Largest fraction of a rope!

Classical Mechanics Level 4

A rope rests on two platforms which are both inclined at an angle θ \theta , as shown. The rope has uniform mass density λ \lambda , and its coefficient of friction with the platforms is μ = 1 \mu=1 . The system has left-right symmetry.

What is the largest possible fraction of the rope that does not touch the platforms?

With F ( θ ) = sin ⁡ θ cos ⁡ θ − sin ⁡ 2 θ F(\theta) = \sin\theta \cos\theta - \sin^2 \theta .

Original Question: Rope between inclines .
F ( θ ) 1 + F ( θ ) \frac{F (\theta)}{1+F (\theta)} F ( θ ) 2 + F ( θ ) \frac{F (\theta)}{2+F (\theta)} F ( θ ) 3 + F ( θ ) \frac{F (\theta)}{3+F (\theta)} None of these

Nishant Rai by Nishant Rai , 25, India

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1 solution

Nishant Rai
May 18, 2015

16 Helpful 0 Interesting 1 Brilliant 0 Confused

can you explain your reasoning

Austin Joseph - 5 years, 5 months ago

very nice sum with a nice solution 🖒🖒liked and upvoted.

rajdeep brahma - 3 years, 4 months ago

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