Pushing a lawnmower

1. The problem statement, all variables and given/known data
Consider a lawnmower of weight w which can slide across a horizontal surface with a coefficient of friction [tex]\mu[/tex]. In this problem the lawnmower is pushed using a massless handle, which makes an angle theta with the horizontal. Assume that [tex]F_{h}[/tex], the force exerted by the handle, is parallel to the handle.

Take the positive x direction to be to the right and the postive y direction to be upward.

A:
Find the magnitude, [tex]F_{h}[/tex] of the force required to slide the lawnmower over the ground at constant speed by pushing the handle.

B:

The solution for [tex]F_{h}[/tex] has a singularity (that is, becomes infinitely large) at a certain angle [tex]\theta_{critical}[/tex]. For any angle [tex]\theta[/tex] > [tex]\theta_{critical}[/tex], the expression for [tex]F_{h}[/tex] will be negative. However, a negative applied force [tex]F_{h}[/tex] would reverse the direction of friction acting on the lawnmower, and thus this is not a physically acceptable solution. In fact, the increased normal force at these large angles makes the force of friction too large to move the lawnmower at all.