Need to calculate power expended by the motor

1. The problem statement, all variables and given/known data



i need to calculate the power used up to carry a vehicle with 433mm diameter wheels,mass of 163kg up a slope of 3%. The horizontal distance of the slope is 2.9km. The surface of the slope is asphalt with rolling resistance of 0.22



From the following motor specs:



Rated Power = 1800 W

Nominal Speed = 1060 RPM

Nominal speed= 111 rad/s

Nominal torque = 16.2 Nm

Nominal Torque = 16.2 Nm

Continuous Torque = 42 Nm (5.0 kW)



2. Relevant equations



P = Energy expended(E) / time (T);



where E = mgh*sin(α)



and T = height(H)/ average speed(Vavg);



3. The attempt at a solution



P = mgHsin(α)/ (H/Vavg)



-> The H cancels and are left with



P = mg*Vavg*sin(α)



→ One of the problems i have is i dont know how to find the average velocity but i think:



Nominal speed * radius = m/s



∴Vavg = 111*0.5*433mm = 24m/s



∴ P = 163*9.81*sin(3%)*24

= 20W



→ i am also not sure what to do about the rolling resistance but i think:



Rolling resistance Force(Frr = mg*rolling resistace(Crr))



Frr = 163*9.81*0.22

= 351N



And i know W = F*d



∴W = 351*2.5km = 877.5KJ



and i know P = w/t



and that t = d/s = 2.9Km/24m/s = 120.8s



∴P = W/t = 877.5KJ/120.8 = 7.26KW



Dont know if i should add or subtract from the previous power...



PLEASE HELP ANY1:cry:...



Thanks in advance:smile: