Editing Newton's laws of motion (section)

==Work and energy==
The concept of [[energy]] was developed after Newton's time, but it has become an inseparable part of what is considered "Newtonian" physics. Energy can broadly be classified into [[kinetic energy|kinetic]], due to a body's motion, and [[potential energy|potential]], due to a body's position relative to others. [[Thermal energy]], the energy carried by heat flow, is a type of kinetic energy not associated with the macroscopic motion of objects but instead with the movements of the atoms and molecules of which they are made. According to the [[work-energy theorem]], when a force acts upon a body while that body moves along the line of the force, the force does ''work'' upon the body, and the amount of work done is equal to the change in the body's kinetic energy.{{refn|group=note|Treatments can be found in, e.g., Chabay et al.<ref>{{Cite journal|last1=Chabay|first1=Ruth|author-link=Ruth Chabay|last2=Sherwood|first2=Bruce|last3=Titus|first3=Aaron|date=July 2019|title=A unified, contemporary approach to teaching energy in introductory physics|journal=[[American Journal of Physics]]|language=en|volume=87|issue=7|pages=504–509|doi=10.1119/1.5109519|bibcode=2019AmJPh..87..504C |s2cid=197512796 |issn=0002-9505|doi-access=free}}</ref> and McCallum et al.<ref>{{Cite book|last1=Hughes-Hallett|first1=Deborah|url=https://www.worldcat.org/oclc/794034942|title=Calculus: Single and Multivariable|last2=McCallum|first2=William G.|last3=Gleason|first3=Andrew M.|last4=Connally|first4=Eric|date=2013|publisher=Wiley|isbn=978-0-470-88861-2|edition=6th|location=Hoboken, NJ|oclc=794034942|display-authors=3|author-link=Deborah Hughes Hallett|author-link2=William G. McCallum|author-link3=Andrew M. Gleason}}</ref>{{Rp|page=449}}}} In many cases of interest, the net work done by a force when a body moves in a closed loop — starting at a point, moving along some trajectory, and returning to the initial point — is zero. If this is the case, then the force can be written in terms of the [[gradient]] of a function called a [[scalar potential]]:<ref name="Boas" />{{Rp|page=303}}
<math display="block">\mathbf{F} = -\mathbf{\nabla}U \, .</math>
This is true for many forces including that of gravity, but not for friction; indeed, almost any problem in a mechanics textbook that does not involve friction can be expressed in this way.<ref name="hand-finch" />{{Rp|page=19}} The fact that the force can be written in this way can be understood from the [[conservation of energy]]. Without friction to dissipate a body's energy into heat, the body's energy will trade between potential and (non-thermal) kinetic forms while the total amount remains constant. Any gain of kinetic energy, which occurs when the net force on the body accelerates it to a higher speed, must be accompanied by a loss of potential energy. So, the net force upon the body is determined by the manner in which the potential energy decreases.