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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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 – Anish Puthuraya · 2 years, 4 months ago

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– Ch Nikhil · 1 year, 2 months ago

Why are there no forces at the hinge joining the 2 sticks ??Log in to reply

– Anish Puthuraya · 1 year, 2 months ago

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

– Ch Nikhil · 1 year, 2 months ago

Got it ! Thanks a lot !!Log in to reply

– Mardokay Mosazghi · 2 years, 4 months ago

Nice explanationLog in to reply

do you know any good book with exersises in rotational dynamics ; – Aris Nikolaidis · 1 year, 9 months ago

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– Pranjal Jain · 1 year, 9 months ago

Try IE Irodov or KrotovLog in to reply