Question

A block slides down an incline plane of $45^{\circ}$ with the horizontal. Starting from rest it covers $10 m$ 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)

$s = ut +\frac{1}{2} at ^{2}$
$10=\frac{1}{2} \times a \times(3)^{2}$
$ \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)$
$1-\mu=\frac{20 \times 1.41}{9 \times 9.8}$
$=\frac{28.2}{88.2}=0.31$
$\mu=0.69$