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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
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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)
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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
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