Physics help : Tips for Dimensional Analysis Problems

It's time for some help for the Scientifically challenged.  Today we deal with problems involving dimensional consistency.  I will be solving problems from my favorite Physics book, "The Fundamentals of Physics" by Halliday, Resnick and Walker 8th ed.






Chapter 1 problem #12.  

To solve this problem we are to considered that all the factors of the numerator are length dimensions so you get a  volume dimension as a result of the multiplication of the cube of a length dimension.  Dividing the numerator with the denominator, you get a length squared dimension which leads to the final result of a length dimension upon taking the square root.

r = [ (s-a)(s-b)(s-c)/s]^1/2

  = ( L^3/L)^1/2
= (L^2)^1/2
= L

the dimensions are consistent.









Chapter 1 problem #13

 First we take note of the dimensions of the quantities called out:

S - length
a - length/length^2, m/s^2
t - time, s

if we were to plug in the values of m = 1 and n =2, the equation would look like this

length = k (length/(time^2))^1 * time^2

with  time cancelling out and not considering the dimensionless k, we find

both sides of the equation reflecting length

Dimensional analysis does not give enough info to determine the value of k









Chapter 1 problem #14

Consider the dimensions of the following quantities:

T - time
l - length
g - length/time^2







the quotient inside the radical results in a time^2 quantity.  Taking the square root results in both sides of the equation having time units.








Chapter 1 problem #15

 

In the case of equation (a), the left hand side of the equation has length/time dimensions. The right hand side of the equation has length/time dimensions for the first term and length^2/time^2 for the second term.  Thus this equation is not dimensionally consistent.  

Equation (b) on the other hand has both length dimensions on either side of the equation making it dimensionally consistent.

Chapter 1 problem #16

 

Force has the units of  kg•m/s^2.  Multiplying this with r^2, and dividing this with kg^2, you get m^3/kg•s^2 for the units of G.

Chapter 1 problem #17

 We first define the first term coefficient A = 1.50 Mft^3/mos.  Converting to ft^3/s we go through the following:

A = 1.5x10^6ft^3/mos x 1mo/30d x 1d/24h x 1h/60m x 1min/60s = 0.579 ft^3/s

in a similar fashion

B = 0.008x10^6 ft^3/mos^2  x (1mon/30d)^2 x (1d/24h)^2 x (1h/60min)^2 x (1min/60s )

   = 0.19 x 10^-9 ft^3/s^2

V = 0.58 ft^3/s t + 1.19 x 10^-9 ft^3/s^2 t^2

How to Deploy Your Own Innovation Programme by Richard Platt

I have been truly blessed to have learned about the Theory of Inventive Problem Solving (TRIZ).  It has helped me throughout my career spanning various positions in Eng'g, Advocacy, Education and the Performing Arts.  Here's a presentation by my mentor Richard Platt outlining our experience in getting TRIZ off the ground at Intel.

13 Key Principles to Develop and Deploy Your Own Innovation Program - The Intel TRIZ Story from Richard Platt

Charting your future with technology trends.

Technology in a lot of ways is not unlike biological systems. For one, the technological marvels of today will become obsolete in the next few years. Just ask kids what a typewriter is and you'll know what I'm talking about. A lot of the have not even heard of an 8 track cassette or a vinyl record! Technology does change with time.

If technology is time dependent are we at its mercy such that we find ourselves one morning left behind? Of course not! Aside from the fact that it takes a while for people to adapt to new technology, it is also a fact that its evolution follows definite trends. In general, a technical system will continue improving towards increasing ideality. This means the quality of useful functions is improved while reducing harmful functions and cost. As an exanple remember the big clutch bag cellphones we had 20yrs ago? These later became the bowling pin phones followed by the fat shampoo bottle types. With the transition to gsm and 3g, phones became smaller and thinner. You see this similar trend with transportation, video, computing, etc.

 The danger in using technological trends is when we take it as a linear, dogmatic timeline.  I recently used an analysis of technology trends in the context of learning as part of social innovation.  When we deal with learning technologies and systems, the trend if to go from a cognitive towards a more experiential mode, from an abstract to a concrete, transformational experience. It will be easy for us to take the normal trend of classroom learning -> tours -> immersion -> independent project as Gospel truth when you can create as system that jumps straight to exploration was what is normally done in the performing arts. Following an exploratory approach makes the learner responsible for his learning.  This also implies that a lot of courses taught in schools and universities are actually inefficient and ineffective.  

