 #1
 24
 4
Homework Statement
Homework Equations
The Attempt at a Solution
The moment of inertia before collapse is for each rod:
BEFORE COLLAPSE:[/B]
I_{b} = ∫(L^{2} + x^{2}) dm = m/L ∫(L^{2} + x^{2}) dx = 4/3 * m * L^{2}
We have 8 of these plus the inertia of the mechanism, giving a total I,
I_{t} = 8 * I_{b} + I_{k} = (32/3 * m * + 40/3 * M) * L^2
The energy is thus:
T_{b} = 1/2 * I_{t}* ω_{o}^{2}
AFTER COLLAPSE:
I_{a} = ∫(x^{2}) dm = m/L ∫(x^{2}) dx = 1/3 * m * L^{2}
And the mechanism is the same:
So we have total of:
I_{t_a} = 8 * I_{a} + I_{k} = (8/3 * m * + 40/3 * M) * L^{2}
The energy is now:
T_{a} = 1/2 * I_{t_a} * ω_{o}^{2}
And energy difference must be:
T_{a}  T_{b} = 1/2 * ω_{o}^{2} * m * (8 / 3  32/3) * L^{2} = ω_{o}^{2} * m * 4 * L^{2}
But the solution stated is: ω_{o}^{2} * M * 6 (note the difference in mass symbol)
What am i doing wrong?
Attachments

66.8 KB Views: 490
Last edited: