https://ejercicios-fyq.com/ Ejercicios Resueltos, Situaciones de aprendizaje y VÍDEOS de Física y Química para Secundaria y Bachillerato es SPIP - www.spip.net https://ejercicios-fyq.com/local/cache-vignettes/L144xH25/siteon0-da713.png?1758361862 https://ejercicios-fyq.com/ 25 144 https://ejercicios-fyq.com/Principle-of-dimensional-homogeneity-8304 https://ejercicios-fyq.com/Principle-of-dimensional-homogeneity-8304 2024-09-11T10:46:47Z text/html es F_y_Q Dimensions SOLVED <p>What is the principle of dimensional homogeneity?</p> - <a href="https://ejercicios-fyq.com/Units-and-magnitudes" rel="directory">Units and magnitudes</a> / <a href="https://ejercicios-fyq.com/Dimensions" rel="tag">Dimensions</a>, <a href="https://ejercicios-fyq.com/SOLVED" rel="tag">SOLVED</a> <div class='rss_texte'><p>What is the <i>principle of dimensional homogeneity</i>?</p></div> <hr /> <div <div class='rss_ps'><p>This principle states that equations relating physical quantities must be consistent, meaning that the same dimensions must appear on both sides of the equation. The best way to understand this is through an example. <br/> <br/> The speed at which an object moves under the influence of acceleration is: <br/> <br/> <img src='https://ejercicios-fyq.com/local/cache-TeX/e0b460db1a312f718d70061752740edb.png' style="vertical-align:middle;" width="117" height="19" alt="\color[RGB]{2,112,20}{\bm{v = v_0 + at}}" title="\color[RGB]{2,112,20}{\bm{v = v_0 + at}}" /> (Ec. 1) <br/> <br/> Speed is the ratio of distance to the time taken to cover it. In terms of dimensions, it is expressed as: <br/> <br/> <img src='https://ejercicios-fyq.com/local/cache-TeX/ea54684dba160033962f928c8fcfaee1.png' style="vertical-align:middle;" width="88" height="55" alt="\color[RGB]{0,112,192}{\bm{[v] = \frac{[L]}{[t]}}}" title="\color[RGB]{0,112,192}{\bm{[v] = \frac{[L]}{[t]}}}" /> <br/> <br/> Acceleration is the ratio of the change in speed to the time taken for that change, so it can be expressed as: <br/> <br/> <img src='https://ejercicios-fyq.com/local/cache-TeX/c77f5d751b5213f8ec8fc9dc4121f887.png' style="vertical-align:middle;" width="91" height="55" alt="\color[RGB]{0,112,192}{\bm{[a] = \frac{[L]}{[t]^2}}}" title="\color[RGB]{0,112,192}{\bm{[a] = \frac{[L]}{[t]^2}}}" /> <br/> <br/> If you apply this to equation (Eq. 1), you will have: <br/> <br/> <p class="spip" style="text-align: center;"><img src='https://ejercicios-fyq.com/local/cache-TeX/6b3f5fdd7ad7d86f719f461d86c8bc2e.png' style="vertical-align:middle;" width="388" height="55" alt="\frac{[L]}{[t]} = \frac{[L]}{[t]} + \frac{[L]}{[t]^2}\cdot [t]\ \to\ \color[RGB]{192,0,0}{\bm{\frac{[L]}{[t]} = \frac{[L]}{[t]} + \frac{[L]}{[t]}}}" title="\frac{[L]}{[t]} = \frac{[L]}{[t]} + \frac{[L]}{[t]^2}\cdot [t]\ \to\ \color[RGB]{192,0,0}{\bm{\frac{[L]}{[t]} = \frac{[L]}{[t]} + \frac{[L]}{[t]}}}" /></p> <br/> As you can see, the dimensions are the same on both sides of the equation.</math></p></div> https://ejercicios-fyq.com/Convertion-of-force-units-3441 https://ejercicios-fyq.com/Convertion-of-force-units-3441 2016-01-03T04:58:22Z text/html es F_y_Q Units conversion SOLVED <p>How many newtons of force are represented by ?</p> - <a href="https://ejercicios-fyq.com/Units-and-magnitudes" rel="directory">Units and magnitudes</a> / <a href="https://ejercicios-fyq.com/Units-conversion" rel="tag">Units conversion</a>, <a href="https://ejercicios-fyq.com/SOLVED" rel="tag">SOLVED</a> <div class='rss_texte'><p>How many newtons of force are represented by <img src='https://ejercicios-fyq.com/local/cache-vignettes/L118xH24/1c709f9e4639217ac135b365a0c13cc9-b4596.png?1733130325' style='vertical-align:middle;' width='118' height='24' alt="3\ kg\cdot m\cdot s^{-2}" title="3\ kg\cdot m\cdot s^{-2}" />?