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

Question

An inclined plane is bent in such a way that the vertical cross-section is given by y = 4 x 2 ​ 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.

$∴ tan θ = \frac{dy}{dx} = \frac{2 x}{4} = \frac{x}{2} = 0.5$

$\Rightarrow x = 1$ 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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