Work & Energy Work & Energy Ideas: ch 11Ideas: ch 11Work either adds or subtracts Work either adds or subtracts energy. We’ll only deal with energy. We’ll only deal with mechanical work (not heat)mechanical work (not heat)

Work & EnergyWork & Energy

Energy Transfer: Energy Transfer: Mechanical means: pull, push, etc. Mechanical means: pull, push, etc. Heat: not covered Heat: not covered

Work: positive or negative?Work: positive or negative? W>0 environment does work on the system W>0 environment does work on the system

and energy goes up.and energy goes up. W<0 system does work on the environment W<0 system does work on the environment

and energy goes downand energy goes down

Energy & WorkEnergy & Work

Work = F x Distance , it’s really the Work = F x Distance , it’s really the amount of force acting in the direction the amount of force acting in the direction the object is moving, or W = Fxcosobject is moving, or W = FxcosΘΘ

When there is a variable force, then the When there is a variable force, then the Work done is the area under the Force Work done is the area under the Force vs. distance curve W = Fdxvs. distance curve W = Fdx

Energy & WorkEnergy & Work

Special Case: what about a force acting Special Case: what about a force acting perpendicular to the direction of motion. perpendicular to the direction of motion.

This is “just like” circular motion where a This is “just like” circular motion where a net centripetal force is acting.net centripetal force is acting.

How much work does the centripetal How much work does the centripetal force do?force do?

Energy & WorkEnergy & Work

Potential Energy and conservative forcesPotential Energy and conservative forces We call gravity a conservative force. The work done We call gravity a conservative force. The work done

by gravity is independent of the path taken…..it only by gravity is independent of the path taken…..it only depends on the starting and ending positions. depends on the starting and ending positions.

Spring force/energy is also conservative, does Spring force/energy is also conservative, does not depend on the path, only the starting and not depend on the path, only the starting and ending postionsending postions

Frictional force is not conservative: the work Frictional force is not conservative: the work done by friction does depend on the path. done by friction does depend on the path.

Energy & WorkEnergy & Work

Finding force from Potential EnergyFinding force from Potential Energy W = F W = F ΔΔx = -U (work = -change in potential x = -U (work = -change in potential

energy)energy) U = -FU = -FΔΔxx Or…F = -Or…F = -ΔΔU/U/ΔΔx ….this is the slope of the U x ….this is the slope of the U

vs. x graphvs. x graph