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 on the readied but unloaded catapult, which is in equilibrium. plank 0 rope fulcrum L (1) Draw a FBD for the plank, assuming that the fulcrum exerts both a normal force and a 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 show five whole forces and two force components. (2) In 1-2 sentences, explain how you chose the direction of the frictional force Fs exerted on the plank by the fulcrum. (3) Several qtys to choose. Identify them all by description and symbol: the plank's length is L = 3.84 m, its mass is M = 29.1 kg the fulcrum is a distance d = (0.297) x L from the plank's left end calculate d in m and round to 3 SF; only list d, not the random value 0.2-0.3 = 732.0 N on the left end of the plank the tension force FT from the rope is directed at an angle 0 = 12.5 below the horizontal the spring exerts a force FE (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 E d. For this question, though, write your own equations for Ko and terms of d and L, based on your FBD, then calculate both KG and Tip: sketch it out on scratch paper first. (7) Calculate the magnitudes TE, TG of the torques due to FE and FG. Kin (8) Starting from Tnet = I , derive an expression for TT, the magnitude of the torque due to the tension force, then use your expression to calculate TT. Show all steps. (9) Calculate the magnitude of the tension force FT. (10) Use N2L for forces to calculate the magnitude FN of the normal force the fulcrum exerts on the plank.