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{"search_formulae_by_concept_name_Wikidata": {"mass-energy equivalence": {"head": {"vars": ["item", "itemLabel", "itemDescription", "formula"]}, "results": {"bindings": [{"item": {"type": "uri", "value": "http://www.wikidata.org/entity/Q35875"}, "formula": {"datatype": "http://www.w3.org/1998/Math/MathML", "type": "literal", "value": "<math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\" alttext=\"{\\displaystyle E=mc^{2}}\">\n <semantics>\n <mrow class=\"MJX-TeXAtom-ORD\">\n <mstyle displaystyle=\"true\" scriptlevel=\"0\">\n <mi>E</mi>\n <mo>=</mo>\n <mi>m</mi>\n <msup>\n <mi>c</mi>\n <mrow class=\"MJX-TeXAtom-ORD\">\n <mn>2</mn>\n </mrow>\n </msup>\n </mstyle>\n </mrow>\n <annotation encoding=\"application/x-tex\">{\\displaystyle E=mc^{2}}</annotation>\n </semantics>\n</math>"}, "itemLabel": {"xml:lang": "en", "type": "literal", "value": "mass\u2013energy equivalence"}, "itemDescription": {"xml:lang": "en", "type": "literal", "value": "physical law relating mass to energy"}}]}}, "gas": {"head": {"vars": ["item", "itemLabel", "itemDescription", "formula"]}, "results": {"bindings": [{"item": {"type": "uri", "value": "http://www.wikidata.org/entity/Q11432"}, "formula": {"datatype": "http://www.w3.org/1998/Math/MathML", "type": "literal", "value": "<math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\" alttext=\"{\\displaystyle PV=nRT}\">\n <semantics>\n <mrow class=\"MJX-TeXAtom-ORD\">\n <mstyle displaystyle=\"true\" scriptlevel=\"0\">\n <mi>P</mi>\n <mi>V</mi>\n <mo>=</mo>\n <mi>n</mi>\n <mi>R</mi>\n <mi>T</mi>\n </mstyle>\n </mrow>\n <annotation encoding=\"application/x-tex\">{\\displaystyle PV=nRT}</annotation>\n </semantics>\n</math>"}, "itemLabel": {"xml:lang": "en", "type": "literal", "value": "gas"}, "itemDescription": {"xml:lang": "en", "type": "literal", "value": "one of the four fundamental states of matter"}}]}}, "pressure": {"head": {"vars": ["item", "itemLabel", "itemDescription", "formula"]}, "results": {"bindings": [{"item": {"type": "uri", "value": "http://www.wikidata.org/entity/Q39552"}, "formula": {"datatype": "http://www.w3.org/1998/Math/MathML", "type": "literal", "value": "<math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\" alttext=\"{\\displaystyle p={\\frac {{\\boldsymbol {e}}_{\\mathrm {n} }\\cdot {\\boldsymbol {F}}}{A}}}\">\n <semantics>\n <mrow class=\"MJX-TeXAtom-ORD\">\n <mstyle displaystyle=\"true\" scriptlevel=\"0\">\n <mi>p</mi>\n <mo>=</mo>\n <mrow class=\"MJX-TeXAtom-ORD\">\n <mfrac>\n <mrow>\n <msub>\n <mrow class=\"MJX-TeXAtom-ORD\">\n <mi mathvariant=\"bold-italic\">e</mi>\n </mrow>\n <mrow class=\"MJX-TeXAtom-ORD\">\n <mrow class=\"MJX-TeXAtom-ORD\">\n <mi mathvariant=\"normal\">n</mi>\n </mrow>\n </mrow>\n </msub>\n <mo>⋅<!-- \u22c5 --></mo>\n <mrow class=\"MJX-TeXAtom-ORD\">\n <mi mathvariant=\"bold-italic\">F</mi>\n </mrow>\n </mrow>\n <mi>A</mi>\n </mfrac>\n </mrow>\n </mstyle>\n </mrow>\n <annotation encoding=\"application/x-tex\">{\\displaystyle p={\\frac {{\\boldsymbol {e}}_{\\mathrm {n} }\\cdot {\\boldsymbol {F}}}{A}}}</annotation>\n </semantics>\n</math>"}, "itemLabel": {"xml:lang": "en", "type": "literal", "value": "pressure"}, "itemDescription": {"xml:lang": "en", "type": "literal", "value": "ratio of force applied over an