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JohanM
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Homework Statement
Consider the rigid beam below, which is loaded by five forces shown. The forces at A and B act to keep the total force on the bar equal to zero and the sum of the moments about point A equal to zero.
a) Find the forces at A and B that satisfy the conditions stated above.
b) Find the sum of the moments about point B.
Homework Equations
[itex]\vec{M} = \vec{r} \times \vec{F}[/itex]
The Attempt at a Solution
For part A, I figured that I can calculate the magnitude of FB by adding all of the moments about point A and separating |Fb|
Force C: creates 0 moment about point A since its direction is towards A (theta=180)
Force D:
[itex]\vec{r} = \left\langle 1000,-200 \right\rangle[/itex]
[itex]\vec{F} = \langle 25 cos(20^\circ), 25 sin(20^\circ) \rangle [/itex]
[itex]\vec{M}=\left| \begin{array}{ccc}\hat{i}&\hat{j}\\1000&-200 \\ 25 cos(20^\circ)&25 sin(20^\circ) \end{array} \right| \approx 3852.04 \hat{k}[/itex]
Force B:
[itex]\vec{r} = \left\langle 1000,-650 \right\rangle[/itex]
[itex]\vec{F} = \langle |\vec{F_{B}}|, 0 \rangle [/itex]
[itex]\vec{M}=\left| \begin{array}{ccc}\hat{i}&\hat{j}\\1000&-650 \\ |\vec{F_{B}}|&0\end{array} \right| = 650 |\vec{F_{B}}| \hat{k}[/itex]
[itex]\sum \vec{M}=O\hat{k}+3852.04...\hat{k}+650|\vec{F_{B}}|\hat{k}=0[/itex]
[itex]|\vec{F_{B}}| \approx -5.92[/itex]
Before I go any further I just want to make sure that I am approaching this correctly... Does it make sense that FB points in the negative x-direction?
Thanks,
Johan
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