An electric train works at power 3000 kW and maintains a constant speed of 160 km h^-1 , on a level track. Calculate the resistance to its motion.
The motor of the electric train needs to output power at 3000 kW to maintain a constant speed of 160 km/h.
Power is the rate at which work is done. Work is the product of force and distance. Power = `(F*d)/t` , but `d/t = v` . This gives `P = F*v` .
A power of 3000 kW is required to maintain a constant speed of 160 km/h. 160 km/h = `160*(1000/3600)` = `400/9` m/s
`3000*10^3 = (400/9)*F`
=> F = `(3000*10^3*9)/400`
=> F = `67.5*10^3` N
The resistance to the motion of the electric train is equal to `67.5*10^3` N