A box is on a flat plane and has a force of 16 N applied downward to it at an angle of 55 degrees. The box has a mass of 28 kg.

What is the minimum horizontal force F needed to make the box start moving in (Figure 1)? The coefficients of kinetic and static friction between the box and the floor are 0.25 and 0.41, respectively.

1 answer

Fap = 16N[55o], Downward.
M*g = 28*9.8 = 274.4 N. = Wt. of box.

Fn = Mg + Fap*Sin55 = 274.4 + 16*sin55 = 287.5 N.

Fs = u*Fn = 0.41 * 287.5 = 117.9 N. = Force of static friction.

F+Fap*Cos55-Fs = M*a.
F+16*Cos55-117.9 = 28*0
F + 9.18 - 117.9 = 0
F = 108.7 N.