Question

A block slides down an incline plane of $45^{\circ }$ with the horizontal. Starting from rest it covers $10m$ in the first 3 seconds. Find the coefficient of kinetic friction between the two.

• A. 0.58
• B. 0.70
• C. 0.69
• D. 0.66

Answer 1

Answer: (C)

$s=ut+\frac{1}{2}a{t}^2$
$10=\frac{1}{2}\times a\times (3{)}^2$
$\Rightarrow \frac{20}{9}=a$
$\therefore a=g(\sin \theta -\mu \cos \theta )$
$\frac{20}{9}=9.8\left(\frac{1}{\sqrt{2}}-\mu \frac{1}{\sqrt{2}}\right)$
$\Rightarrow \frac{20}{9}=\frac{9.8}{\sqrt{2}}(1-\mu )$
$1-\mu =\frac{20\times 1.41}{9\times 9.8}$
$=\frac{28.2}{88.2}=0.31$
$\mu =0.69$