Conservative ForcesPath DependenceGravitational WorkElastic WorkReversible ProcessClosed PathNonconservative ForceConservative ForcesConservative ForcesPath DependencePath DependenceWhat happens to work as a What happens to work as a rollercoaster goes down hill rollercoaster goes down hill then up again?then up again?What if the roller coaster What if the roller coaster took a less steep path?took a less steep path?Gravitational WorkGravitational WorkThe work done by the force of gravity only depends The work done by the force of gravity only depends on the vertical distance.on the vertical distance.dF = mghmghdmgdFW )sin(hmghyymgrdFW )(21The path taken doesn’t mattery2y1Elastic WorkElastic WorkThe elastic force exerted by The elastic force exerted by a spring becomes work.a spring becomes work.•WW = = (1/2) (1/2) kxkx22 •The work done by the spring The work done by the spring as it compresses is negative.as it compresses is negative.Like gravity the path taken Like gravity the path taken to the end doesn’t matter.to the end doesn’t matter.-yWs = ky2Fs = -k(-y)Reversible ProcessReversible ProcessIf an object is acted on by gravity or elastic force has If an object is acted on by gravity or elastic force has its path reversed the work done is the opposite sign.its path reversed the work done is the opposite sign.This represents a This represents a reversiblereversible process. process.y1F = mghmghyymgdFW )(12y2Closed PathClosed PathIf the work done by a force doesn’t depend on the If the work done by a force doesn’t depend on the path it is a path it is a conservativeconservative force. force.Conservative forces do no work on a closed path.Conservative forces do no work on a closed path.From 1 to 2, the path A or B doesn’t matterFrom 1 to 2 and back to 1, the path A then the reverse path B gives no workNonconservative ForceNonconservative ForceNot all forces are conservative.Not all forces are conservative.In particular, friction and drag are not conservative.In particular, friction and drag are not conservative.nextNegative work is done by friction to get here Negative work is also done returning the boxF = FNddF =
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