</math></p></div> <hr /> <div <div class='rss_ps'><p>Considering Newton's Second Law: <br/> <br/> <img src='https://ejercicios-fyq.com/local/cache-TeX/3eabc93e650d3645cc880c6ec00cbf68.png' style="vertical-align:middle;" width="91" height="15" alt="\color[RGB]{2,112,20}{\bf F =m\cdot a}" title="\color[RGB]{2,112,20}{\bf F =m\cdot a}" /> <br/> <br/> And focusing on the units, you can obtain: <br/> <br/> <img src='https://ejercicios-fyq.com/local/cache-TeX/7f7d2aa8b9a31be874f290623744ef61.png' style="vertical-align:middle;" width="145" height="24" alt="F = kg\cdot m\cdot s^{-2}" title="F = kg\cdot m\cdot s^{-2}" /> <br/> <br/> As you can see, 1 newton is equal to <img src='https://ejercicios-fyq.com/local/cache-TeX/5270109ffcbbbe782d60d86e43202c49.png' style="vertical-align:middle;" width="117" height="24" alt="1\ kg\cdot m\cdot s^{-2}" title="1\ kg\cdot m\cdot s^{-2}" />. This means that the question is representing <b>3 newtons</b> or <b>3 N</b>.</math></p></div> https://ejercicios-fyq.com/Converting-ounces-to-pounds-3433 https://ejercicios-fyq.com/Converting-ounces-to-pounds-3433 2015-12-25T06:26:32Z text/html es F_y_Q Units conversion SOLVED <p>Convert 7 678 ounces to pounds.</p> - <a href="https://ejercicios-fyq.com/Units-and-magnitudes" rel="directory">Units and magnitudes</a> / <a href="https://ejercicios-fyq.com/Units-conversion" rel="tag">Units conversion</a>, <a href="https://ejercicios-fyq.com/SOLVED" rel="tag">SOLVED</a> <div class='rss_texte'><p>Convert 7 678 ounces to pounds.</p></div> <hr /> <div <div class='rss_ps'><p>To convert ounces to pounds, you need to know the conversion factor between ounces and pounds. One pound is equal to 16 ounces. <br/> <br/> <p class="spip" style="text-align: center;"><img src='https://ejercicios-fyq.com/local/cache-TeX/5570be2600c1fe3b8d8b4d6806823001.png' style="vertical-align:middle;" width="405" height="46" alt="7\ 678\ \cancel{oz}\cdot \frac{1\ lb}{16\ \cancel{oz}} = 479.88\ lb\equiv \fbox{\color[RGB]{192,0,0}{\bm{4.8\cdot 10^2\ lb}}}" title="7\ 678\ \cancel{oz}\cdot \frac{1\ lb}{16\ \cancel{oz}} = 479.88\ lb\equiv \fbox{\color[RGB]{192,0,0}{\bm{4.8\cdot 10^2\ lb}}}" /></p> </math></p></div> https://ejercicios-fyq.com/Conversion-of-units-1930 https://ejercicios-fyq.com/Conversion-of-units-1930 2012-11-08T06:23:14Z text/html es F_y_Q Units conversion Temperature units SOLVED <p>a) The normal body temperature is . Express this value in K. <br class='autobr' /> b) If an object has a temperature of 354 K, what is its temperature in Celsius?</p> - <a href="https://ejercicios-fyq.com/Units-and-magnitudes" rel="directory">Units and magnitudes</a> / <a href="https://ejercicios-fyq.com/Units-conversion" rel="tag">Units conversion</a>, <a href="https://ejercicios-fyq.com/Temperature-units" rel="tag">Temperature units</a>, <a href="https://ejercicios-fyq.com/SOLVED" rel="tag">SOLVED</a> <div class='rss_texte'><p>a) The normal body temperature is <img src='https://ejercicios-fyq.com/local/cache-vignettes/L41xH13/19e4988079aaa4352ab58d82e9414d66-e0cd8.png?1733060875' style='vertical-align:middle;' width='41' height='13' alt="37\ ^oC" title="37\ ^oC" />. Express this value in K.</p> <p>b) If an object has a temperature of 354 K, what is its temperature in Celsius?</math></p></div> <hr /> <div <div class='rss_ps'><p>a) The convertion formula form Celsius to Kelvin is: <br/> <br/> <img src='https://ejercicios-fyq.com/local/cache-TeX/7d7955fc25a3426b5c8d274149743a36.png' style="vertical-align:middle;" width="420" height="28" alt="{\color[RGB]{2,112,20}{\bm{K = ^oC + 273}}}\ \to\ (37 + 273)\ K = \fbox{\color[RGB]{192,0,0}{\bf 310 K}}" title="{\color[RGB]{2,112,20}{\bm{K = ^oC + 273}}}\ \to\ (37 + 273)\ K = \fbox{\color[RGB]{192,0,0}{\bf 310 K}}" /> <br/> <br/> b) The convertion formula from Kelvin to Celsius is: <br/> <br/> <img src='https://ejercicios-fyq.com/local/cache-TeX/395a4b64febdef42bf8bbf60144a6050.png' style="vertical-align:middle;" width="435" height="28" alt="{\color[RGB]{2,112,20}{\bm{^oC = K - 273}}}\ \to\ (354 - 273)\ ^oC = \fbox{\color[RGB]{192,0,0}{\bm{81\ ^oC}}}" title="{\color[RGB]{2,112,20}{\bm{^oC = K - 273}}}\ \to\ (354 - 273)\ ^oC = \fbox{\color[RGB]{192,0,0}{\bm{81\ ^oC}}}" /></math></p></div>