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## QuestionPhysicsClass 11

Calculate the power of an engine , which can just pull a train of mass 5000 quintals up an incline of 1 in 50 at the rate of $${54}{k}{m}/{h}$$ . The resistance due to friction is$${0.8}{N}/\text{quintal}$$. Take $${g}={9.8}{m}/{s}^{{{2}}}$$ .

Here , power , $${P}'=?{M}={5000}\text{quintals}={5}\times{10}^{{{5}}}{k}{g}$$
$${\sin{\theta}}=\frac{{{1}}}{{{50}}},{v}={54}{k}{m}/{h}=\frac{{{54}\times{1000}}}{{{60}\times{60}}}={m}{s}^{{-{1}}}={15}{m}{s}^{{-{1}}}$$
Force of friction , $${F}={0.8}{N}/\text{quintal}={0.8}\times{5000}{N}={4000}{N}$$
$${P}'=\frac{{{W}}}{{{t}}}={\left({m}{g}{\sin{\theta}}+{F}\right)}\times\frac{{{S}}}{{{t}}}={\left({m}{g}{\sin{\theta}}+{F}\right)}\times{v}$$
$${P}'={\left({5}\times{10}^{{{5}}}\times{9.8}\times\frac{{{1}}}{{{50}}}+{4000}\right)}{15}$$
$${P}'={\left({98000}+{4000}\right)}\times{5}={1530000}{W}={1530}{k}{m}$$ .