Fundamentals of
Medical Physics
In this chapter we will study;
1.1 Equilibrium and Stability
1.2 Equilibrium Considerations for the Human Body
1.3 Stability of the Human Body under the Action of an External Force
1.4 Skeletal Muscles
1.5 Levers
1.6 The Elbow
1.1 Equilibrium and Stability;
The Earth exerts an attractive force on the mass of an object; in fact, every small
element of mass in the object is attracted by the Earth. The sum of these forces is the
total weight of the body. This weight can be considered a force acting through a single
point called the center of mass or center of gravity.
What are the ways to make a body to be more stable..?
1.2 Equilibrium Considerations for the Human Body;
The center of gravity (c.g.) of an erect person with arms at the side is at
approximately 56% of the person’s height measured from the soles of the feet.
The center of gravity shifts as the person moves and bends.
The act of balancing requires maintenance of the center of gravity above the feet.
A person falls when his center of gravity is displaced beyond the position of the feet.
COG lies inside or outside the body.
When carrying an uneven load, the body tends to compensate by bending and
extending the limbs so as to shift the center of gravity back over the feet.
What about people who have lost an arm..?
https://www.youtube.com/watch?v=6rICsj0zFfQ
Stability against a toppling force is also increased by spreading the legs,
as shown in Fig. 1.7 and discussed in Exercise 1-1.
1.3 Stability of the Human Body under the Action of an External Force;
The body may of course be subject to forces other than the downward force of
weight. Let us calculate the magnitude of the force applied to the shoulder (Fa) that
will topple a person standing at rigid attention. The assumed dimensions of the
person are as shown in Fig. If F is applied force and T is the torque then;
(At Equilibrium)
Fa (N)
t (m)
Fa = (mg x a) / t
To resist amount of force toppling)we must:
1- Increasing of mass (m)
2- Increasing of pivoted distance (a)
3- Decreasing of length (t)
a (m)
Actually, a person can withstand a much greater
sideways force without losing balance by bending
the torso in the direction opposite to the applied
force (Fig. 1.6). This shifts the center of gravity
away from the pivot point A, increasing the
restoring torque produced by the weight of the
body.
1.4 Skeletal Muscles;
The skeletal muscles producing skeletal movements consist of many thousands of
parallel fibers wrapped in a flexible sheath that narrows at both ends into tendons (Fig.
1.8). The function of most muscles to pull and not to push.
From measurements, it has been estimated that a muscle can exert a force of about
7 × 106 dyn/cm2 of its cross-sectional area.
• 1.5 Levers;
A lever is a rigid bar free to rotate about a fixed point called the fulcrum. The position
of the fulcrum is fixed so that it is not free to move with respect to the bar.
Levers are used to lift loads in an advantageous way and to transfer movement from
one point to another.
There are three classes of levers, as shown in Fig. 1.9.
First class
Second class
Third class
(FLA)
Many of the limbs movements of animals are performed by Class 3 levers.
W
M
F
M
First class
W
M
F
Second class
F
W
Third class
(FWM)
The three lever classes and schematic examples of each In the body. W Is a force that could be
the weight, F Is the force at the fulcrum point, and M Is the muscle force.
At Equilibrium F x d2 = W x d1
Mechanical advantage; is a measure of the force amplification achieved by using a tool.
M ; Class I can be > or < 1.
Class II lever is > 1.
Class III is always < 1.
d2
d1
L1/d1 = L2 /d2
v1 = L1 / t1
v2 = L2 / t2
When t1 = t2
v 1 / v 2 = d 1/ d 2
M= d2/ d1
M; Class I can be > or < 1.
Class II lever is > 1.
Class III is always < 1.
v ; Class I can be > or < 1.
Class II lever is < 1.
Class III is always > 1.
1.6 The Elbow;
The two most important muscles producing elbow movement are the biceps and the
triceps (Fig. 1.11).
https://human.biodigital.com/
Online human anatomy;
Figure 1.12a shows a weight W held in the hand with the elbow bent at a
100◦ angle. A simplified diagram of this arm position is shown in Fig. 1.12b.
The dimensions shown in Fig. 1.12 are reasonable for a human arm, but they
will, of course, vary from person to person.
The calculations will be performed by
considering the arm position as a Class 3
lever, The x- and y-axes are as shown in Fig.
1.13. we need to calculate the muscle force
Fm,.
30
100⁰
(Slice no 21)
4
Our calculations show that the force exerted by the muscle is much
greater than the weight it holds up.
This is the case with all the skeletal muscles in the body.
They all apply forces by means of levers that have a mechanical
advantage less than one.
As mentioned earlier, this arrangement provides for greater speed of
the limbs.
A small change in the length of the muscle produces a relatively
larger displacement of the limb extremities.
In fact, the speeds attainable at limb extremities are remarkable.
A skilled pitcher can hurl a baseball at a speed in excess of 100 mph
(161 km/h). Of course, this is also the speed of his hand at the point
where he releases the ball.
Online unit converter;
http://www.unitconverters.net/common-converters.html
‫بسم هللا الرحمن الرحيم‬
‫س َ‬
‫س ِن ََ ْق ِِيم «‬
‫ان فِي أَحْ َ‬
‫اْلن َ‬
‫«لَقَ ْد َخلَ ْقنَا ْ ِ‬
‫صدق هللا العظيم‬
‫(الَين‪)4‬‬
Homework 1
Exercises page 21
1-1. (a) Explain why the stability of a person against a toppling force is
increased by spreading the legs as shown in Fig. 1.7. (b) Calculate the force
required to topple a person of mass = 70 kg, standing with his feet spread 0.9
m apart as shown in Fig. 1.7. Assume the person does not slide and the weight
of the person is equally distributed on both feet.
1-2. Derive the relationships stated in Eqs. 1.6, 1.7, and 1.8.
1-4. Using the data provided in the text, calculate the maximum weight that
the arm can support in the position shown in Fig. 1.12.
Chapter 1
1-1(b). F 254N
1-2.
1-4. Maximum weight ≈ 335N
In this chapter we will study;
1-Friction
2-Frictional force
3-Friction within the bone
If we examine the surface of any object, we observe that it is irregular. It has
protrusions and valleys. Even surfaces that appear smooth to the eye show
such irregularities under microscopic examination. When two surfaces are in
contact, their irregularities intermesh, and as a result there is a resistance to
the sliding or moving of one surface on the other. This resistance is called
friction. If one surface is to be moved with respect to another, a force has to
be applied to overcome friction.
μs
μk
Oiled steel
0.1
0.05
Friction is everywhere around us. It is both a nuisance and an
indispensable factor in the ability of animals to move. Without
friction an object that is pushed into motion would continue to
move forever (Newton’s first law). The slightest force would send
us into eternal motion. It is the frictional force that dissipates
kinetic energy into heat and eventually stops the object (see
Exercise 2-1).
Without friction we could not walk; nor could we balance on an
inclined plane (see Exercise 2-2). In both cases, friction provides
the necessary reaction force. Friction also produces undesirable
wear and tear and destructive heating of contact surfaces.
Engineers attempt to maximize friction where it is necessary and
minimize it where it is destructive.
Friction is greatly reduced by introducing a fluid such as oil at the
interface of two surfaces. The fluid fills the irregularities and
therefore smooths out the surfaces. A natural example of such
lubrication occurs in the joints of animals, which are lubricated by
a fluid called the synovial fluid.
This lubricant reduces the coefficient of friction by about a factor
of 100. As is evident from Table 2.1, Our God provides very
efficient joint lubrication. The coefficient of friction here is
significantly lower than for steel on ice.
Exercises page 29
2-2
2-2(a). μ 0.067