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A 10 metric ton truck drives up a hilly ...

A 10 metric ton truck drives up a hilly road of gradient 1 in 50 at a speed of `36kmh^(-1)` if the coefficient of kinetic friction between the road and tyres is 0.2, calculate the power delivered by the engine `(g=10ms^(-2))`

Text Solution

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Hint : Weight, W = mg
Component of weight down the incline `=F = mg sin theta`
Frictional force, `F_(r)=mu_(k)mg`
Total force, `F.= mg sin theta+F_(r)`
Power = F.v
Weight of the truck, `mg=10xx10^(3)xx10N=10^(5)N`
Component of weight of the truck down the incline,
`=mg sin theta =10^(5)xx(1)/(50)=2000N`
Frictional force, `F_(r)=mu_(k)mg=0.2xx10^(5)=20,000N`
`"Total force, "F.=mg sin theta +F_(r)=2,000+22,000N`
`"Power"="Force"xx"Velocity"=22,000xx10=22xx10^(4)W`
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