×

# 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.

Note by Aritra Jana
3 years, 1 month ago

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears 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} $$\boxed{123}$$

Sort by:

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

- 3 years, 1 month 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.

- 3 years, 1 month ago

could you explain as to why this will hold true?

thanks

- 3 years, 1 month 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?

- 3 years, 1 month ago