict the economic growth for a period of time. Also, complex mathematical models track storms and space flights, predict ocean currents and land erosion, and help scientists conduct complex experiments.
In short: physical models are typically used to gain insight into physical systems, while mathematical models are typically used to gain insight (but not necessarily into a physical system).
A physical model is a model of a physical phenomenon. Such models are often quantitative (or often aim to be), but don’t strictly have to be. For example, a force diagram that has no values is a model of a physical system, and I would say that qualifies as a physical model.
A mathematical model, on the other hand, is quantitative in nature, and does not necessarily have anything to do with a physical system. For example, we can model a thought experiment having nothing to do with physical systems. A concrete example would be a probability thought experiment in which we think of selecting colored objects at random from some large pool of such objects. If we want to know the probability of selecting a specific sequence of colors, that is a thought experiment that has nothing to do with the physics of, say, physically grabbing one of the objects and putting it aside.
Physical models are three-dimensional representations of reality. Two types of physical models exists: mock-ups and prototypes. The first type of physical model is designed to show people how a product or structure will look. This type of model is an appearance model or Conceptual, Physical, and Mathematical Models mock-up. It is used to evaluate the styling, balance, color, or other aesthetic feature of a technology artifact. Mock-ups are generally constructed of materials that are easy to work with. Commonly these materials include wood, clay, Styrofoam, paper, and various kinds of cardboard.
The second type of physical model is a prototype. A prototype is a working model of a system, assembly, or a product. Prototypes are built to test the operation, maintenance, and/or safety of the item. They are generally built of the same material as the final product. It would be impractical to make a prototype of a skyscraper to full scale. Prototypes and other models should be used to test and evaluate the solutions.
Mathematical models
Mathematical models show relationships in terms of formulas. For example, the relationship among voltage, amperage, and resistance in an electrical circuit is shown by the formula E = IR, where E = electromotive force measured in volts, I = electrical current in amperes, and R = electrical resistance measured in ohms. In a similar way, the relationship between the force needed to move an object and the distance it is lifted is shown in the formula for work: Work = Force x Distance. The examples given so far are for simple mathematical models. Individuals use more complex models with thousands of formulas to predict the results of complex relationships.
For example, these formulas can be part of economic models that predict the economic growth for a period of time. Also, complex mathematical models track storms and space flights, predict ocean currents and land erosion, and help scientists conduct complex experiments.
In short: physical models are typically used to gain insight into physical systems, while mathematical models are typically used to gain insight (but not necessarily into a physical system).
A physical model is a model of a physical phenomenon. Such models are often quantitative (or often aim to be), but don’t strictly have to be. For example, a force diagram that has no values is a model of a physical system, and I would say that qualifies as a physical model.
A mathematical model, on the other hand, is quantitative in nature, and does not necessarily have anything to do with a physical system. For example, we can model a thought experiment having nothing to do with physical systems. A concrete example would be a probability thought experiment in which we think of selecting colored objects at random from some large pool of such objects. If we want to know the probability of selecting a specific sequence of colors, that is a thought experiment that has nothing to do with the physics of, say, physically grabbing one of the objects and putting it aside.
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