1. A door with rectangular shape is hinged along an axis having direction a lying in the xz place. The door is supported by a cable that has a tensile force F=100N. Determine the moment of F about line a.
2. A machine for smoothing the surface of wet concrete is shown (the guard for the paddles is removed). If the concrete applies force F=8lb to each paddle, where all forces F lie in the xy plane, determine the force P and orientation α needed so the resultant couple moment of the foces shown is zero. Forces P are parallel to the yz plane.
3. A casting supports the forces and moment (double-headed arrow) shown where the 100N forces are parallel to the xy plane and the moment at C has direction angles θx=60°, θy=60°, and θz=135°. Determine the equivalent force system acting at point O.
4. A bookshelf holding 11 books is supported by brackets at points A and B. The weights and thicknesses of the books are given in the table. Determine the support reactions.
5. A wind tunnel is used to experimentally determine the lift force L and drag force D on a scale model of an aircraft. The bracket supporting the aircraft is fitted with an axial spring with stiffness k = 0.125 N/mm and a torsional spring with stiffness kt = 50 N*m/rad. By measuring the deflections δ and θ of these springs during a test, the forces L and D may be determined. If the geometry shown occurs when there is no airflow, and if the springs are calibrated so that δ = 0 and θ = 0° when there is no airflow, determine L and D if δ = 2.51mm and θ = 1.06° are measured.
