College Physics

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A rod of mass 4.3 kg and length 4.3 m hangs from a hinge as shown in Figure P9.28. The end of the rod is then given a “kick” so that it is moving at a speed of 2.3 m/s. How high will the rod swing? Express your answer in terms of the angle (in degree) that the rod makes with the vertical.

Hinge --> 0
i
i <-- Steel rod
i
-------> swings this way

  • College Physics -

    w=2.3/4.3= 1 rad per second.

    Now, the moment of Inertia for the rod swinging about an end is... 1/3 ml^2

    initial KE= 1/2 I w^2=1/6 ml^2 figure all that out given m, l

    now, final PE= mgh were h is to the center of mass. Drawing the figure, then

    h+lcosTheta=lor
    h= l(1-cosTheta)
    finally we have
    1/6ml^2=mgl(1-cosTheta)
    L/6g=1-cosTheta
    costheta= 1- 4.3/6g
    theta= arc cos ( above)

    check all this.

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