Joule has different faces

Article status:                              Draft
Time Estimate for Reading:        15 min
Learning Objectives:                   Concept of Moment and Work
Effort Required:                          Medium
Pedagogy Model:                        Evolution based
Prior Physics Concepts:             displacement, velocity, acceleration, mass, power, force
Prior Math Tools:                       Secondary school level Arithmetic, geometry and algebra


It has been a great journey so far. Starting from space, time and mass, we have come quite some distance from tower of Pisa and Galileo. or should i say displacement?

Looking back at our journey,

Considering only space and time, we added displacement, velocity and acceleration to our vocabulary. That is all an object can do. May be remain at rest or continue in motion. Motion being of uniform velocity or of uniform acceleration. We carefully avoided 'jerk' in our journey. jerk is non-uniform acceleration and is not a comfortable experience.

Different objects, distinguished by its mass can be in motion. So, motion should take the mass of object into consideration. so, we discussed about power of motion and power of rest. The power of rest introduced us to the concept of force. The concept of force led us to the concept of mass and with that we were able to distinguish between mass, weight and force.

With that in perspective, there are few more concepts that we may add to our vocabulary. As much as we deduced force from power of rest, we shall also deduce the the concept of Work and Energy from the power of motion.

We shall look at the concept of power objectively  and also take a peek at the way the concept of work evolved. The concept of energy has to wait for one more article.

Objective perspective:
power = mass * acceleration * velocity

Power is measured in Watt's.

When there is more than one variable (m, a and v in this case) mathematicians, scientists and physicists always like to play with them or try different combinations. shall we say cook things with the same ingredient but different recipes.

p = m * a * d/s   (velocity is m/s)

What are the different combinations. Mathematically speaking we have two choices. Use permutations or combinations. We choose to use combinations instead of permutations (as order is not important).

mass * a has been given the word force .  Force measured in Newton's.

- mass/second does not seem to make any meaning (in fluids we shall introduce mass flow rate).
- acceleration per second or rather change is acceleration per second has been carefully ignored
- mass * displacement also does not seem to make any meaning.

Can we make out something by F * d (force into displacement). A big Yes. But not from manipulating the formula. It comes from analyzing the concept of Lever. Lever would be the first of simple machines. The famous Archimedes (300 BC) statement of "Give me a Lever and the earth shall be lifted"

                                              


Examining the picture of Archimedes with lever, The triangle, rather a 3 dimensional prism, is the support point (fulcrum). The effort is to be applied by the hand of Archimedes. The load to be lifted is the earth.

For a little review of the historical importance, you may take a look at this link.

Now is the time to introduce the concept of rigid body. In the articles so far, we have been discussing about a particle at rest or in motion. A particle necessarily we assumed as a spherical object, with all of its mass concentrated at a single point.

A rigid body need not be spherical. It can have different shapes. May be imagine balancing a broom stick
                        

Observe that the support point is not the geometrical center, but shifted to one side. The point on the object at which support is provided is called the center of mass or center of gravity (since gravitational acceleration is constant at the surface of earth).

Request you to take some time off to watch some videos on application of this lever and center of mass principle. The Equipois and Steadycam. Salute to Mr Garett Brown, the self taught innovator.

The principle of the lever:

                                  
For the lever to be equilibrium (equilibrium is the word used for rigid body at rest),
- provide a support at the center of mass.
- The product of weight and distance on either side should be equal.

This product of W and d is given a word called moment.  We may replace Weight with Force. Force is a more generic word and provides a more generic definition for moment. Moment is the product of force and perpendicular distance from the point of support.

At this juncture, recall that, there is another word called momentum which is a product of mass and velocity. Watch out the effect of adding 2 letters 'um'. It leads to a totally different meaning.

We were discussing on the concept of rest when we considered a particle. Similarly, for a rigid body to be at rest we need to introduce the concept of equilibrium.  So, for a rigid body to be at rest, it should be in both force equilibrium (center of gravity should not move) and moment equilibrium (rigid body should not rotate).

Having discussed on the concept of center of mass, moment, force equilibrium and moment equilibrium let us move forward to get to the concept of work.

Using the concept of moment equilibrium (otherwise called as lever principle), we can
lift any object. may be that is why Archimedes said he can lift the earth. Just put in the mass of earth (5.972 × 10^24 kg) and mass of Archimedes (approx 100 kg) in the formula. We would require a lever of length approx 5.972 × 10^22 meters. Compare this with circumference of earth 4.0075 * 10^4 m. we need a lever roughly 20 orders of magnitude.

Evolution of Work as a concept in physics:

Leaving that aside, we also understand from our experience that, nature does not offer any free lunch. To gain something we need to loose something. 

