How Do You Calculate Frictional Force with Multiple Normal Forces?

[amcavoy]

I know that $F_f=\mu N$ where mu is the coefficient of friction. I'm not concerned whether it's kinetic or static now, but I have a problem with the normal force. If I have two normal forces (for example, pushing a mop you have the normal from gravity and the normal from the angle at which the force is applied) how do I figure out the frictional force? Would I add the two normal vectors together? Or is the rule only to use the normal force from gravity?

Thanks,

Alex

 

[hotvette]

Would I add the two normal vectors together?

Yes, you would add them together. Whatever contributes to the force in the normal direction would need to be included. If the mop were on the space station, there'd still be friction if you were pushing on it, although you'd need to be braced against something to do it.

 

[mezarashi]

In fact, there is only ONE normal force to any surface. The surface doesn't care whether the reaction is due to gravity or you pushing on it. All the surface "knows" is that if you push something onto it, it will push back equally as hard (Newton's first law), given the surface doesn't break :P

The method then would be to use force analysis again. With Fgrav going down, Fpush going down, and Fnormal going up. The equation looks something like Fgrav + Fpush - Fnormal = 0. If there are any other forces, add them in. Fnormal will change accordingly, and Fnormal is the force you are looking for in Ffrict = Fnormal x coefficient of friction. ^^

An example of you pulling instead of pushing: Fgrav - Fpull - Fnormal = 0.