Asked by min
A NON-UNIFORM board of length L and mass M has a center of mass at 5/6L. If the fulcrum is placed at the center of the board and a block of mass m is placed at the right of the board, then where must a block of mass 3m be placed to balance the board?
I assumed new variables for the distances mass m and mass 3m are from the fulcrum, but the non-uniformity/center of mass is throwing me off. Help please?
I assumed new variables for the distances mass m and mass 3m are from the fulcrum, but the non-uniformity/center of mass is throwing me off. Help please?
Answers
Answered by
drwls
You do not have to know how the mass is distributed, only that the center of mass is 5/6 of the way from one end.
Require that the total moment about the fulcrum be zero. The lever arm to the center of mass from the fulcrum will be
L/2 - L/6 = L/3
Let x be the location where the mass 3M is placed on the opposite side of the fulcrum from the center of mass. QWe will measure the distance x from the fulcrum (center of board).
L/3 * M = 3M*x for equilibrium
x = L/9
Require that the total moment about the fulcrum be zero. The lever arm to the center of mass from the fulcrum will be
L/2 - L/6 = L/3
Let x be the location where the mass 3M is placed on the opposite side of the fulcrum from the center of mass. QWe will measure the distance x from the fulcrum (center of board).
L/3 * M = 3M*x for equilibrium
x = L/9
Answered by
min
Gotcha, thank you!
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