A toy chest and its contents have a combined weight of 180N. The coefficient of static friction between toy chest and floor is 0.42.The child in Figure attempts to move the chest across the floor by pulling on an attached rope. (a) If θ is 42^o, what is the magnitude of the force F that the child must exert on the rope to put the chest on the verge of moving??

(b) Write an expression for the magnitude F required to put the chest on the verge of moving as a function of the angle 0. Determine

(c) The value of θ for which F is a minimum and?

(d) That minimum magnitude.