notes8a - Example problem If it takes 4.00 J of work to...

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Unformatted text preview: Example problem If it takes 4.00 J of work to stretch a Hooke’s law spring 10.0 cm from its unstretched length, determine the extra work required to stretch it an additional 10.0 cm. Conservative and Non-conservative Forces Conservative Force: a force for which the work it does on an object does not depend on the path. Gravity is an example. We know we can obtain the work from the relation If the force is conservative, then W=W c and this work can be related to the change in potential energy W = F cos φ ∗ d W c = −Δ U h y m A B C A mg d W = F cos φ d = mgh W = ( mg sin θ ) d = ( mg sin θ ) h sin θ = mgh W = mgh mg mg d d θ B C • Non-conservative Force - a force for which the work done depends on the path- friction- air resistance If both conservative and non-conservative forces act on an object, the work-energy theorem is modified C i f NC i f NC C total W K K W K K W W W − − = − = + = For the case of gravity ) ( ) ( ) ( ) ( i i f f i f i f NC f i i f NC f i i f NC f i C g U K U K U U K K U K W mgy mgy K K W y y mg K K W y y mg W W + − + = − + − = Δ + Δ = + − − = − − − = − = = θ m g N x N m g θ θ f k f k d d i f NC E E W − = If no net non-conservative forces Then, conservation of mechanical energy holds E E E W i f NC = = ⇒ = U K Δ − = Δ Crate on Incline Revisited FBD h W...
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This note was uploaded on 12/10/2011 for the course PHY 1111 taught by Professor Stencil during the Fall '11 term at University of Georgia Athens.

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notes8a - Example problem If it takes 4.00 J of work to...

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