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phy131studiof15:lectures:chapter14 [2015/10/16 09:27]
mdawber [14.P.042]
phy131studiof15:lectures:chapter14 [2015/10/19 08:33]
mdawber [Hanging sign solution]
Line 116: Line 116:
 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 =====
 +
 +{{f11finalq3fig.png}}
 +
 +$\theta=\tan^{-1}\frac{30}{60}=26.57^{o}$
 +
 +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? =====
  
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