area"}}]}}, "gravitational potential": {"head": {"vars": ["item", "itemLabel", "itemDescription", "formula"]}, "results": {"bindings": [{"item": {"type": "uri", "value": "http://www.wikidata.org/entity/Q1544012"}, "formula": {"datatype": "http://www.w3.org/1998/Math/MathML", "type": "literal", "value": "<math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\" alttext=\"{\\displaystyle U=-{\\frac {GMm}{r}}}\">\n <semantics>\n <mrow class=\"MJX-TeXAtom-ORD\">\n <mstyle displaystyle=\"true\" scriptlevel=\"0\">\n <mi>U</mi>\n <mo>=</mo>\n <mo>−<!-- \u2212 --></mo>\n <mrow class=\"MJX-TeXAtom-ORD\">\n <mfrac>\n <mrow>\n <mi>G</mi>\n <mi>M</mi>\n <mi>m</mi>\n </mrow>\n <mi>r</mi>\n </mfrac>\n </mrow>\n </mstyle>\n </mrow>\n <annotation encoding=\"application/x-tex\">{\\displaystyle U=-{\\frac {GMm}{r}}}</annotation>\n </semantics>\n</math>"}, "itemLabel": {"xml:lang": "en", "type": "literal", "value": "gravitational potential"}}]}}, "frequency": {"head": {"vars": ["item", "itemLabel", "itemDescription", "formula"]}, "results": {"bindings": [{"item": {"type": "uri", "value": "http://www.wikidata.org/entity/Q11652"}, "formula": {"datatype": "http://www.w3.org/1998/Math/MathML", "type": "literal", "value": "<math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\" alttext=\"{\\displaystyle f={\\frac {1}{T}}}\">\n <semantics>\n <mrow class=\"MJX-TeXAtom-ORD\">\n <mstyle displaystyle=\"true\" scriptlevel=\"0\">\n <mi>f</mi>\n <mo>=</mo>\n <mrow class=\"MJX-TeXAtom-ORD\">\n <mfrac>\n <mn>1</mn>\n <mi>T</mi>\n </mfrac>\n </mrow>\n </mstyle>\n </mrow>\n <annotation encoding=\"application/x-tex\">{\\displaystyle f={\\frac {1}{T}}}</annotation>\n </semantics>\n</math>"}, "itemLabel": {"xml:lang": "en", "type": "literal", "value": "frequency"}, "itemDescription": {"xml:lang": "en", "type": "literal", "value": "inverse of period duration of a periodic phenomenon"}}]}}, "free fall": {"head": {"vars": ["item", "itemLabel", "itemDescription", "formula"]}, "results": {"bindings": [{"item": {"type": "uri", "value": "http://www.wikidata.org/entity/Q140028"}, "formula": {"datatype": "http://www.w3.org/1998/Math/MathML", "type": "literal", "value": "<math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\" alttext=\"{\\displaystyle v(t)=-gt+v_{0}}\">\n <semantics>\n <mrow class=\"MJX-TeXAtom-ORD\">\n <mstyle displaystyle=\"true\" scriptlevel=\"0\">\n <mi>v</mi>\n <mo stretchy=\"false\">(</mo>\n <mi>t</mi>\n <mo stretchy=\"false\">)</mo>\n <mo>=</mo>\n <mo>−<!-- \u2212 --></mo>\n <mi>g</mi>\n <mi>t</mi>\n <mo>+</mo>\n <msub>\n <mi>v</mi>\n <mrow class=\"MJX-TeXAtom-ORD\">\n <mn>0</mn>\n </mrow>\n </msub>\n </mstyle>\n </mrow>\n <annotation encoding=\"application/x-tex\">{\\displaystyle v(t)=-gt+v_{0}}</annotation>\n </semantics>\n</math>"}, "itemLabel": {"xml:lang": "en", "type": "literal", "value": "free fall"}, "itemDescription": {"xml:lang": "en", "type": "literal", "value": "motion of a body where its weight is the only force acting upon it; any motion of a body where gravity is the only force acting upon it"}}]}}, "Hooke's law": {"head": {"vars": ["item", "itemLabel", "itemDescription", "formula"]}, "results": {"bindings": [{"item": {"type": "uri", "value": "http://www.wikidata.org/entity/Q170282"}, "formula": {"datatype": "http://www.w3.org/1998/Math/MathML", "type": "literal", "value": "<math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\" alttext=\"{\\displaystyle F=k\\Delta l}\">\n <semantics>\n <mrow class=\"MJX-TeXAtom-ORD\">\n <mstyle displaystyle=\"true\" scriptlevel=\"0\">\n <mi>F</mi>\n <mo>=</mo>\n <mi>k</mi>\n <mi mathvariant=\"normal\">Δ<!