Consider a lawnmower of weight w which can slide across a horizontal surface wit

Question

Consider a lawnmower of weight w which can slide across a horizontal surface with a coefficient of friction mu. In this problem the lawnmower is pushed using a massless handle, which makes an angle theta with the horizontal. Assume that F_h, the force exerted by the handle, is parallel to the handle.

Find the magnitude, F_h, of the force required to slide the lawnmower over the ground at constant speed by pushing the handle.

The solution for F_h has a singularity (that is, becomes infinitely large) at a certain angle theta_critical. For any angle heta > heta_{ m critical}, the expression for F_h will be negative. However, a negative applied force F_h 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.

Find an expression for an( heta_{ m critical}).

Explanation / Answer

Given Force exerted by the handle is Fh Coefficient of friction, is Angle made by the handle is Net force on the lawn mower is ma = Fh cos - N But the lawn mower is moving with constant speed , a = 0 Now,  Fh cos = N where N = mg + Fh sin where mg is the weight of the lawn mower Then Fh cos = (mg + Fh sin) Fh = mg / ( cos - sin) is the magnitude of the force exerted by the handle

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