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A person pushes with force F on a box which remains at rest on a rough floor as shown in the top figure. The bottom figures illustrates all the force acting on the box.

a) What condition must be satisfied by all the force acting on the box so that it remains at rest? Draw a vector diagram that illustrates how the forces must combine to satisfy this condition.

b) Suppose the box has weight W = 100 N and the friction force magnitude f is 80% of the normal force magnitude N. That is, f = 0.8N. If the person pushes down at an angle of θ = 35◦ determine the magnitude of the force F the person exerts on the box.