17lecture2a08

17lecture2a08 - Physics 2A Lecture 17: Feb 15 Vivek Sharma...

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Physics 2A Lecture 17: Feb 15 Vivek Sharma UCSD Physics
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Elastic Potential Energy 22 1 2 onS 2 1 Work done by man, on spring, to stretch 11 it from : W x x kx kx →= Man extends spring+block from equilibrium position Equilibrium x=0 x Force by to stretch spring by distance x F an x m =k
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Force & Work Done By A Stretched Spring rd 12 3 law Spring exerts on block does negative work when dis restoring fo placed fro rce m xx ⇒→ At another instant when spring “relaxes” (unstretched) then pulls on block x 1 > x 2 & spring does positive work on block which speeds up spring F & displacement are || s G G 22 byS onS el 1 2 11 W= - W 0 kx kx = −<
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Elastic Potential Energy 2 1 efine Elastic Potential Energy U = 2 kx 22 el el 12 1 2 ork done W by spring on blo 11 W 2 ck 2 kx kx U U U =−= = Δ 21 e l decrease tretched spring W & potential U incre s ases xx ⇒> e l elaxed spring increases & potential U decre ases ⇒< If spring is compressed or stretched more, its potential energy U increases el When compressed spring compressed more, W 0 <
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21 Compressed spring displacements negative with respect to reference x = 0 |x | |x | < 2 el 1 U= k Potential energy is ALWAYS posit x 2 ive !
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tot 2 1 W-E Theorem W K -K ⇒= tot el 1 2 If spring force is the that does work on block W= W = U - U only force Combining this with W-E theorem 21 1 tot 1 122 2 K- K K+U U =K U or - +U = 22 11 Explicitly: Conservation of Mechanical Energy E =K+U mv kx mv kx += + in case of frictionless, massless spring
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F spring = - kx Conservation of Mechanical Energy In Spring-Block syst
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Conservation of Mechanical Energy In Spring-Block syst
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In Presence of Additional Forces On Block o tot el ot tot 2 t her 1 her I W= W n presence of additional forces, W-E Theor +W em which do work W & K - K 1 1 other 22 11 e2 l1 K+U+W =K+ Since WU - 2 U 2 U other or mv kx W mv kx ++= + = Work done by all forces other than elastic force equals change in the total mechanical energy E=K+U of system other other If W 0
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This note was uploaded on 05/08/2008 for the course PHYS 2A taught by Professor Hicks during the Winter '07 term at UCSD.

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17lecture2a08 - Physics 2A Lecture 17: Feb 15 Vivek Sharma...

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