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EEJ MAIN Physics QUESTION #7015
Question 1
A block of mass $m$ is positioned on a surface defined by the vertical cross-section $y = \frac{x^3}{6}$. If the coefficient of static friction is $0.5$, determine the maximum height above the ground at which the block can remain at rest without slipping.
  • $\frac{1}{3} m$
  • $\frac{1}{2} m$
  • $\frac{1}{6} m$✔️
  • $m$
Correct Answer Explanation
To find the maximum height, we use the condition for slipping: $\tan \theta = \mu$. Since $\tan \theta$ is the slope $\frac{dy}{dx}$, we differentiate $y = \frac{x^3}{6}$ to get $\frac{dy}{dx} = \frac{x^2}{2}$. Setting $\frac{x^2}{2} = 0.5$ gives $x = 1$. Substituting $x=1$ back into the original equation $y = \frac{1^3}{6}$ gives $y = \frac{1}{6}$.