Calculating the power required to move a load up a gradiant

[Aquadust]

HI

Any help with this problem would be much appreciated.

I am designing a system in which a cart type machine needs to be able to carry a load up a hill with almost no help from the person pushing, My question is how do I calculate how much power is needed by the motor to move the load.

I know:
Total Load = 40KG
Maximum Incline = 14Degrees
The speed it will travel between is 1-4 MPH


I believe the relevant equations are P=MxGxSIN(Angle)xV
Also I am not sure but J=FxD

D=Distance
F=Force
J=Joules
M=Mass
G=Gravity
V=Velocity
P=Power

I believe its 40x9.81xSin14x1.78m/s = 169w

I just want to make sure this equation is right and if not what equation I need to use. it would be handy to have an equation as the variables are constantly changing.

Many thanks in advance for your help.

 

[PhanthomJay]

Looks OK to me, at 4 mph max speed. 169 w is about a quarter horsepower. Due to inefficiencies in the motor, I'd opt for a half a horse motor.