The spacecraft rotates in the plane of the paper Max angular velocity is 1 rpm o Max angular acceleration is 5 rpm^2 Assume the beam is a cylinder with a diameter of 10mm. Spacecraft 10.0 m X m* boom = 2 kg/m Z minstrument = 25 kg Find the reactions at the fixed location Find the max shear and bending moment, and create their diagrams. Must use singularity functions to create shear/bending diagrams. Note, you may ignore tension force in shear/bending moment diagrams, as they do not create a moment. Extra Credit: Find the maximum deflection in the beam Once again must use singularity functions to find deflection. Note, you may ignore tension force in finding deflection, as they do not create a moment. Deflection may be in terms of "El"y= Find the maximum (absolute) principle stresses in the beam Identify where in the beam the stress is maximum. Requires combining any of the relevant stresses, possibly including transverse shear, bending and normal stress. Ensure this includes all forces and loads in the diagram below. Extra Credit: Suggest a lightweight material for protoflight levels based on yield. State the density of said material. What failure theory would you use for this material, and show where you are on the failure zone graph with axis A and B. What is your margin of safety on the material? 10.0 m 'reaction _react Mr F y_react W boom F. instrument Fcenta X W boom F = m*. *x* boom Wboom=2(kg/m)*x (m)* 8.73*10^-3 (rad/s^2)=1.75*10^-2 (N/m^2)*x(m) instrument= Minstrument*x*= 25 (kg)*10 (m)* 8.73*10^-3 (rad/s^2)=2.18 N centa = minstrument* w^2*L+ w^2 *m*p F = centa boom *x dx 25 (kg)*0.105 (rad/s)^2*10 (m)+1/2*2(kg/m)*0.105 (rad/s)^2*10(m)^2=3.84(N) Wboom and Finstrument are loads normal to the beam F is a load axial to the beam centra