                               

Observe the displacement of load and displacement of effort. Force * displacement along the line of application of force. Effort has to applied over a longer distance to lift the load through a shorter distance.  So, it is only natural for physicist's to come up with another concept. The concept of Work. Work is the product of Force and displacement along the line of application of force

W = F * d. Force in Newton's and displacement in meters. The unit of work is Nm. Like force is measured in Newton's, Work (Nm) is measured in Joules. Work is just an abstract concept but as we move on, we shall understand the importance of it application in modeling physical systems.

With the introduction of work, Power gets a proper definition. it is the rate of doing work.

P = W/s and is measured in watt's.

For the sake of completeness, Simon Stevin's inclined plane experiment seems to have helped establish the concept of Work. With this experiment, Stevin used the concept of Weight * displacement along the inclined plane. Earlier to this people seem to have tried to establish a relationship with force and angle of inclination.

We began with Galileo (Momentum=mv), Watt (Power = w/s), Newton (Force=ma) and now we have reached Joule (Work=Fd).

But Joule seems to have multiple faces. To know about the different faces of Joule, we need to understand yet another abstract concept called energy. Rather potential and kinetic energy. 

Joule's different Faces:

Moment                  = f*d   measured in Nm

Work                       = f*d  measured in Nm  again

Potential Energy     = m*g*h measured in Nm  again

Kinetic Energy        = 1/2 m*v^2  measured in Nm  again

We have been considering only straight line motion so far. once we complete our discussion on energy (potential and kinetic) in the following article, we can connect the dots and clear the missing links.

By now we have collected enough tools to tread into the field of 2 dimensional rotational motion. There are 2 more concepts which have the same unit as Nm.

Torque                     = Force * radius measured in Nm

Couple                    = Force *distance measured in Nm again

There are 6 concepts in physics with the same unit of Nm. Joule seems to have six faces and it would be nice to know them all. On a lighter note, just imagined joule with six faces and wondered how joule would listen and talk to six people at a time. Really enjoyed the thought experiment. Leave alone the challenge of we talking to a person with six faces.

Now back to physics, this was the area which took a lot of time to crack. it took close to 7 years for me to get to terms. it was a tough journey. may be my IQ levels are low. End of the day, happy that i made it this far.

Let us move on with our journey into yet another abstract concept; Energy. 

References:
https://www.math.nyu.edu/~crorres/Archimedes/Lever/LeverLaw.html

Mass, Weight and Force

Article status:                              Draft
Time Estimate for Reading:       20 min
Learning Objectives:                  Difference between mass, weight and force
Effort Required:                         Medium
Pedagogy Model:                       Evolution, Formula Analysis
Prior Physics Concepts:             displacement, velocity, acceleration, mass, power, force
Prior Math Tools:                       Secondary school level Arithmetic, geometry and algebra

Space, Time and Mass. The three fundamental concepts on which the whole of science is built. rather that is how we try to understand nature.

We have discussed on space in the article "Euclid has Point". We are yet to discuss on time. The focus of this article is mass.

Mass, Weight and Force. This a cause of confusion for most beginners of science. And there have been many efforts from different perspectives to give a clear understanding of this. This is one such effort from yet another perspective (after all each one learns from a different perspective).

By definition, weight is perceived gravity and force is a general term referring to the product of mass * acceleration. mass has multiple definitions and are summarized at the end of this article.

Similar to mass and weight, for beginners in electricity, the direction of conventional current, electromotive force (which is not a force. we should not even say work. we should say it is potential difference) etc are some pitfalls to watch out for.

This is one of the simplest examples i could come across to understand the difference between mass and weight. or rather to define weight.

By now, you should have got it. if not, continue reading.

Let us begin with mass. The textbook definition says "amount of matter". What is the matter with that definition?

From our experience, if someone asks us to buy, say "salt", we will ask how many grams or kilograms. depending on the shop, assuming we were living in the days of Galileo, it may be measured with a simple balance or a spring balance. The digital scales are yet to arrive.

The word 'mass' is yet to have a clear definition. The term heaviness and weight were used for comparing quantities. So, we could say the weight or heaviness of salt is 1 kg.

We are also aware of the fact from Galileo's experiments that every object on the surface of earth has the same acceleration; independent of their heaviness.

Newton with his experiments and observation finds that gravitational acceleration is different on earth and moon. If we carry the same quantity of salt to moon and weigh it with spring balance, it will show a different value as the gravitational acceleration of moon is different.

This is not an acceptable situation. Say, for example we weigh gold with a spring balance and carry it to a place which is much higher in altitude, it would show a different value. With increase in altitude, the gravitational acceleration would decrease. you may refer to the graph on this page for variation of gravitational acceleration with altitude. Notice here that the simple balance is a comparison device and can be used to measure weight independent of altitude.

