Chapter 11., Problem 059 The figure is an overhead view of a thin uniform rod of

Question

Chapter 11., Problem 059 The figure is an overhead view of a thin uniform rod of length 0.666 m and mass M rotating horizontally at angular speed 28.4 rad/s about an axis through its center. A particle of mass M/3 initially attached to one end is ejected from the rod and travels along a path that is perpendicular to the rod at the instant of ejection. If the particles speed vp, is 1.59 m/s greater than the speed or the rod end just after ejection, what is the value of Vp? Number Units the tolerance is +/-2% Click if you would like to Show Work for this question: Open Show Work

Explanation / Answer

centre of mass of rod and insect

cm = [M*0 + M/3 * .333]/(M + M/3)

      = .08325 m from centre of the rod

conservation of momentum

[M + M/3]* v = M*0 + M/3 * (v +1.59)

   4v/3 = v/3 + .53

    v = .53 m/s

so Vp = .53+1.59 = 2.12 m/s

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