10-31-08LectPHY2048

10-31-08LectPHY2048 - Review Chap 7-11 Work Kinetic Energy...

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Review Chap. 7-11 Work, Kinetic Energy, Potential Energy & the Conservation of Energy ff f f ii i i rx y z y z W F dr Fdx Fdy Fdy =⋅ = + + ∫∫ G G G G The energy transferred to or from an object by a force as the object moves from position to is, F G i r G f r G Kinetic energy of an object of mass m moving with speed v is: 2 1 Km v 2 = The work-kinetic energy theorem relates the change in an objects kinetic energy to the net work done on (or by) the object: fi KK K W Δ =− =
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Near the surface of the earth the work done by gravity when an object changes its height by an amount h is, g Wm g h + if moved in the direction of - if moved in direction opposite An ideal (Hook’s law) spring , that is fixed at one end and has its other end displaced from its equilibrium position by an amount x supplies a restoring force that is given by, s Fk x = − The spring does an amount of work in the displacement of, 2 s 1 Wk x 2 x h g F G g F G s F G equilibrium position + if displacement towards equilibrium - if displacement away from equilibrium
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(gravity) and (spring) are conservative, the force of kinetic friction, , is not (said rather to be dissipative). Consider two distinct positions of an object P and Q. A force acting on the object is said to be conservative if the work done by the force is independent of the path taken in going from P to Q. For conservative forces we can define a potential energy , s F G g F G k f G f i x fi x UU U W F ( x ) d x Δ= = = integral form: differential form: dU(x) F(x) dx =−
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Only changes in potential energy are meaningful. Hence we are free to designate the zero of potential energy as convenient e.g. for gravity: fi f i UUm g ( yy ) =− we can set U i = 0 when the position is y i , then if h is measured from y i (i.e. h = 0 at y i ) we can write, g Um g h = For a spring it makes the most sense to designate the potential energy as zero at the spring’s equilibrium position so that, 2 s 1 Uk x 2 = s U0 = at x0 =
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Conservation of Energy: mech th int WEE E E =Δ =Δ The change in the total energy of a system equals the work done on or by the system: where, mech EU K Δ= Δ + Δ th k Ef d (kinetic friction, f k , constant over the displacement d ) int Eo t h e r (other source or sink of energy internal to the system: e.g. chemical, biochemical, nuclear …) (total mechanical energy)
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m M h h Effectively massless frictionless pulley k μ Example Block of mass M has coefficient of kinetic friction with the floor .
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10-31-08LectPHY2048 - Review Chap 7-11 Work Kinetic Energy...

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