Editing Work (physics) (section)

==Constraint forces==
Constraint forces determine the object's displacement in the system, limiting it within a range. For example, in the case of a [[slope]] plus gravity, the object is ''stuck to'' the slope and, when attached to a taut string, it cannot move in an outwards direction to make the string any 'tauter'. It eliminates all displacements in that direction, that is, the velocity in the direction of the constraint is limited to 0, so that the constraint forces do not perform work on the system.

For a [[mechanical system]],<ref name="goldstein">{{cite book | last=Goldstein | first=Herbert | title=Classical mechanics | publisher=Addison Wesley | publication-place=San Francisco | year=2002 | isbn=978-0-201-65702-9 | oclc=47056311 | edition=3rd}}</ref> constraint forces eliminate movement in directions that characterize the constraint. Thus the [[virtual work]] done by the forces of constraint is zero, a result which is only true if friction forces are excluded.<ref>{{cite book |last1=Rogalski |first1=Mircea S. |title=Advanced University Physics |date=2018 |publisher=Chapman and Hall/CRC |location=Boca Raton |isbn=9781351991988 |edition=2nd}}</ref>

Fixed, frictionless constraint forces do not perform work on the system,<ref name="Feynman">{{cite web |title=The Feynman Lectures on Physics Vol. I Ch. 14: Work and Potential Energy (conclusion) |url=https://feynmanlectures.caltech.edu/I_14.html |website=feynmanlectures.caltech.edu}}</ref> as the angle between the motion and the constraint forces is always [[right angle|90°]].<ref name="Feynman"/> Examples of workless constraints are: rigid interconnections between particles, sliding motion on a frictionless surface, and rolling contact without slipping.<ref>{{cite book |last1=Greenwood |first1=Donald T. |title=Classical dynamics |date=1997 |publisher=Dover Publications |location=Mineola, N.Y. |isbn=9780486138794}}</ref>

For example, in a pulley system like the [[Atwood machine]], the internal forces on the rope and at the supporting pulley do no work on the system. Therefore, work need only be computed for the gravitational forces acting on the bodies. Another example is the [[centripetal force]] exerted ''inwards'' by a string on a ball in uniform [[circular motion]] ''sideways'' constrains the ball to circular motion restricting its movement away from the centre of the circle. This force does zero work because it is perpendicular to the velocity of the ball.

The [[magnetic force]] on a charged particle is {{math|1='''F''' = ''q'''''v''' × '''B'''}}, where {{mvar|q}} is the charge, {{math|'''v'''}} is the velocity of the particle, and {{math|'''B'''}} is the [[magnetic field]]. The result of a [[cross product]] is always perpendicular to both of the original vectors, so {{math|'''F''' ⊥ '''v'''}}. The [[dot product]] of two perpendicular vectors is always zero, so the work {{math|1=''W'' = '''F''' ⋅ '''v''' = 0}}, and the magnetic force does not do work. It can change the direction of motion but never change the speed.