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# Exercise 2.36 Two sticks and a wall

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 $$\theta$$→$$\frac{\pi}{2}$$

Note by Beakal Tiliksew
3 years, 7 months ago

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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

- 3 years, 7 months ago

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

- 2 years, 5 months ago

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

- 2 years, 5 months ago

Got it ! Thanks a lot !!

- 2 years, 5 months ago

Nice explanation

- 3 years, 7 months ago

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

- 3 years ago

Try IE Irodov or Krotov

- 2 years, 12 months ago