What’s New for Physics Education:
           Formulas and Quantities

Jason Martinez & Daniele Carevolo

Improvements to Step-by-Step in Formulas

Prior to this year, Step-by-Step functionality for formulas was limited to the most straightforward cases: single purely algebraic equations lacking conversion factors beyond constants like the speed of light.

Extended Coverage: Formulas with Multiple Equations

Many formulas contain multiple equations, situations were one results relies on another or where we want to calculate several parameters at once.

Basic Examples

“horizon distance”

Recursive Solutions

A major wrinkle of dealing with multiple equations is the case where the results for one variable depend on solving for other variables first.

“depth of field”

Extended Coverage: Unnamed Formulas

Previously when a formula was unnamed, specified in terms of its parameters instead of a name, Step-by-Step functionality was unavailable.

Unnamed formulas

"m=28.45g V=25mL density"

Parse that return multiple formulas

"dilution equation calculator 3 ml, 5 ml, 3 mol/ml"

Extended Coverage: Quantity Factors

Many empirical formulas use quantity factors not directly related to physical constants. Handling these in Step-by-Step requires some extra handling. This requires converting factors into units more compatible with the input units:

Improved Unit Conversions

A major category of improvements in the past year relate to improvements to unit conversions.

Improved displays

Improvements in handling the summation of different units when convert to a common unit:

Unit Choice

Sum of Quantities Step-by-Step

Expanded Descriptions

Average angular displacement

Mechanical Power

MechanicalPower:Work:Time

MechanicalPower:Force:Speed

Extended Definition Schematics

Solving Problems from Physical Principles

Kinematics

Motion of a projectile from the ground, 45°

Motion of a projectile starting from a certain height, angle = 135°

Dynamics

Algebra based

StepByStepPendulum[] // sbsView

Calculus Based

StepByStepPendulum["SimpleForm" -> False] // sbsView

Integrate the Calculus Step By Step to find the analytic solutions!

Conservation Laws

Projectile Motion

Angle 45° starting from the origin

Angle 45° starting from the a certain height

Pendulum

Wolfram|Alpha Notebook Edition and Wolfram Language Improvements

Step-by-Step in all forms of the Wolfram Language

Improved Wolfram Language Interpretations for Formulas

To expand our results beyond algebraic formulas, we’ve added  Wolfram Language interpretations to built in functions and those from the Wolfram Function Repository for some formulas.

Built In Functions

Learn about the typical measurements and milestones for a child.

HumanGrowthData[Association["Age" -> (Quantity[5, "yr", years, "Years"]), "Gender" -> "Female"]]

Wolfram Function Repository

Compare the heat index of 100 F and 30% humidity to that at 60% humidity

({{"[◼]", "HeatIndex" }})[{(Quantity[100, "°F", degrees Fahrenheit, "DegreesFahrenheit"]), (QuantityPostfix[30, "%", percent, "Percent"])}]

({{"[◼]", "HeatIndex" }})[{(Quantity[100, "°F", degrees Fahrenheit, "DegreesFahrenheit"]), (QuantityPostfix[60, "%", percent, "Percent"])}]

Improved handling of pulldown menus

Many formulas include a range of choices to pick from such monoatomic or diatomic molecules or high or low elevation. Recent improvements in formula interpretation ensures that users are provided a reasonable value for these formula variables, even if they haven’t specified them.

FormulaData Improvements

Classes of Formulas

FormulaLookup["Classes"]//Shallow

FormulaLookup["EarthScience"]

FormulaLookup[{"Physics","Relativity"}]

FormulaLookup["Physics",RequiredPhysicalQuantities->{"Speed","Distance","Height"}]

FormulaData["OhmsLaw","Classes"]

Future Developments

Future Plans

Addition of more Expanded Definitions

Incorporation of Solving Problems from Physical Principles to formulas

Expansion of Step-by-Step functionality for more formulas such as those containing hidden conversion factors or piecewise functionality

Inclusion of significant digits into Step-by-Step and support for Around in FormulaData