College Physics
posted by Anon .
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

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(1cosTheta)
finally we have
1/6ml^2=mgl(1cosTheta)
L/6g=1cosTheta
costheta= 1 4.3/6g
theta= arc cos ( above)
check all this.
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