4. Forces

Forces  Hooke’s Law – force by an elastic body is proportional to its extension, provided the limit of proportionality has not been exceeded.  Equilibrium of Forces o Condition 1: Sum of forces in any directions is zero o Condition 2: Sum of moments about any point is zero  Further application on moments F x equilibrium 1 2 3 4 1 2 3 4 Magnitude of Force: Elastic Potential Energy (Area): 10 kg 40° 10 cm Total length of rod is 50 cm and mass 12 kg Cable tension T 70° Condition 1 ∑Fx = FHinge, x – Tsin 70° = 0 ∑Fy = FHinge, y – (12+10)(0.981) + Tcos 70° = 0 Condition 2 Taking moments about the hinge, Sum of clockwise moment = Sum of anticlockwise moments (12)(9.81)(0.25cos 20°) + (10)(9.81)(0.50cos 20°) = T(0.40sin 40°) Lines of action of three non-parallel and coplanar forces must pass through the same point d F F Couple Forces  Equal Magnitude  Opposite direction  Acting on same body  Line of action of forces is parallel but separated Torque of a Couple

 Upthrust o A net upward forces by a fluid on a body due to the pressure difference experience by the top and bottom of the body. Archimedes’ Principle Magnitude of upthrust on the object is calculated from the weight of the fluid the object displaces. Principle of Flotation Weight of fluid displaced = Weight of Object For fully submerged object, V’ = V. V’ V ρO ρF Fluid pressure at this level: h