7. Use distances to find angle between rope and vertical. Forces will have same angle between them. Upward components of tension from each rope segment equal weight.
9. Use known tension in vertical segment to find tension in angle segment. Then horizontal component of angle segment equals horizontal tension, supplied by friction.
12. Upward support forces equal weight of man + bridge. Write torque equation in terms of relative distances measured from one support force and find other force. Find second force using force equation.
16. (a) Find angle of ladder with ground. Write torque equation using weights and horizontal distances from wall, outward force from window, and vertical height of ladder. (b) Use translational equilibrium: upward forces (or components) = downward forces or components and forces (or components) to the left = forces (or components) to the right.
32. (a) Each hinge supports half the weight (b) Horizontal forces are also equal but opposite in direction. Together their torque must offset torque caused by the door's weight.
33. (a) Write torque equation about the hinge using each force (two weights and one tension) and its perpendicular distance from the hinge point. Write distances in terms of strut length and angles. The length will cancel out. Solve for the tension. (b & c) Write vertical and horizontal force equations to find the vertical and horizontal force.
42. At the point of tipping, the normal force acts at the edge of the block.Write the torque equation around that edge to find force P. If the cube doesn't slide, P< fs,max
47. (a) Strain = change in length / normal length (b) Stress = force / X-sec area (c) E = stress / strain
50. (a) see 47-b (b) G = stress / (deflection/length)