-- \u0394 --></mi>\n <mi>l</mi>\n </mstyle>\n </mrow>\n <annotation encoding=\"application/x-tex\">{\\displaystyle F=k\\Delta l}</annotation>\n </semantics>\n</math>"}, "itemLabel": {"xml:lang": "en", "type": "literal", "value": "Hooke's law"}, "itemDescription": {"xml:lang": "en", "type": "literal", "value": "principle of physics that states that the force (F) needed to extend or compress a spring by some distance X scales linearly with respect to that distance"}}]}}, "gravitational force": {"head": {"vars": ["item", "itemLabel", "itemDescription", "formula"]}, "results": {"bindings": [{"item": {"type": "uri", "value": "http://www.wikidata.org/entity/Q11412"}, "formula": {"datatype": "http://www.w3.org/1998/Math/MathML", "type": "literal", "value": "<math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\" alttext=\"{\\displaystyle {\\vec {F}}_{g}=-{\\frac {Gm_{1}m_{2}}{r^{2}}}{\\hat {r}}}\">\n <semantics>\n <mrow class=\"MJX-TeXAtom-ORD\">\n <mstyle displaystyle=\"true\" scriptlevel=\"0\">\n <msub>\n <mrow class=\"MJX-TeXAtom-ORD\">\n <mrow class=\"MJX-TeXAtom-ORD\">\n <mover>\n <mi>F</mi>\n <mo stretchy=\"false\">→<!-- \u2192 --></mo>\n </mover>\n </mrow>\n </mrow>\n <mrow class=\"MJX-TeXAtom-ORD\">\n <mi>g</mi>\n </mrow>\n </msub>\n <mo>=</mo>\n <mo>−<!-- \u2212 --></mo>\n <mrow class=\"MJX-TeXAtom-ORD\">\n <mfrac>\n <mrow>\n <mi>G</mi>\n <msub>\n <mi>m</mi>\n <mrow class=\"MJX-TeXAtom-ORD\">\n <mn>1</mn>\n </mrow>\n </msub>\n <msub>\n <mi>m</mi>\n <mrow class=\"MJX-TeXAtom-ORD\">\n <mn>2</mn>\n </mrow>\n </msub>\n </mrow>\n <msup>\n <mi>r</mi>\n <mrow class=\"MJX-TeXAtom-ORD\">\n <mn>2</mn>\n </mrow>\n </msup>\n </mfrac>\n </mrow>\n <mrow class=\"MJX-TeXAtom-ORD\">\n <mrow class=\"MJX-TeXAtom-ORD\">\n <mover>\n <mi>r</mi>\n <mo stretchy=\"false\">^<!-- ^ --></mo>\n </mover>\n </mrow>\n </mrow>\n </mstyle>\n </mrow>\n <annotation encoding=\"application/x-tex\">{\\displaystyle {\\vec {F}}_{g}=-{\\frac {Gm_{1}m_{2}}{r^{2}}}{\\hat {r}}}</annotation>\n </semantics>\n</math>"}, "itemLabel": {"xml:lang": "en", "type": "literal", "value": "gravity"}, "itemDescription": {"xml:lang": "en", "type": "literal", "value": "fundamental force attracting uneven distribution of masses together"}}]}}, "Pythagorean theorem": {"head": {"vars": ["item", "itemLabel", "itemDescription", "formula"]}, "results": {"bindings": [{"item": {"type": "uri", "value": "http://www.wikidata.org/entity/Q11518"}, "formula": {"datatype": "http://www.w3.org/1998/Math/MathML", "type": "literal", "value": "<math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\" alttext=\"{\\displaystyle c^{2}=a^{2}+b^{2}}\">\n <semantics>\n <mrow class=\"MJX-TeXAtom-ORD\">\n <mstyle displaystyle=\"true\" scriptlevel=\"0\">\n <msup>\n <mi>c</mi>\n <mrow class=\"MJX-TeXAtom-ORD\">\n <mn>2</mn>\n </mrow>\n </msup>\n <mo>=</mo>\n <msup>\n <mi>a</mi>\n <mrow class=\"MJX-TeXAtom-ORD\">\n <mn>2</mn>\n </mrow>\n </msup>\n <mo>+</mo>\n <msup>\n <mi>b</mi>\n <mrow class=\"MJX-TeXAtom-ORD\">\n <mn>2</mn>\n </mrow>\n </msup>\n </mstyle>\n </mrow>\n <annotation encoding=\"application/x-tex\">{\\displaystyle c^{2}=a^{2}+b^{2}}</annotation>\n </semantics>\n</math>"}, "itemLabel": {"xml:lang": "en", "type": "literal", "value": "Pythagorean theorem"}, "itemDescription": {"xml:lang": "en", "type": "literal", "value": "relation in Euclidean geometry among the three sides of a right triangle"}}]}}, "speed": {"head": {"vars": ["item", "itemLabel", "itemDescription", "formula"]}, "results": {"bindings": [{"item": {"type": "uri", "value": "http://www.wikidata.org/entity/Q3711325"}, "formula": {"datatype": "http://www.w3.org/1998/Math/MathML", "type": "literal", "value": "<math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\" alttext=\"{\\displaystyle v=s/t}\">\n <semantics>\n <mrow class=\"MJX-TeXAtom-ORD\">\n <mstyle displaystyle=\"true\" scriptlevel=\"0\">\n <mi>v</mi>\n <mo>=</mo>\n <mi>s</mi>\n <mrow class=\"MJX-TeXAtom-ORD\">\n <mo>/</mo>\n </mrow>\n <mi>t</mi>\n </mstyle>\n </mrow>\n <annotation encoding=\"application/x-tex\">{\\displaystyle v=s/t}</annotation>\n </semantics>\n</math>"}, "itemLabel": {"xml:lang": "en", "type": "literal", "value": "speed"}, "itemDescription": {"xml:lang": "en", "type": "literal", "value": "magnitude of velocity of motion"}}]}}, "ideal gas law": {"head": {"vars": ["item", "itemLabel", "itemDescription", "formula"]}, "results": {"bindings": [{"item": {"type": "uri", "value": "http://www.wikidata.org/entity/Q191785"}, "formula": {"datatype": "http://www.w3.org/1998/Math/MathML", "type": "literal", "value": "<math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\" alttext=\"{\\displaystyle PV=Nk_{\\mathrm {B} }T}\">\n <semantics>\n <mrow class=\"MJX-TeXAtom-ORD\">\n <mstyle displaystyle=\"true\" scriptlevel=\"0\">\n <mi>P</mi>\n <mi>V</mi>\n <mo>=</mo>\n <mi>N</mi>\n <msub>\n <mi>k</mi>\n <mrow class=\"MJX-TeXAtom-ORD\">\n <mrow class=\"MJX-TeXAtom-ORD\">\n <mi mathvariant=\"normal\">B</mi>\n </mrow>\n </mrow>\n </msub>\n <mi>T</mi>\n </mstyle>\n </mrow>\n <annotation encoding=\"application/x-tex\">{\\displaystyle PV=Nk_{\\mathrm {B} }T}</annotation>\n </semantics>\n</math>"}, "itemLabel": {"xml:lang": "en", "type": "literal", "value": "ideal gas law"}, "itemDescription": {"xml:lang": "en", "type": "literal", "value": "equation of state of a hypothetical ideal gas; approximation of the behavior of many gases under many conditions (although it has several limitations)"}}, {"item": {"type": "uri", "value": "http://www.wikidata.org/entity/Q191785"}, "formula": {"datatype": "http://www.w3.org/1998/Math/MathML", "type": "literal", "value": "<math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\" alttext=\"{\\displaystyle PV=nRT}\">\n <semantics>\n <mrow class=\"MJX-TeXAtom-ORD\">\n <mstyle displaystyle=\"true\" scriptlevel=\"0\">\n <mi>P</mi>\n <mi>V</mi>\n <mo>=</mo>\n <mi>n</mi>\n <mi>R</mi>\n <mi>T</mi>\n </mstyle>\n </mrow>\n <annotation encoding=\"application/x-tex\">{\\displaystyle PV=nRT}</annotation>\n </semantics>\n</math>"}, "itemLabel": {"xml:lang": "en", "type": "literal", "value": "ideal gas law"}, "itemDescription": {"xml:lang": "en", "type": "literal", "value": "equation of state of a hypothetical ideal gas; approximation of the behavior of many gases under many conditions (although it has several limitations)"}}]}}}}