Force Warning: You are not logged in. Your IP address will be publicly visible if you make any edits. If you log in or create an account, your edits will be attributed to your username, along with other benefits.Anti-spam check. Do not fill this in! === Kinematic integrals === {{main|Impulse (physics)|l1=Impulse|Mechanical work|Power (physics)}} Forces can be used to define a number of physical concepts by [[integration (calculus)|integrating]] with respect to [[kinematics|kinematic variables]]. For example, integrating with respect to time gives the definition of [[Impulse (physics)|impulse]]:<ref>{{Cite book |title=Engineering Mechanics |first1=Russell C. |last1=Hibbeler |publisher=Pearson Prentice Hall |year=2010 |edition=12th |isbn=978-0-13-607791-6 |page=222 }}</ref> <math display="block">\vec{J}=\int_{t_1}^{t_2}{\vec{F} \, \mathrm{d}t},</math> which by Newton's Second Law must be equivalent to the change in momentum (yielding the [[Impulse momentum theorem]]). Similarly, integrating with respect to position gives a definition for the [[work (physics)|work done]] by a force:<ref name=FeynmanVol1/>{{rp|((13-3))}} <math display="block" qid=Q42213>W= \int_{\vec{x}_1}^{\vec{x}_2} {\vec{F} \cdot {\mathrm{d}\vec{x}}},</math> which is equivalent to changes in [[kinetic energy]] (yielding the [[work energy theorem]]).<ref name=FeynmanVol1/>{{rp|((13-3))}} [[Power (physics)|Power]] ''P'' is the rate of change d''W''/d''t'' of the work ''W'', as the [[trajectory]] is extended by a position change <math> d\vec{x}</math> in a time interval d''t'':<ref name=FeynmanVol1/>{{rp|((13-2))}} <math display="block"> \mathrm{d}W = \frac{\mathrm{d}W}{\mathrm{d}\vec{x}} \cdot \mathrm{d}\vec{x} = \vec{F} \cdot \mathrm{d}\vec{x},</math> so <math display="block">P = \frac{\mathrm{d}W}{\mathrm{d}t} = \frac{\mathrm{d}W}{\mathrm{d}\vec{x}} \cdot \frac{\mathrm{d}\vec{x}}{\mathrm{d}t} = \vec{F} \cdot \vec{v}, </math> with <math qid=Q11465>\vec{v} = \mathrm{d}\vec{x}/\mathrm{d}t</math> the [[velocity]]. Summary: Please note that all contributions to Christianpedia may be edited, altered, or removed by other contributors. If you do not want your writing to be edited mercilessly, then do not submit it here. You are also promising us that you wrote this yourself, or copied it from a public domain or similar free resource (see Christianpedia:Copyrights for details). Do not submit copyrighted work without permission! Cancel Editing help (opens in new window) Discuss this page