A large crate with mass rests on a horizontal floor. The coefficients of frictio

Question

A large crate with mass rests on a horizontal floor. The coefficients of friction between the crate and the floor are u_s and u_k. A woman pushes downward at an angle theta below the horizontal on the crate with a force F.

-What magnitude of force is required to keep the crate moving at constant velocity?
Express your answer in terms of m ,g, theta and u_k.

Answer: F=(u_k*m*g)/(cos(theta)-u_k*sin(theta))

-If u_s is greater than some critical value, the woman cannot start the crate moving no matter how hard she pushes. Calculate this critical value of u_s .

Express your answer in terms of theta.

Explanation / Answer

Applied force F = F Angle = Coefficient of kinetic friction k = k Normal force N = mg + F sin Kinetic fictional force f = k N                                     = k [ mg + F sin ] If frictional force is equal to applied force in horizontal direction then it moves with constant speed. i.e., k [ mg + F sin ] = F cos                    k mg   = F cos - k F sin                                    = F [  cos - ksin ] From this F = k mg    / [  cos - ksin ]

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