Kinesiology 201
Worked Solutions
Introduction
These sets of questions along with the worked solutions are designed as an affordable
aid to lecture notes and text readings in an undergraduate biomechanics course.
Obviously these problems are designed for use in conjunction with my lectures and the
biomechanics textbook.
Learning basic mechanical laws like Newton’s laws of motion will give you the essential
knowledge base. However, solving biomechanical problems is a skill that has to be
practised. You have to actively try to solve numerous problems to develop this skill and
move to a fuller understanding of biomechanics.
A good analogy is learning a language. Reading a passage in French or listening to
someone speaking in French is obviously useful. This is testing your passive
understanding of the language. However, your passive understanding will be better
than your active skills of writing and speaking the language. This is because when
reading or listening you don’t have to solve any problems such as how to conjugate a
verb in the correct tense, somebody has already done that for you. In addition when
reading you can develop a sense of the context of the passage and guess at the
meaning of some unknown words. Similarly, if you watch your biomechanics instructor
solve a problem it usually makes sense (we hope) and you will feel comfortable with that
specific problem. However, this is a passive process, come exam time you must be
able to actively solve problems.
The purpose of this set of worked examples is to help you develop the active skills of
solving biomechanical problems. The problems are grouped into the major sections of
most undergraduate biomechanics courses. The level of difficulty of the questions
varies, but the questions are not ranked in order of difficulty. Each section has a file
with the questions and a file with the worked solution to each of these problems. This is
the unique feature of the way I present these problems. Most biomechanical texts only
have a few worked examples per chapter due to the space they take up. Many have
problems at the end of the chapter with the answer given in brackets. I believe this is
only useful if you get the answer right. If you get the answer wrong you do not know
where you went wrong. For example, you could be making a major fundamental
mistake like trying to solve the problem with the wrong equations, or you may have
simply made a transcription error like writing 0.866 as 0.886. With only the answer, you
cannot easily identify the error, if at all. This series of worked examples will help you
follow the process of solving the questions you had difficulty solving.
It is vitally important that you try each problem before you look at the solution. If you
immediately look at the solution it is like reading a paragraph in French that you were
supposed to write yourself. This is not an effective method of study. The solution to
any of these problems may seem logical when you look at the answer, but the real
question is whether you could have solved the problem on your own. How are your
active problems solving skills? The ability to define problems and work to their solution
is an essential skill in today’s world. This does not mean you should not work with
others in solving these problems. Often working together with one or more partners can
help you develop a better understanding of the problem. If you do work in a group be
careful not to be a passive member of that group.
The following link supports the argument I have made in support of this method of study.
As you work through the problems available via the website it will be easy to see why
problem based learning helps students develop the skills necessary to succeed in
biomechanics and in today’s changing job market.
Note: All the links in this preamble are also on the Kin 201 course web page
http://www.sfu.ca/~leyland/Kin201/PBL.pd
The format of lectures and tutorials do not allow us to use a classic PBL format but the
spirit of the method will be adopted.
The following link discusses the need and method for drawing Free Body diagrams.
http://www.sfu.ca/~leyland/Kin201/Freebody.pdf
When drawing diagrams to help in the solution to a problem you may want to draw coordinate axes (frames of reference) clearly in the corner of the page. This can help in
keeping the direction of the vectors clear (usually positive in the x-direction is
horizontally to the right, positive in the y-direction is vertically upwards, and positive
moments are drawn with a curved arrow counter-clockwise. Keep in mind that it is
sometimes useful to have a reference system other than horizontal and vertical.
Marks for Questions
The marks allocated to the questions in my exams are given with the question in bold
square brackets. This is to help give you a guide as to my subjective evaluation of how
difficult the question is. Sometimes you will “see” the problem clearly and be able to
complete it quickly and think, “that was worth 7 marks? I had more trouble with the 2mark question!" That is to be expected, but I believe including the marks allocated to
the questions will help you.
Names of Sections
The names of the various questions and solutions sections are only a rough guide as to
the main topic examined in the question. Many questions include a combination of
areas. Just because a question is in a section "Angular Kinematics" does not mean that
linear equations will not be required.
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Mathematical Accuracy
Generally I am not concerned about calculating the answers to a large number of
significant figures. This is because the approximations in dealing with link-segment
models and gross-body mechanics are significantly large that being overly concerned
with the final number is not warranted. I usually calculate to 3 significant figures (I use 9.81 ms-2 for gravity for example) so depending on when you round, your answers
should be the same as the solutions presented for 2 significant figures and somewhat
close on the third. The most important factor is that the process you were working with
was correct.
Equations
In the exam booklets there will be a page containing the most common equations you
will need in solving these problems. You have to decide which equations apply to which
question. I have not included any trigonometry functions as the ability to break vectors
into components is assumed.
The following link shows a typical equation page from a final exam.
http://www.sfu.ca/~leyland/Kin201/Equations.pdf
Anthropometry
The four lists form the link below are a compilation of anthropometric data sets for the
50% male.
http://www.sfu.ca/~leyland/Kin201/Anthropometry.pdf
When modelling humans it is important we use anthropometry as specific to the
subject(s) as possible. Limb length can often be directly measured. However, segment
masses are usually estimated as a percentage of total body weight and the location of
the limbs centre of gravity and the limbs moment of inertia are similarly derived from
data sets which match your population group or subject.
However, anthropometry is not the focus of Kin201 and my concern is that you
understand how to use anthropometry in out models rather than understanding how
different anthropometric databases are compiled. It is important but it is the focus of
Kin303 not Kin201 (or even Kin380). To reduce the amount of data you have to have,
many of the problems in these worked examples use the data presented in the above
link. This is simply a compiled database for the average (50%tile male). I am not being
sexist here; more data is available for males. However, some questions use different
anthropometric data that may have to be derived from information given in the question.
Note that the sample exams give anthropometric information and the final provides
moment of inertia information in addition to these three tables.
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