Two sticks are connected, with hinges, to each other and to a wall. The bottom stick is horizontal and has length \(L\), and the sticks make an angle of \(\theta\) with each other, as shown in Figure above. If both sticks have the same mass per unit length, \(\rho\), find the horizontal and vertical components of the force that the wall exerts on the top hinge.

Also show that the magnitude goes to infinity for both \(\theta\)→ \(0\) and \(\theta\)→\(\frac{\pi}{2}\)

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## Comments

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In the above figure, I have marked all the forces that are present in the system. Let the masses of the two rods be \(\displaystyle m_1\) and \(\displaystyle m_2\).

Thus,

\[m_1 = \rho L\sec\theta\] \[m_2 = \rho L\]

Considering the torque about the point A,

\[h_1(L\tan\theta) = (m_1+m_2)g\frac{L}{2}\]

\[h_1(L\tan\theta) = \rho L (1+\sec\theta)g\frac{L}{2}\]

\[\boxed{h_1 = \rho\frac{1+\sec\theta}{\tan\theta}\frac{gL}{2}}\]

Ill do the vertical force later..Ill post it as a comment

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Nice explanation

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Why are there no forces at the hinge joining the 2 sticks ??

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There are forces at the hinge joining the sticks, but they are internal forces. So, they cancel each other off..

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do you know any good book with exersises in rotational dynamics ;

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Try IE Irodov or Krotov

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The vertical force can be found using the pivot point B. It is -(rho

lg/2)(1+2sec(theta)).Log in to reply