- #1
skateza
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A thin, unirform rod (I=1/3ML^2) of length L and mass M is pivoted about one end. A small metal ball of mass m=2M is attached to the road a distance d from the pivot. The rod and ball are realeased from rest in a horizontal position and allowed to swing downward without friction or air resistance.
a) show that when the rod reaches the vertical position, the speed of its tip is:
v = \sqrt{3gL}\sqrt{(1 + 4(d/L))/(1 + 6(d/L)^{2})}
b) At what finite value of d/L is the speed of the rod the same as it is for d=0? (This value of d/L is the center of percussion, or "sweet spot" of the rod.)
For part a i know its Ei = Ef, but I am not sure what you should be using to calculate it..
The rod has Ei = MgL, and Ef=1/2I\omega^{2} + Mg(L/2) But i don't know what i should calculate for the ball, potential at the top and rotational kinetic at the bottom?
i haven't even looked at part b yet.
a) show that when the rod reaches the vertical position, the speed of its tip is:
v = \sqrt{3gL}\sqrt{(1 + 4(d/L))/(1 + 6(d/L)^{2})}
b) At what finite value of d/L is the speed of the rod the same as it is for d=0? (This value of d/L is the center of percussion, or "sweet spot" of the rod.)
For part a i know its Ei = Ef, but I am not sure what you should be using to calculate it..
The rod has Ei = MgL, and Ef=1/2I\omega^{2} + Mg(L/2) But i don't know what i should calculate for the ball, potential at the top and rotational kinetic at the bottom?
i haven't even looked at part b yet.
