A block of mass $10$ kg slides down an inclined plane that makes an angle of $37°$ with the horizontal. The coefficient of kinetic friction between block and plane is $0.25$. Find the block's acceleration. (Take $g = 10$ m/s², $\sin 37° = 0.6$, $\cos 37° = 0.8$.)
A$2$ m/s²
B$3$ m/s²
C$4$ m/s²
D$5$ m/s²
Answer & Solution
Correct answer: C. $4$ m/s²
Component of gravity along the incline drives the block; friction opposes it.
$a = g(\sin\theta - \mu_k \cos\theta) = 10(0.6 - 0.25 \times 0.8) = 10 \times 0.4 = 4$ m/s².
Forgetting the friction term gives $g \sin\theta = 6$ m/s² — that's why $5$ (option D, halfway between) looks tempting.
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