Summary
Biomechanics book summary
- Course
- Institution
Biomechanics book summary
[Show more]
Seller
Follow
annerixtvanderwal
Content preview
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
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller annerixtvanderwal. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $5.89. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
67474 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now