Sliding Down An Inclined Plane

Classical Mechanics Level 4

A small mass slides down an inclined plane of inclination \(\theta = 60^\circ \) with respect to the horizontal. The acceleration of the block varies as \(a = k x^{2}\), where \(x\) is the distance through which the mass slides down and \(k\) is a constant. The coefficient of friction is 1 when the block covers a distance of \(\sqrt{10}\). Find the value of \(k\).

Details and Assumptions:
Take \(g=10 \text{ m/s}^2\).
Every quantity is in SI unit.


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