Physics 214: General Physics Professor: Ricky J. Sethi

Example	Physics Overview	Economic view	Physical View	Another Example
Have some cash	Have some energy	Financial worth: - Cash/Goods - Real Estate - Credit Cards	Mechanical KE & PE, Internal KE & PE, etc.	Have some gravitational PE
You want to buy a BigMac	You want to change the motion	Use these monetary resources to buy or exchange goods (to pay for them) - Change in goods is what makes life interesting	4. ENERGY is used to "pay" for Forces; Work is the actual payment of the force, and the amount 1. Change in motion is what makes life	Want to drive a nail in the ground (change its motion)
Pay the cashier -- Getting the BigMac was facilitated by paying the cashier (a financial transaction), which converted your cash into a change of goods Transaction details ⇒ actual transaction ⇒ actual exchange of cash for goods (how much, with cash or credit, etc.)	Force changes the motion Transaction details ⇒ actual transaction ⇒ actual exchange of energy for motion mediated by Work, which determines how much Force, over what distance, in same direction as displacement, etc.	This exchange of monetary resources (in the change of goods) is conducted via financial transactions - Financial transactions are how you change your goods	2. Change in motion is caused by Forces (conducted via Forces) 3. Forces change motion	Driving the nail into the ground (changing its motion) was facilitated by the Work, or Force over a certain distance, which converted your Gravitational PE to KE of the nail

Economic analogy: goods are like motion; change in goods, or change in motion, is what's interesting. Goods are exchanged or transformed in financial transactions, which can be monetary, credit, real estate, etc. These financial transactions are like Force. Financial transactions are paid for by (or exchanged with) cash if monetary transaction, credit if credit transaction, real estate if real estate transaction, etc. The transaction itself, including the amount exchanged, is like Work (Force * distance). Energy is the monetary basis, whether cash, credit cards, real estate, etc. How much money you have, your financial worth, is like the amount of energy you have. You can have a lot of cash (KE), a lot of investments (PE), a lot of real estate (Chemical Energy), etc.

We like to figure out the WHAT. What is happening now, what happened in the past, what will happen in the future? If we're very lucky, we might even be able to answer the HOW. But all we can do is Hope to know the WHY.

For example: You want to eat some food. You have some cash so you can buy the food (exchange of goods). You take your cash (monetary resource) and buy some food (extra food is the change in goods). When you pay the cashier, that is a financial transaction and that is how the exchange of goods (buying the Big Mac) was facilitated.

In Physics, you might want to drive a nail into the ground (change its motion -- the motion is equivalent to the food you wanted to eat). You have some gravitational potential energy (the cash) because you're on a cliff. You take your gravitational PE (like your cash) and convert some of it to motion of the nail (the food). You transfer this energy via a Force applied over a certain distance (like the financial transaction of paying the cashier) and cause a change in motion (the buying of the Big Mac, or the exchange of goods).

Energy is the ability to do work and work is moving something against a force, like the force of gravity. From www.qrg.ils.nwu.edu/projects/vss/docs/space-environment/1-what-is-energy.html

Add to energy discussion:
http://home.pacifier.com/~ppenn/whatis.html
http://home.pacifier.com/~ppenn/whatis2.html

* Energy isn't anything real in the sense of a sunset or a rock. It is just a convenient book keeping index that scientists can use to compare many different kinds of systems in terms of their ability to do interesting things. It can be quantified in terms of ergs or joules which is the common currency. Systems that have or can produce the same number of joules, are said to be similar, and can be converted one into the other given the right circumstances.

From www.rider.edu/users/suler/zenstory/thisthing.html

(mechanical energy) E = KE + PE

It turns out that, in addition to this mechanical energy, a system can also have internal energy! Imagine a balloon, filled with H₂ gas. If I throw this balloon in space towards the Moon, it will have mechanical KE due to the motion, or velocity, I gave it. In addition, the individual particles that make up the gas will have a motion independent of the motion of the system (the balloon) as a whole. That internal KE, due to the motion of the individual atoms and molecules, will be measured as Temperature (on the Kelvin scale). In addition to this internal KE, the atoms and molecules that make up the system will also have some internal PE. This can be the PE from binding (which lowers energy); and the bound atoms or molecules aren't just rigid structures; they have some elasticity between them. So they vibrate back and forth and have vibrational PE; they can also rotate and so have rotational PE, etc. It turns out that the INTERNAL ENERGY of the system is:

(internal energy) U = (KE + PE)_atoms

We talked about how changes in motion are what define life, what define our existence. And we talked about how these changes in motion are mediated by Forces (since a = F/m) and paid for by Energy. And that the energy is actually transferred or transformed via Work (this is what we called the transaction itself, above). So Work, it turns out, is energy in transition; that is energy being transferred or transformed (like actually paying the cashier). In other words, that is energy being changed. That's easy enough to do for mechanical/macroscopic systems where we defined it as F*d but how do we figure out changes in the internal energy?

Well, we could look at each individual particle and compute the microscopic KE and PE of each individual particle. But any macroscopic system (like our balloon) has about 10²³ particles... that's 1 followed by twenty-three zeros! That's a lot of particles... and we can't really catch each individual one, check its KE and PE, and toss it back into the mix!

