(25 points) A thin shelf of mass m = 10kg and length L = 0.5m is nailed to a wall and supported by a wire at its opposite end as shown in the diagram above. The nail exerts a force on the shelf with components Fx and Fy. The shelf is held in static equilibrium. Y Fy Wire 30 Center of Mass L (a) (5 points) Draw a free body diagram for the shelf. (b) (5 points) Find the tension force exerted by the wire, T. (c) (5 points) Find the vertical component of the force exerted by the nail, Fy. (d) (5 points) Find the horizontal component of the force exerted by the nail Fx (e) (5 points) Calculate the magnitude and direction of the force exerted by the nail.