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The solution for has a singularity (that is, becomes infinitely large) at a certain angle . For any angle , the expression for will be negative.
The solution for has a singularity (that is, becomes infinitely large) at a certain angle . For any angle , the expression for will be negative. However, a negative applied force 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.