The uniform dresser has a weight of 85 lb and rests on a til

The uniform dresser has a weight of 85 lb and rests on a tile floor for which ?s = 0.21. If the man pushes on it in the direction ? = 30?, determine the smallest magnitude of force F needed to move the dresser. Also, if the man has a weight of 156 lb , determine the smallest coefficient of static friction between his shoes and the floor so that he does not slip

Determine the smallest magnitude of force F needed to move the dresser.

Solution

Apply the Newton\'s second law, the horizontal force is

Fcos30-0.21*N =0

Along the vertical direction

N-85-Fsin30=0

Solve the two equations, we get

N=96.73 lb

F=23.46 lb. ......answer

...........

The normal force is

Nm = 156 -Fsin30 = 144.27 lb

The force is

Fm = Fcos30=20.3 lb

Hence the coefficient of friction

u = Fm/Nm =0.14