(16) Conservative and Non-Conservative Forces

(16) Conservative and Non-Conservative Forces - Lecture 16...

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Lecture 16 Conservative and Non-Conservative Forces Examples.
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ACT: Falling objects Three objects of mass m aredropped from a height h. Onefalls straight down, one slides down a frictionless inclineand one swings at theend of a pendulum. What is therelationship between their speeds when they reach theground? h v F v P v I A. v F > v I > v P B. v F > v P > v I C. v F = v I = v P DEMO: Two tracks
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In all three cases, the only forcedoing work is gravity mechanical energy is conserved. Samefinal speed i 0 E mgh = + 2 f 1 0 2 E mv = +
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Oscillations A glider of mass m = 0.5 kg on a horizontal frictionless surface is attached to a spring with k = 200 N/m. Theglider is pulled 3 cm away from theequilibrium position and released. Find its speed when thespring has been compressed 1 cm. x 2 = 1 cm x = 0 x 1 = 3 cm
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A glider of mass m = 0.5 kg on a horizontal frictionless surfaceis attached to a spring with k = 200 N/m. Theglider is pulled 3 cm away from theequilibrium position and released. Find its speed when thespring has been compressed 1 cm. x 2 = 1 cm x = 0 x 1 = 3 cm 2 2 1 1 1 1 1 2 2 E mv kx = + 2 2 2 2 2 1 1 2 2 E mv kx = + 0 2 2 2 1 2 2 1 1 1 2 2 2 kx mv kx = + ( 29 2 2 2 1 2 k v x x m = - ( 29 2 2 2 (200 N/ m) 0.03 0.01 m 0.57 m/ s 0.5 kg = - = Careful with the units DEMO: Glider on a track
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EXAMPLE: Vertical spring A 50-g ball is shot by a vertical spring compressed over a distancex = 2.0 cm. It reaches a height h = 2.5 m abovetheinitial position. Determine the spring constant k. h x
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Mechanical energy of the ball: = + + 2 2 1 1 2 2 E mv mgh kx (with theappropriatechoiceof zero potential energies, seefigure) 2 init ial 1 Bef ore t he shot : ( 0) 2 E kx v = = t op At t he t op: ( 0) E mgh v = = 2 1 2 kx mgh = 2 2 2(0.05 kg)(9.8 m/ s )(2.5 m) 6100 N/ m (0.02 m) k = = h x 1 U g = 0 U el = 0 2 2mgh k x = DEMO: Hopper- popper and ball
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Mechanical energy with non- conservativeforces.
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