Well, it turns out, we don't have to! It turns out, we can compute the change in Internal Energy by examining certain macroscopic properties of the system. Those properties are the P, V, and T. These are related to the change in Internal Energy via the following:

(change in internal energy) ΔU = Q_in + W_on

We know that the Work done on a system is F*d. But, for example, if we wanted to figure out how much work is done if we drop a particle from the top of a building, the d is simply the Δh (change in height). So, W = F*d = F*Δh. But we also know that p = F/A and so F = pA. So if we substitute this in, we get W = F*d = pA*Δh. But, A*h = V and so W = pΔV! That's the amount of work done on the system (actually, since the Volume was decreasing (the particle fell from a higher height to a lower one), the work done on the system is really: W = - pΔV).

And what about the Q? Well, Q can be transferred via conduction (solids and liquids), convection (liquids and gases), or radiation (em radiation). But how do we quantify how much? Well, we can define the specific heat capacity as the amount of Q needed to raise the temperature of 1-kg of the substance by 1 Kelvin and then empirically (experimentally) measure this c for various materials. It turns out Q = mcΔT.

And so, knowing just the p, V, and T of a system, we can figure out the change in Internal Energy! We don't need to know a whit about any of the individual molecules and particles in order to know exactly how much their internal energy changes!!! But, in the last 125 or so years, we actually started looking at the individual particles. But given their massive numbers, how do we do it? E.g., if I said the population of the US was 280 million, how could I figure out how many of those are adult males over the age of 18? Well, I could go to each individual household and ask. But that would be incredibly time-consuming and variable (someone might die or just turn 18 after I check their house but before I'm done with the survey itself). So how do we do it?

We take samples! We do a statistical analysis and extrapolate from a statistical sample, using statistical methods to ascertain or discern that information. And that's exactly what we do here. Since the number of particles in any macroscopic system is so large, we examine them via statistical means. And, as it turns out, this statistical approach exactly confirms the Thermodynamic one, which doesn't address the issue of the microscopic particles at all! In fact, it doesn't even need to know about it at all!

QUICK SUMMARY: So what kind of energies do we have again? Mechanical KE and PE. Atoms also have this: that's the Internal Energy, which comes in the form of INTERNAL KE and INTERNAL PE (from binding, vibration, rotation, etc.). Temperature is a measure of the INTERNAL KE. This Internal Energy can be transferred via heat and thermodynamic work. Heat is transferred via conduction, convection, and radiation.

And we know that changes in energy account for changes in motion. And that this energy is changed or transformed via work. So you can think of work as energy in transition. It is energy changing from one form to another or from one object to another. In the same way, you can think of HEAT as energy in transition in the Thermodynamic world! Heat IS energy, just like work is. Except Work was done by Force and Heat is transferred by conduction, convection, or radiation.¹

In fact, we know HEAT is also transferred via radiation and radiation is waves and waves carry energy but don't have mass and so, in a way, waves can also be considered as energy in transition!

Things you should know 10 years down the line:

If you see:	You should think:
Scalar vs. Vector	• Scalar: just a number • Vector: number plus direction • ALWAYS keep track of units in everything
Δ	Change In
Velocity (speed)	Δd/Δt
Acceleration	Δv/Δt
Force	ma
Weight	• is not mass • is measured in N or lb • is the Force due to g (acceleration due to gravity, ag)
Momentum	Conservation of Momentum (pi = pf)
Energy	Conservation of Energy (KE & PE) -- Ei = Ef
Power	Energy/time = E/t
Work	Energy in transition
Heat	Also energy in transition (flows from Thigh to Tlow)
Waves	v = f λ → for light, v = c = f λ
Electricity	V = IR and P = VI = I2R
Quantum Mechanics	• At the microscopic level, all aspects of nature seem to be quantized (come in discrete, or whole, multiples)2 • Energy comes in packets called quanta with units of E = hf • Wave-particle duality: at its fundamental level, everything seems to have both a wave and a particle nature (λ = h/mv = h/p) • Heisenberg Uncertainty Principle: we can't know nature with any absolute or arbitrary precision • Instead of Bohr orbits, atoms are described by Energy Levels
Special Relativity	• The laws of physics are the same in any inertial frame of reference • Matter and Energy are different aspects of the same thing, with c2 serving as the conversion factor: Eo = mc2 • When you go really fast, someone at rest relative to you will measure time as slowing down for you3, lengths becoming smaller for you, and mass becoming greater for you

¹ Work is implemented by Force and so (mechanical) energy transition happens via the Forces that are present. If Force is in the same direction as the displacement, it changes both PE and KE. If it's not in the same direction, then only KE is changed (since velocity changes whenever there's an acceleration).
² For example, you already know matter, and thus mass, is quantized (into molecules, atoms, etc.) although we don't usually think of it as discrete and are used to matter as seeming continuous. This isn't that strange since all these weird aspects of nature are very far outside the normal experience we evolved to perceive at our macrscopic level.
³ The stationary observer is who observes your time as taking longer if you're moving relative to them. To you, everything seems absolutely normal. This is because the laws of physics are identical for everyone in an inertial frame of reference in linear, uniform motion (this is the principle of relativity).