Help in mechanics!!

in the given figure:

the two planks are equally inclined at an angle $\theta$ with the horizontal.

three identical cylinders, which are in contact with each other are arranged in the shown way.

Find the critical angle $\theta_c$ such that the system doesn't collapse.

#Equilibrium #Mechanics #HelpMe! #MechanicalSystem #Rotationalmechanics

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Comments

@Ronak Agarwal @deepanshu gupta @Satvik Golechha @Adarsh Kumar @satyendra kumar sir @Michael Mendrin sir could you put some light?

Aritra Jana - 6 years, 6 months ago

You may add @shubhendra singh

Parth Lohomi - 6 years, 5 months ago

Put a straight line over the planks which also touches the top cylinder. You will get a triangle. The minimum angle made by planks with the base for which this big triangle is similar to the equilateral triangle formed by joining the centers of the cylinders, is the critical angle.

Anurag Roy - 6 years, 6 months ago

could you explain as to why this will hold true?

thanks

Aritra Jana - 6 years, 6 months ago

Form an equilateral triangle by joining the centres of the cylinder. The triangle is always equilateral if they touch each other. So, the system is no more stable if the equilateral triangle formation breaks. The triangle thus have angles equal to 60 degree. Now two sides of the triangle and the two planks form a parallelogram. Agree? So the angle between the planks is 60 too.from here i think you can easily find theta (c) which should be 60 too. Please do verify with others. If i miss anything, then i might be wrong with the answer. Or do you know the answer already? Is it 60?

Anurag Roy - 6 years, 6 months ago

So the answer should be 60 degree if i aam not wrong.

Anurag Roy - 6 years, 6 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}`	$\boxed{123}$