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