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phy131studiof15:lectures:chapter14 [2015/10/16 09:27] mdawber [14.P.042] |
phy131studiof15:lectures:chapter14 [2015/10/19 08:32] mdawber [Hanging sign problem] |
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What are the horizontal and vertical components of the force exerted by the hinge on the rod? Take the positive directions to be up and to the right. | What are the horizontal and vertical components of the force exerted by the hinge on the rod? Take the positive directions to be up and to the right. | ||

+ | ===== Hanging sign solution ===== | ||

+ | |||

+ | $\theta=\tan^{-1}\frac{30}{60}=26.57^{o}$ | ||

+ | |||

+ | Vertical forces, up is positive $T\sin\theta+Fh_{y}=m_{sign}g+m_{rod}g$ | ||

+ | |||

+ | Horizontal forces, right is positive $-T\cos\theta+Fh_{x}=0$ | ||

+ | |||

+ | Torques $0.6T\sin\theta=0.8m_{sign}g+0.4m_{rod}g$ | ||

+ | |||

+ | $T=\frac{0.8\times3\times9.8+0.4\times1\times9.8}{0.6\times\sin26.57^{o}}=102.24\mathrm{N}$ | ||

+ | |||

+ | $Fh_{y}=4.981-102.24\sin26.57^{o}=-6.53\mathrm{N}$ | ||

+ | |||

+ | So force points down. | ||

+ | |||

+ | $Fh_{x}=102.24\cos26.57^{o}=91.4\mathrm{N}$ | ||

+ | |||

+ | Force points to the right | ||

===== Will the ladder slip? ===== | ===== Will the ladder slip? ===== | ||