## GavinxFiasco one year ago The massless bar, hinged at A, is inclined at an angle θ = 46.0° and subjected to horizontal and vertical forces F1 and F2, as shown. If L1 = 4.00 m, L2 = 1.00 m, F1 = 10 N, and the beam is in static equilibrium, what is the magnitude of F2?

1. GavinxFiasco

2. AllTehMaffs

|dw:1383951629230:dw| Only the components of the force perpendicular to the bar (phi=90, psi=90) produce torque, so sum of the torques $\sum \tau = \big(L_1F_1\sin\theta \big)\sin\phi - L_2F_2 \cos \theta\sin\psi =0$ solve for F2 I think

3. AllTehMaffs

Rewrite $\sum \tau = \big ( L_1 F_1 \sin \theta \big) \sin \varphi-\big ( L_2 F_2 \cos \theta \big) \sin \psi=0$ $F_2=\frac{\big ( L_1 F_1 \sin \theta \big)}{L_2\cos\theta}$ $F_2=F_1\tan\theta\frac{L_1}{L_2}$ makes sense; if theta=0, F2 = 0 because F1 will supply no torque. If theta=90, F1 has to be zero or the function is undefined. hooray!

4. GavinxFiasco

Thanks @AllTehMaffs

5. AllTehMaffs

^_^

6. AllTehMaffs

hmmm - there should be a negative sign there I think. blah :P

7. GavinxFiasco

Aha no it's correct no worries it worked out to be the right answer

8. AllTehMaffs

hooray! ^_^