Consider a Lawnmower of mass m which can side across a horizontal surface with a

Question

Consider a Lawnmower of mass m which can side 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_b.the force exerted by the handle, is parallel to the handle. Take the positive x direction to be to the right and the to be upward. Use g for the magnitude positive y direction of the acceleration due to gravity. Find the magnitude, F_h of the force required to slide the lawnmower over the ground at constant speed by pushing the handle Express the required force in terms of given quantities.

Explanation / Answer

friction Ff = µ*Fn = µ*(mg + Fh*sin)
applied horizontal force Fa = Fh*cos
For equilibrium ("constant speed"), these are equal:
µmg + µ*Fh*sin = Fh*cos
µmg = Fh(cos - µsin)
Fh = µmg / (cos - µsin)

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