Free fallin', now I'm free fallin'
Now I'm free fallin',
Now I'm free fallin'

("Free Fallin," by Tom Petty and Jeff Lynne, 1989)

BEGINNING THE LIST OF PRESSURE MUST-KNOWS

This PTOA Segment starts focusing on the list of PV Pressure "Must Knows" that all PTOA Readers and Students must understand to truly "get" what the PV Pressure is all about.

Pressure depends upon two things:

• A Force that has a magnitude and direction.
• The Area over which that Force is applied.

Area is an easy concept to visually understand.

So the purpose of this PTOA Segment #142 is to focus on what is meant by "Force!"

And that means we need to first focus on the forces created by gravity ... because ...

Spoiler Alert!

If there was no such thing as gravity...

there would be no such thing as pressure!

 

 

WHY DOES AN APPLE FALL DOWN INSTEAD OF UP?

The focus on Force begins with Sir Isaac Newton ... who in real life was not nearly as happy looking as shown in the nearby cartoons. Frankly, he would have greatly benefitted from a few more hugs in life.

Anyway the rumor is that this Englishman sat under an apple tree in the English countryside one day and an apple fell on his head. Your Mentor doesn't really think that happened but its a nice story so I am spreading the rumor.

 

Isaac began to wonder ... why did that apple fall down ...instead of fall sideways ... or even up?

Sir Isaac Newton had begun his investigation of gravity's impact on freely falling objects.

 

 

 

Nowadays ... we Earthlings have grown up watching astronauts floating around in zero gravity and take for granted the concept of being held on earth by the downward force of gravity ... but this Newton dude actually figured all of that out for us.

Isaac got around to publishing his ideas in 1687 ...

So that means that even though the Universe had incorporated gravity from the get-go ... human beings have only known about it for 350 years.

It took that long before Isaac Newton successfully math modelled the relationship between free falling objects and the forces that are created when those objects hit the ground because of gravity.

And Newton's ideas were a big deal because gravitational forces predict how anything on earth moves upward, downward, sideways and around! Including this dude on a snowboard:

 

ANOTHER STRATEGIC TRIANGULAR RELATIONSHIP

PTOA Readers and Students who are reading the PTOA Segments in the intended sequential order learned about the Ohm's Law strategic triangle that depicts three mathematical relationships between the components of Voltage (V),Current (I), and Resistance(R).

Well...

Newton figured out the below definition for a force that is created by gravity attracting a mass and making it fall downward:

F= M*A

The mathematical relationship that defines the gravity-created force can also be represented in the nearby handy dandy strategic triangle.

F is the Force of the apple as it hit Isaac's head.

M is the mass of the apple ... we are going to assume that it is one pound.

A is how much the velocity of the apple increased while falling through the vertical distance before it hit Isaac's head.

There are several interesting points to make at this juncture:

1. A constantly changing velocity that is increasing is called Acceleration. If the apple had fallen from a higher branch, the velocity of the apple would have had more time to constantly increase as it fell. Thus, the force Newton would have felt as the apple made contact with his noggin would have been of a greater magnitude.
2. Newton calculated the downward acceleration of the apple caused by the Earth's gravitational pull to be 32.2 ft/sec2.
3. Newton figured out that this acceleration caused by gravity was the same for any free falling mass. So don't be surprised if instead of an "a for acceleration" you see a "g for gravitational force" in the mathematical definition for force ... because that's short hand for signaling the acceleration is coming from the gravitational pull of the Earth.

This was amazing news 350 years ago!

Newton's work confirmed what had been noticed by Galileo a hundred years earlier.

Galileo threw two objects with significantly different masses off of the Leaning Tower of Pisa and noticed that .. even though one was much heavier than the other ... they both hit the ground at the same time.

Galileo did not realize at the time ... because it took a 100 more years for Newton to figure it out ... that freely falling objects with differing masses hit the ground with substantially different forces ... but their acceleration is the same because the gravitational pull on all falling objects is a constant.

Yes, Indeedo!

