A very simple catapult is constructed by resting a long rigid plank on a fulcrum near the left end, attaching a spring to the left end, and then tying a rope to the right end. The catapult is readied by pulling the rope until the plank is level, stretching the spring and storing elastic potential energy. Cutting the rope releases the stored energy and launches a projectile placed on the right end of the ' plank This assignment analyzes the forces and torques acting spring i Wlu on the readied but unloaded catapult which is in equilibrium. fulcrum L static frictional force on the plank. and that the stretched spring pulls straight down on the plank. Use standard x-y axes (horizontal & vertical), and draw both components of FT, the tension force from the rope. The completed FBD should showve \"whoie \" forces and two force components. (2) In 12 sentences, explain how you chose the direction of the frictional force F5 exerted on the plank by the fulcrum. (3) Several gtys to choose. Identify them all by description and symbol: 0 the plank's length is L = 3.84 1n, its mass is M = 29.1 kg 0 the fulcrum is a distance d : (0.297) x L from the plank's left end 0 calculate d in m and round to 3 E only list of, not the random value 0.2-0.3 0 the tension force FT from the rope is directed at an angle 9 : 12.5O below the horizontal 0 the spring exerts a force F E : 732.0 N on the left end of the plank (4) Add a torque axis (dot) to your FBD, right at the top of the fulcrum. Why do neither FN nor Fs generate torques about this axis? Explain in one sentence. (5) List the directions (CW or CCW) of the torques about this axis due to the other three (whole) forces acting on the plank. No explanation needed. (6) In a bit, when you calculate the torque TE due to the elastic force FE, your FBD should make it easy to see that 31:6: d. For this question, though, write your own equations for m and g; in terms of d and L, based on your FBD, then calculate both 1:53, and 51, Tip: sketch it out on scratch paper first. (7) Calculate the magnitudes TE, To of the torques due to FE and Fe. (8) Starting from "rm : 17$, derive an expression for 151', the magnitude of the torque due to the tension force , then use your expression to calculate IT. Show all steps. (9) Calculate the magnitude of the tension force FT. (10) Use N2L for forces to calculate the magnitude F N of the normal force the fulcrum exerts on the plank