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4-1.Newton's Laws of Motion
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એક ટ્રેન ઢોળાવ વગરના $30 \;m$ ત્રિજ્યાવાળા વર્તુળાકાર ટ્રેક પર $54\; km / h$ ની ઝડપથી દોડી રહી છે. ટ્રેનનું દળ $10^{6}\; kg$ છે. આ હેતુ માટે કેન્દ્રગામી બળ કોના દ્વારા પુરું પાડવામાં આવે છે -ઍન્જિન કે રેલ ? રેલના પાટાનો ઘસારો અટકાવવા માટે ઢોળાવનો કેટલો કોણ કેટલો રાખવો પડે ?
Option A
Option B
Option C
Option D
Solution
Radius of the circular track, $r=3$
Speed of the train, $v=54\, km / h =15 \,m / s$
Mass of the train, $m=10^{6}\, kg$
The centripetal force is provided by the lateral thrust of the rail on the wheel. As per Newton's third law of motion, the wheel exerts an equal and opposite force on the rail.
This reaction force is responsible for the wear and rear of the rail
The angle of banking $\theta$, is related to the radius ( $r$ ) and speed $(v)$ by the relation:
$\tan \theta=\frac{v^{2}}{r g}$
$=\frac{(15)^{2}}{30 \times 10}=\frac{225}{300}$
$\theta=\tan ^{-1}(0.75)=36.87^{\circ}$
Therefore, the angle of banking is about $36.87^{\circ} .$
Speed of the train, $v=54\, km / h =15 \,m / s$
Mass of the train, $m=10^{6}\, kg$
The centripetal force is provided by the lateral thrust of the rail on the wheel. As per Newton's third law of motion, the wheel exerts an equal and opposite force on the rail.
This reaction force is responsible for the wear and rear of the rail
The angle of banking $\theta$, is related to the radius ( $r$ ) and speed $(v)$ by the relation:
$\tan \theta=\frac{v^{2}}{r g}$
$=\frac{(15)^{2}}{30 \times 10}=\frac{225}{300}$
$\theta=\tan ^{-1}(0.75)=36.87^{\circ}$
Therefore, the angle of banking is about $36.87^{\circ} .$
Standard 11
Physics