The world had to wait for Newton's work to learn that it was the acceleration due to the gravitational force of Earth which drew the two masses downward at an equivalent rate ... and that rate could be quantified as 32.2 ft/s².

Pretty cool to determine the force of gravity assigned to the Earth by the Universe, Isaac Newton!  Way to go!

But it sure would have been nice if Sir Isaac had made one little adjustment while in the process of mathematically defining the force that is created by gravity acting upon a freely falling mass.

 

GEE THANKS ... SIR ISAAC NEWTON!

Let's cut Newton a little slack and assume that he was preoccupied contemplating how to define gravity-created forces.

So maybe that explains the everlasting confusion he left to the rest of us to deal with.

Take another look at the definition of Force that Sir Isaac came up with:

Force = mass * acceleration.

aka

Gravity Created Force = mass * acceleration of gravity

In the process of defining the magnitude of a force created when the acceleration of gravity pulled a 1 pound mass of apple downward, Newton took the easy way out when defining the units of force and declared the force was simply "a pound of force."

Since he was simultaneously defining the concepts of force and the constant acceleration of gravity ...  he had a sole license to call these things whatever he wanted to.

For example ...

He could have called the Force that resulted when a one pound mass accelerates downward due to gravity "a forcie."

He could have called it "an applesmack."

But NOOOooo!

He had to go and call it a "pound of force" ...

which evermore necessitates those few of us left using English measuring units to clarify the confusion between "pound of force" and "pound of mass"!

Admittedly ... "pound of force" has more gravitas than "forcie" or "applesmack" would have had in Newton's Principia ...

Nevertheless, those of us still using the English system must use subscripts to clarify which pound type we're referring to:

pound of mass has the units lb_m

pound of force has the units lb_f

There has been a  half hearted attempt to eliminate the  "pound of mass" as the English system mass unit and replace it with a "slug."

For example ...

 

The nearby chart cross references which units to use for Length, Force, Mass, Time, and Pressure ... depending upon if you are using the MKS, CGS, or English system (first column).

The SI system is the MKS system. What a pity that isn't clarified in the chart.

As you can see the word "Slug" appears as the English unit for mass.

And this makes us wonder two things ...

• what the heck is a slug?
• why doesn't it say pound (of mass) in that place on the table?

 

In summary ...the concept of a slug never really caught on as an English unit of mass.

 

 

The SI (aka MKS) system actually did what Your Mentor suggested that Newton should have done and assigned the units of Force something totally different than the units used for Mass.

In the MKS (aka SI) system of measurement the units of Force are "Newtons."

So ...in the SI units of measurement:

A Newton is the force that results when one kilogram of mass free falls to earth while accelerating at 1 meter/sec². Now you know!

 

FRED IS STRESSED OUT

Fred is telling me that he is still a little fuzzy understanding the difference between:

Pound of Force (lb_f)

and

Pound of Mass (lb_m)

Don't stress out, Fred!

That will be covered in the next PTOA Segment!

 

TAKE HOME MESSAGES: Pressure has two components: (1) A force with a magnitude and direction (2) the Area over which the force impacts.

Gravitational forces are caused by gravity pulling down on a mass.

Newton correctly math modelled forces created by gravity with the mathematical expression:

F=MA

The mathematical expression Newton developed indicates that there are  two components of gravity-created forces:

• The mass that is free falling.
• The acceleration of gravity pulling the mass down toward earth.

The acceleration of gravity is constant at 32.2 ft/s² and is sometimes called g.

Therefore F=MA is sometimes written F=mg.

Newton called F "a pound of force" which is written lb_f.

In English units the "m" is a pound of mass which is written lb_m.

The use of both types of pounds used in the English system of measurement often causes confusion.

In the SI Units of measurement, the unit of Force is called a Newton which is quite different that the unit of mass which is a kilogram.

A Newton is the force that results when one kilogram of mass free falls to earth while accelerating at 1 meter/sec²

©2016 PTOA Segment 0142
PTOA Process Variable Pressure Focus Study Area
PTOA Introduction to PV Pressure Focus Study

 

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