## Cart on an inclined slope

Hey guys,

I am trying to figure out which motor to order for a side project of mine. I am trying to push a 1000 pound cart up a 10 degree incline. The cart has four elastomer wheels, and may possible encounter carpeted surfaces. I'm not quite sure what to expect in regards to a coefficient of friction yet on a carpeted surface, but I wanted to check my math a bit to understand if I am approaching this problem correctly:

Coefficient of Friction = Cf
Required Force = Fr
Weight = Fw
Force Normal to Slope = Fn = = Cf*Fw*Cos(10)
Force Parallel to Slope = Fw*Sin(10)

So Fr = [Cf*Fw*cos10] + [Fw*Sin(10)]?

Thanks for any help in advance!

I just wanted to double check if I am doing my statics correctly.
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 The motor power depends on how fast you want to go up the slope eg power = force * velocity. The static force gives you the minimium torque required. This equation.. Force Parallel to Slope = Fw*Sin(10) is correct but I'm not so sure about the friction term. I think what you have used.. Cf*Fw*Cos(10) .. is the friction between wheels and ground. For the driving wheels that force is actually acting up the slope not down it. I think you also need to find the rolling resistance instead. I'm not sure if that's typically the same. Edit: I checked and they are very different. If the wheel doesn't slip no power is dissipated overcoming friction between tyre and ground. You need to use the rolling coefficient instead.
 Thanks for the response. The coefficient of friction method seemed like it was returning really high values. Is the COF based on a surface to surface contact and the rolling resistance is based on a point to surface contact? It seems like that would results in some more reasonable values.

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