84 - ?? ?? ? (b) The spring does 31.0 J of work and this...

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84 . (a) To stretch the spring an external force, equal in magnitude to the force of the spring but opposite to its direction, is applied. Since a spring stretched in the positive x direction exerts a force in the negative x direction, the applied force must be F = 52.8 x + 38.4 x 2 , in the + x direction. The work it does is 1.00 1.00 2 2 3 0.50 0.50 52.8 38.4 (52.8 38.4 ) 31.0 J. 2 3 W x x dx x x = + = ? + ? =
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Unformatted text preview: ?? ?? ? (b) The spring does 31.0 J of work and this must be the increase in the kinetic energy of the particle. Its speed is then v K m = = = 2 2 310 217 535 . . . . J kg m s b g (c) The force is conservative since the work it does as the particle goes from any point x 1 to any other point x 2 depends only on x 1 and x 2 , not on details of the motion between x 1 and x 2 ....
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