237_Physics ProblemsTechnical Physics

237_Physics ProblemsTechnical Physics - Chapter 8 k = 2.50...

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Chapter 8 239 P8.56 k 250 10 4 . N m , m = 25 0 . kg x A =− 0100 m , UU g x s x = = == 0 0 0 (a) EK U U Ag As A mech =+ + Em g x k x AA mech + 0 1 2 2 E E mech 2 mech kg m s m ±Nm ±m J J J + = 25 0 9 80 0 100 1 2 24 5 125 100 4 2 .. . . bg ej af (b) Since only conservative forces are involved, the total energy of the child-pogo-stick-Earth system at point C is the same as that at point A . KU U U Cg Cs CAg A ++= ++ : 0 250 980 0 0 245 125 + +=− + . kg m s J J 2 x C x C = 0410 m (c) KU U KU U Bg Bs BAg A : 1 2 25 0 0 0 0 24 5 125 2 kg J J v B ++=+− + v B = 284 . m s (d) K and v are at a maximum when aF m 0 (i.e., when the magnitude of the upward spring force equals the magnitude of the downward gravitational force). This occurs at x < 0 where kx mg = or x = × 25 0 9 8 980 10 4 3 . . kg m s Nm m 2 Thus, KK = max at x m m (e) U U U U A g x sA s x max . .
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