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 $\theta$ → $\frac{\pi}{2}$

#Mechanics #Statics

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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 - 5 years, 9 months ago

Nice explanation

Mardokay Mosazghi - 5 years, 9 months ago

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

CH Nikhil - 4 years, 7 months ago

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

Anish Puthuraya - 4 years, 7 months ago

@Anish Puthuraya – Got it ! Thanks a lot !!

CH Nikhil - 4 years, 7 months ago

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

aris nikolaidis - 5 years, 2 months ago

Try IE Irodov or Krotov

Pranjal Jain - 5 years, 2 months ago

The vertical force can be found using the pivot point B. It is -(rholg/2)(1+2sec(theta)).

Harsh Bhardwaj - 1 year, 8 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$