EQUILIBRIUM I

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. Cuting the rope releases the stored SIST energy and launches a projectile placed on the right end of the plank. This assignment analyzes the forces and torques acting on the readied but unloaded catapult, which is in equlilibrium.\f(1) Draw a FBD for the plank, assuming that the fulcrum exerts both a normal force and a static fricional 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 vector components of Fr, the tension force from the rope. The completed FBD should show five "whole" forces and two force components, all drawn as arrows. DO NOT POST ASSIST (2) In 1-2 sentences, explain how you chose the direction of the frictional force Fs exerted on the plank by the fulcrum. POST DO NOT ASSIST DO NOT POST DO NOT ASSIST DO NOT POST DO NO ASSIST (3) RNG Several qtys to choose. Identify them all by description and symbol: NOT POST DO NOT ASSIST Do the plank's length is _ = 3-5 m, its mass is M= 10-30 kgoT ASSIST DO NOT POST DO NOT ASSIST D the fulcrum is a distance d = (0.2-0.3) x _ from the plank's left end DO NOT POST DO NOT ASSIST DO N o calculate d in m and round to 3 SF; only list d, not the random value 0.2-0.3 ST DO NOT ASSIST . the tension force Fr from the rope is directed at an angle 0 = 10-30 below the horizontal D . the spring exerts a force FE = 500-1000 N on the left end of the plank DO NOT ASSIST (4) Add a torque axis (dot) to your FBD, right at the top of the fulcrum. Why do neither FN nor Fs generate ASSIST torques about this axis? Explain in one sentence.POST DO NOT ASSIST DO NOT POST DO NOT ASSIST (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. ASSIST (6) In a bit, when you calculate the torque re due to the elastic force FE, your FBD should make it easy to see that = = d. For this question, though, write your own equations for re and ry in terms of d and L, based on your FBD, then calculate both re and rr Tip: sketch it out on scratch paper first. DO NOT POST DO NOT ASSIST (7) Calculate the magnitudes TE; To of the torques due to FE and FG. SSI ASSIST (8) Starting from The = / a , derive an expression for rr, the magnitude of the torque due to the tension force , then use your expression to calculate rr. Show all steps. DO NOT ASSIST DO NOT POST DO NOT ASSIST (9) Calculate the magnitude of the tension force FT.ST DO NOT ASSIST DO NOT POST DO NOT ASSIST (10) Use N2L for forces to calculate the magnitude Fy of the normal force the fulcrum exerts on the plank. SIST