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Biomechanics book summary
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Biomechanics, StaticsChapter 1
Length is used to locate the position of a point in space and thereby describe the size of a
physical system.
Time is conceived as a succession of events.
Mass is a measure of a quantity of matter that is used to compare the action of one body
with that of another.
Force is considered as a push or pull exerted by one body on another.
Idealizations are used in mechanics in order to simplify application of the theory. These are 3
important idealizations:
1. Particle, a particle has a mass, but a size that can be neglected.
2. Rigid body, a rigid body can be considered as a combination of a large number of
particles in which all the particles remain at a fixed distance from one another, both
before and after applying a load.
3. Concentrated force, represents the effect of a leading which is assumed to act at a
point on a body.
Newton’s three laws of motion
First law: a particle originally at rest, or moving in a straight line with constant velocity, tends
to remain in this state provided the particle is not subjected to an unbalanced force.
Second law: a particle acted upon by an unbalanced force F experiences an acceleration a
that has the same direction as the force and a magnitude that is directly proportional to the
force. If F is applied to a particle of mass m, this law may be expressed mathematically as
F=ma.
Third law: the mutual forces of action and reaction between two particles are equal,
opposite and collinear.
F=Gx(m1m2 : r^2)
SI units – metric system
10^9 giga (G)–10^6 mega (M)–10^3 Kilo (k)–10^-3 milli (m)–10^-6 micro (u)–10^-9 nano (n)
Do not use mm, cm, dm for example if N/mm write kN/m
Dimensional homogeneity, that is that each term of an equation must be expressed in the
same units.
Use engineering notation for significant figures, meaning three significant numbers.
As a general rule, any numerical figure ending in a number greater than five is rounded up
and a number less than five is not rounded up -> 3,5587 becomes 3.56.
Read the problem and try to correlate the actual physical situation with the theory studied.
Tabulate the problem data and draw to a large scale any necessary diagrams.
Apply the relevant principles, generally in mathematical form. When writing any equations,
be sure they are dimensionally homogeneous.
Solve the necessary equations, and report the answer with no more than 3 signs. Figures.
, Study the answer with tech. judgment and common sense to determine whether it seams
reasonable.
Chapter 2
Scalar is any positive or negative physical quantity that can be completely specified by its
magnitude.
Vector is any physical quantity that requires both a magnitude and a direction for its
complete description.
If a vector is multiplied by a + scalar, its magnitude is increased by that amount. X by a
negative scalar will also change the directional sense of the vector.
1. Join the tails of the components at a point
2. From the head of B draw a parallel line to A. Draw another line from the head of A
parallel to B. These two lines intersect at point P to form the adjacent sides of a
parallelogram.
3. The diagonal of this parallelogram that extends to P forms R, which then represents
the resultant vector R = A + B
We can also add B to A by using the triangle rule, whereby vector B is added to A in a head
to tail fashion the resultant R extends from the tail of A to the head of B. R = A + B = B + A
If A and B are collinear R = A + B.
R’ = A – B + A + (-B)
The rules from vector addition also apply to vector subtraction.
F1 + F2 = Fr
Fr is a resultant force
To find the two components of a force we use the reverse parallelogram
Addition of sevral forces Fr = (F1 + F2) + F3
Cosine law: C: the root of (A^2 + B^2 -2AB cos c)
Sine law: A:sin a = B:sin b = C: cos c
Scalar notation F = Fx + Fy
Fx = Fcos0 & Fy = Fsin0
Whenever italic symbols are written near vector arrows in figures, they indicate the
magnitude of the vector, which is always a positive quantity.
Cartesian vecor notation i&j. F = Fxi + Fyj
Coplanar force resultants
Fr = the root of ((Fr)x ^2 + (Fr)y^2)
0 = tan^-1 ((Fr)y : (Fr)x)
Chapter 3
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