Consider a lawnmower of mass m which can slide across a horizontal surface with a coefficient of friction μ. In this problem the lawnmower is pushed using a massless handle, which makes an angle θ with the horizontal. Assume that Fh, the force exerted by the handle, is parallel to the handle.
Find the magnitude, Fh, of the force required to slide the lawnmower over the ground at constant speed by pushing the handle.
The solution for Fh has a singularity (that is, becomes infinitely large) at a certain angle θcritical. For any angle θ>θcritical, the expression for Fh will be negative. However, a negative applied force Fh 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 tan(θcritical).
Answers: 1
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