WEEK 1 - SURG0035 PDF

WEEK 1 An Introduction to Biomechanics PART A - the Framework Mechanics Mechanics is the branch of physics concerned with the behaviour of physical bodies when subjected to forces (kinetics) or displacements (kinematics). Generally, one produces the other. Scientists such as Galilea, Kepler, and Esp...

WEEK 1 An Introduction to Biomechanics PART A - the Framework Mechanics Mechanics is the branch of physics concerned with the behaviour of physical bodies when subjected to forces (kinetics) or displacements (kinematics). Generally, one produces the other. Scientists such as Galilea, Kepler, and Especially Isaac Newton, laid the foundation for what is now known as classical mechanics. Classical mechanics deals with Particles that are at rest or are moving with velocity Mx'= -100.x From [2'] & Mb' + Mf' =0 so 0.8Fd - 100. (x-0.1) = 0, and rearranging gives Fb = (100.0.8)(x-0.1) And substituting for Fb in gives: Fa = 112.5 - 125x and Fb = 125x - 12.5 Try x = 0.5, Fa = 50, Fb = 50, for x =0.1, Fa = 100, Fb = 0, for x = 0.9, Fa = 0, Fb =100 Another free body diagram example Identify the forces; Along the slope: Fμ = -μFn Fmsinθ + Fμ = 0 Normal to the slope: FN + Fmcosθ =0 Subsituting into and then into And rearranging gives: μ = Fmsinθ/ Fmcosθ = tanθ Therefore θ = atan(μ) Dynamic Equilibrium Example Work out static forces at a speed of 100km/h = 100000/360 = 277.7778 27.8m/s FN = -Fmass = -mg = -(2000 * -9.81) = 19620N, so Frr = μFn = 0.01 * 19620 = 196.2N Fair = 0.5 * 1.29 * (27.8)2 *.3 * 2.5 = 373.8N Fdrive = Fair + Frr = 373.8 + 196.2 = 570N Now do the kinetics τw (torqie at rear wheels) = F r = 570 * 0.45/2 = 128.3 Nm Wheel circumference = πD = 0.45π = 1.41m Therefore wheel revs = 27.8/1.41=19.7rps = 123.9 rad/s Power at wheel = torque x rad/s = 128.3 * 123.9 W = 15896W = 15.9kW Power at flywheel = 15.9/.85 = 18.7kW (about 25bhp) Material Stress & Stain Stress When we apply a force to an object, we stress it. Stress is a measure of the applied force over a given surface area Stress can be compressive, tensile (both perpendicular) or shear (parallel to surface) It is a vector quantity as it has direction, usually normally to the surface SI unit is Pascals (N/m2), but often use MPa (MN/m2 pr N/mm2). The symbol is σ When force is applied to a solid we call it stress, when applied to a liquid or a gas we call it pressure (but its still force per unit area)  Gases/Liquids under pressure but static (i.e. within a container) tend to exert the same pressure on all surfaces. What is atmospheric pressure? o It is the weight of a 1m2 column of air at the earths surface. Air pressure at the earth's surface. Air pressure at the earth's surface is approx. 100kPa (0.1 MPa) The stress exerted on the floor by an 85Kh person is: o Area of 1 foot ~ 0.2m2, so stress is 85 x 9.81 / (2 x 0.2) = ~ 2,000Pa Strain When we stress something, we deform it Strain is defined as the ratio of the deformation to the original dimension. Calculated as, δL/L so it is a dimensionless property, given the symbol ε. Because deformations are generally very small we often use the tern ' micro-strain'