As innovators and technical professionals, it is to our best interest to determine the maturity of the technology we work with. This way we will be able to maximize the innovation that can be done with these. By predicting technology trends we will be able to take leadership of the great industries of tomorrow

posted from Bloggeroid

The Humanity of Innovation and Design

As Innovators and Designers, we are often faced with the temptation to go through our technical problems from an Ivory tower.  More often than not, it is easier for us to do our calculations, simulations and design renderings devoid of any considerations of the humans that use or interact with the systems we work with.  While it is true that it is more convenient for us to create self-sustaining automated systems that are able to give us reliable and repeatable results, let us not forget the purpose of technology.  Technology, first and foremost is created to improve the quality of life of the human species.  It is inevitable that the systems we create will somehow interact with humans.  To expand this further, considering the primary purpose of technology, it is to our best interest as designers that our designs also safeguard the interests of the ecology it interacts with as the human species is bound to its ecosystem. It is of utmost peril and stupidity if we ignore the prime purpose of technology.

To avoid this we designers should comprehend the accumulation of knowledge from the people who use and interact with our intended designs.  We are to take their stories and translate these into key bits of information and insights we can use in the creation of truly humane technology.  Even better  if we are able to immerse ourselves into the very context of which the technology is to be used.  I remember as a young engineer, when I was tasked to solve complicated problems that spanned different factory types across the supply chain, the best answers came from the insights I learned by spending time with the technicians on the factory floor. By really joining them on the front lines,  I really saw what the issues were which could not be seen otherwise from some remote terminal scouring scientific journal. It is the empathy with the users and the affected population that gives potency to an invention. A true designer is first and foremost and observer and the precision of his/her observations determines the effectivity of the technical solution he/she proposes.

Let us therefore remember that the greatness of a design pales in comparison to the greatness of the human behind it.

How to Make Sense of Ideality

In innovation, Ideality plays a very important role in the development of any system.  As a matter of fact, Ideality is the main driver of technological evolution.  In a previous post, I mentioned that Ideality is measured by the following equation:

Let us stop and think, however, as to what does this really mean?  The beauty of the ideality equation is that it can actually be expressed as a Benefit/Cost ratio although this really depends on the available information and the analysis required by the audience that requires the calculations.  The best scenario would be to express benefits in terms of potential revenue and harmful effects in terms of $ values.  Putting this $ value on Benefits may not always be possible considering a lot of inventions are really radical.   Some people consider it difficult to put values on Harmful Effects, but this task is actually easier to do than that for Benefits.

Based on my experience Harmful Effects are either Social ( involving Humans and Human settlements) or Ecological.  On this premise, we can then proceed towards using standard valuation paradigms on Social and Ecological impact.  We can go about doing this by estimating actual damage cost ( economic loss because of Social and Ecological damage),  adaptation cost (cost of deploying measures to help affected areas to cope with damage), mitigation cost ( cost of deploying measures to prevent the damage).  Deciding which cost to use is not that simple as detailed information needs to be assessed for each case.  It is however prudent to use the highest among the 3 costs in assessing the ideality of the system.    In the end, the numerator of the Ideality equation, is in fact, a triple bottom line expression of cost as that of Ecological Economics.

How to solve tough problems with Abstraction

I recently published a post on abstraction. Made me reflect more on the power of this tool in my career and my life. When we are faced with challenges, whether it be technical or personal, being in the thick of things entangles us emotionally and prevents us from seeing a creative solution to the issue. It also leads us into what is called “ psychological inertia“ where we are stuck with thought patterns we are comfortable with. To radically break this, it is necessary for us to step back and look at the underlying physical laws and principles at work.

In my previous example, removing dental tartar is simply the separation of deposited films which have likely been solved in the industrial cleaning or microelectronics industries. The joining of metal and plastic in fashion accessories may have been tackled in automotive and industrial machinery scenarios. The key is to get into the underlying mechanisms and use that as a springboard for ideation.

So how do you solve a problem with Abstraction.  The first step is to clearly identify the symptoms of the problem that you face.  This is followed by identifying the general problem that covers the symptoms you observed.  If it's an electric fan whose blades turn slow then the general problem is either there is not enough torque driving the fan or there is a strong resistance against the torque.  The third step is to spell out the general solution in this case it is to increase the torque and minimize the resistance against it.  Finally you formulate the specific solution to your problem. In doing this make sure you check out what other industries and technical fields have done to address the same general problem.

As you try the Abstraction approach you'll likely find problem solving a bit easier and pleasurable.

posted from Bloggeroid

Ideality in Innovation

A great invention stems from considering the ideal state of a system under consideration. An Ideal product gives you all the benefits you want without any cost or harmful effects.  A good way to assess the ideality of a product is by means of the ideality equation:

Harmful effects may be equated either as damage costs, mitigation costs or adaptation costs. When technology is new, cost and harmful effects are high.  As maturity comes, these negative factors are minimized.