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Medical Physics Chapter 2 Forces on and in the Body Chapter 2 Forces on and in the Body l Fundamental forces m Gravitational force m Electrical force m Strong nuclear force (and weaker nuclear force) 2.1 Statics m Equilibrium Ÿ Stationary (static) object is in the state of equilibrium Ÿ ∑F = 0 Translational equilibrium: i i Ÿ Rotational equilibrium: ∑T = 0 i i ù ù ù Torque: T = r × F Moment: M = F r sinθ , magnitude of torque Moment arm: d = r sinθ ù Direction of torque: right-hand rule, ⊥ to r and F m Levers: Fig. 2.1 moment arm of M d F Ÿ Mechanical advantage of M against W = = moment arm of W dW Ÿ Ÿ Ÿ First class: mechanical advantage or disadvantage Second class: mechanical advantage (force amplification) Third class: mechanical disadvantage (motion amplification), most common in human body m Lever model of the elbow Ÿ Model ù ù ù ù Ÿ Bone ⇒ lever Muscles ⇒ force (tension) Tendons ⇒ string Joint ⇒ pivot Fig. 2.2: ∑T = 0 i i -1- KHU, EI 468 Medical Physics ù ù Ÿ Chapter 2 Forces on and in the Body M d M = W dW M d M = W dW + Hd H Fig. 2.3: ∑T = 0 i i Ÿ ù M d M cos α = W dW cos α + Hd H cos α ù Fig. 2.4: maximum force vs. length of muscle Fig. 2.4: ∑T = 0 i i ù Ÿ Ÿ T × 18 × sinα = 36 × W1 + 72 × W2 or T = 2W1 + 4W2 sinα Fig. 2.6 and Fig. 2.7 Fig. 2.8 2.2 Frictional Forces m Modeling: Fig. 2.9 Ÿ Maximum force of friction, f = µN where N is a normal force Coefficient of friction, µ (Table 2.1) ù Depends on two materials in contact ù Independent of surface area m Lubricant Ÿ Joint lubrication (possibly by synovial fluid) Ÿ Salvia Ÿ Slippery mucus of organs (heart, lung, etc.) Ÿ 2.3 Dynamics m Linear acceleration or deceleration ∆ (mv ) ∆t Ÿ Newton’s second law: F = ma or F = Ÿ Ÿ Ÿ Ÿ Ÿ Ÿ Example 2.1 Example 2.2 Apparent increase of weight during systole Stiff-legged landing Whiplash (Fig. 2.10) Auto collision (Fig. 2.11) -2- KHU, EI 468 Medical Physics Chapter 2 Forces on and in the Body m Effects of acceleration Ÿ Ÿ Ÿ Ÿ Ÿ Apparent increase or decrease in body weight ⇒ weightlessness in an orbiting satellite Change in internal hydrostatic pressure Distortion of the elastic tissue of the body ⇒ tearing or rupture Tendency of solids with different densities suspended in a liquid to separate ⇒ centrifuge Loss of control (muscle force < acceleration force) Ÿ Blood pooling ⇒ blackout and unconsciousness m Oscillatory motion or resonance behavior Ÿ Fig. 2.13: pain or discomfort due to vibration Ÿ Motor vehicles: 8 Hz or less Ÿ Aircraft: higher frequency m Centrifuge l Homework m Review questions: #4, #6, #7, #8, #9 -3- KHU, EI 468