Is my statics approach correct for pushing a 1000lb cart up an inclined slope?

[KramerKotz]

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.

 

[CWatters]

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.

 

[KramerKotz]

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.