A railway engine weighing 40 metic ton is travelling along a level track at aspeed of 54 km H^(-1) What additional power is required to maintain the same speed up an incline of1 in 49 given mu = 0.1g= 9.8ms^(-2) .

A railway engine weighing 40 metic ton is travelling along a level tra

1.	A railway engine weighing 40 metic ton is travelling along a level track at aspeed of 54 km H^(-1) What additional power is required to maintain the same speed up an incline of1 in 49 given mu = 0.1g= 9.8ms^(-2) .
Answer» Solution :Here ` m =40` metric ton `= 40 xx 10^(3) kg` `UPSILON = 54 km h^(-1) = (54 xx 1000)/(60 xx 60) = 15 ms^(-1)` Now, `cos theta = sqrt(1 - sin^(2) theta) = sqrt(1 - (1//49)^(2)) = 1` Power required on level TRACK ` P_(1) = F xx upsilon = mu mg xx upsilon` Power required up an incline `P_(2) = (mg sin theta + mu mg cos theta) upsilon` Additional power required `P =P_(2) P_(1) = [ mg sin theta + mu mg cos theta - mu mg] upsilon = [ mg sin theta + mu mg xx 1 - mu mg] upsilon = mg sin theta xx upsilon` `=40 xx 10^(3) xx 9.8 xx (1)/(49) xx 15 = 120 xx 10^(3) "watt" = 120 kW`.