This issue was put to rest by newton. He introduced the concept of force which is equal to mass * acceleration. f= ma.

At this point, for a detailed discussion on f=ma, you may refer to the article http://openneuron.blogspot.in/2016/03/acceleration-bridge-between-space-time.html

On earth, f = m * 9.81 m/s^2.

What if we define the unit of force as 1 Newton which is equal to 1 kg mass * 1 m/s^2. That is 1 Newton of Force.

So, going back to our salt example which we measured with spring balance, it will contain the acceleration component of 9.81 m/s^2.

Try converting this weight into Newtons. We have to multiply 1kg by 9.81m/s^2
which is = 9.81 Newtons.

Now we can say that mass of the object = 1 kg and Weight (or force) of the object is 9.81 Newtons.

This brings us to another question. Is weight and force the same?

No. Weight has been given an new definition. Weight is defined as perceived gravity. What does that mean?

This is where we take help from E M rogers toy. Alternative example is of measuring our weight in a lift.

When the toy is at rest, the weight of the ball (mg) and force exerted by the spring (kx), balance each other. But, when we allow the toy to fall down, the force exerted by the spring will remain the same, but weight of the ball will reduce and the ball will be pulled by the spring to the top. The component of 'g' will have a lesser value and hence the weight becomes lesser. So, we can say that weight of an object changes with accelerated (or decelerated) motion and hence the definition "perceived gravity ".

We have discussed about weight and understood the concept of perceived gravity with the simple toy.

Now, discussing about force, force is a general term. it may be applied to gravitation force, electric force, magnetic force etc. Weight is similar to force but used only in the context of gravitational force.

Having settled the matter with weight, force and mass, the story does not end here.

Almost all practical applications use weight for calculations. So, what is the need for mass? Every object we take for analysis has a gravitational force acting on it which forces us to take ‘weight’ for analysis. So, is mass just a theory?

Imagine in next 100 years, we colonize few galaxies (am I being too optimistic?). You weigh something here and transport them to some planet in Andromeda. Obviously, the gravitational acceleration there would be different which depends on the mass of the planet (Newtons law of gravitation G*(m1*m2) / r^2). That’s a different story. You export gold and they decide not to pay what you ask for, since it weighs way less than in earth. Chaos!

This would force us a generalized term for measurement. Generalization is possible only if we could remove the variable. In this case, acceleration due to gravity. Remove that ‘g’ from weight and we are left with mass.

In order to make life more interesting, Mass has different names or definitions.
mass:                       density/volume  (we would discuss this in fluids)
Gravitational mass: m * g
Inertial Mass:          m * a  (linear motion):  m=f/a.
Inertial Mass:          mr^2 * alpha  (rotational motion). Here inertial mass is mr^2 and not just m.
Amount of matter:  Given a mass m, we can find the number of atoms or molecules present.                                                 Avogadro number is the link.

                               Mass = moles * Atomic Mass Unit  (1 mole of a substance will weigh AMU gms)
                               As much as 1 dozen is 12, 1 mole represents a number which is 6.023 * 10^23

                               So from our example, we may ask the question, how many molecules of NaCl are                                present in 1 kg mass of salt.

                               From the periodic table, we find that the molecular mass of  NaCl is                                                     22.989 + 35.453 grams.
                              These many grams will contain 1 mole or 6.023 * 10^23. From this we can find                                   out the amount of matter or number of molecules contained in 1 kg mass of salt.
Relativistic Mass:  The change is mass at higher velocities










The story of mass has is yet to see its end.  It seems to make a beginning. Einstein comes in and says that mass and energy are convertible and related by the most famous equation E = mc^2. The Mass energy equivalence.

Science is simpler than psychology

It is so common to hear from students and parents that "i am not good in science. so am choosing arts, commerce, visual communication etc., as a career option"

Too good to be true. not really. lets argue.

The argument goes like this.



Scene 1: That is our friend Hachi from the famous Hachiko movie.



- Can we predict which way will our friend go? To the left, to the right or just turn around and walk back. There may be one too many reasons for our friend to choose an option. It gets almost unpredictable.




Scene 2: The financial market. Can we predict which way would it go?

Scene 3: Global economy. How is the currency value decided?









Scene 4: How about an art something like this. This one of Escher's.

All these scenes above require very high level of skills. Skills like group theory, statistics, probability and more importantly creativity. Add to this the regime of chaos, fractals and self-organizing systems. Mind boggling.


Compare this with science.



Science deals with predictions of motion of inanimate objects. They don't think on their own. All we requires is the concept of acceleration and and a few mathematical tools like arithmetic, geometry and calculus.

With the advent of simulation software's, things have got much simpler.



So, can we say science is simpler than psychology?