Question

An engine of mass one metric ton is ascending on a inclined plane, at an angle $\theta ={\tan }^{-1}\left(\frac{1}{2}\right)$ with horizontal, with a speed of $36km/h$. If the coefficient of friction of surface is $\left(\frac{1}{\sqrt{3}}\right)$ then the power (in watts of engine is):

• A. $94.4\times {10}^3$ watt
• B. $9.44\times {10}^3$ watt
• C. 944 watt
• D. 94.4 watt

Answer 1

Answer: (A)

$94.4\times {10}^3$ watt

P$=(mg\sin \theta +\mu mg\cos \theta )V$
$=(1000\times 9.8\times \frac{1}{\sqrt{5}}+\frac{1}{\sqrt{3}}\times 1000\times 9.8\times \frac{2}{\sqrt{5}})\times 36\times \frac{5}{18}$
$=94.4\times {10}^{3}W$
$\tan \theta =\frac{1}{2}$
$\cos \theta =\frac{2}{\sqrt{5}}$
$\sin \theta =\frac{1}{\sqrt{5}}$