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  4. A mass of 4 kg rests on a horizontal plane. The plane is gradually inclined until at an angle φ=15° with the horizontal, the mass just begins to slide. What is the coefficient of static friction between the block and the surface?

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Q. A mass of $4 \,kg$ rests on a horizontal plane. The plane is gradually inclined until at an angle $\phi=15^{\circ}$ with the horizontal, the mass just begins to slide. What is the coefficient of static friction between the block and the surface?

Laws of Motion

Solution:

$m g \sin \theta=f_{s}$
$m g \cos \theta=N ; \tan \theta=\frac{f_{s}}{N}$
But $\left(f_{s}\right)_{\max }=\mu_{s} \cdot N$
or $\mu_{s}=\frac{\left(f_{s}\right)_{\max }}{N}=\tan \theta_{\max }=\tan 15^{\circ}=0.27$
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