An inclined plane is bent in such a way that the vertical cross-section is given by y = x 2 4 where y is in vertical and x in horizontal direction. If the upper surface of this curved plane is rough w

Question

An inclined plane is bent in such a way that the vertical cross-section is given by y = x 2 4 where y is in vertical and x in horizontal direction. If the upper surface of this curved plane is rough with coefficient of friction μ = 0 . 5 , the maximum height in cm at which a stationary block will not slip downward is________ cm .

TestHub · Accepted Answer

At maximum ht. block will experience maximum friction force. Therefore if at this height slope of the tangent is $\tan θ,$ then $θ =$ Angle of repose

$∴ \tan θ = \frac{d y}{d x} = \frac{2 x}{4} = \frac{x}{2} = 0.5$

$\Rightarrow x = 1$ and therefore $y = \frac{x^{2}}{4} = 0.25 m$

$= 25 cm$

$∴$ Answer is $25 cm$

(Assuming that $x$ & $y$ in the equation are given in meter)

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