Blue Jean, look out world, you know I've got mine.

("Blue Jean," by David Bowie, 1984)

 

THE DIFFERENCE BETWEEN
MASS ... MEASURED IN lb_m
FORCE ... MEASURED IN lb_f
AND
WEIGHT ... ALSO MEASURED IN lb_f

PTOA Readers and Students who are reading the PTOA Segments in the intended sequential order know that Fred was left hanging at the end of PTOA Segment #142 and isn't clear in his head on the difference between:

• The English unit for mass ...aka "a pound of mass" or "lb_m" for short.
• The English unit for force ..."a pound of force" or "lb_f" for short.

 

 

What Fred clearly understood from PTOA Segment #142 was:

• Pressure is a Force spread out over an Area.
• Newton defined Force. He figured out F = m*a where m is a mass and a is acceleration.
• The definition changes to F =m*g when the acceleration is caused by gravity.

Newton's definition of force shows that the amount of force created is determined by

1. The amount of mass that is moving.
2. The constantly changing velocity ... aka acceleration ... that reveals the increasing speed and direction that the mass is moving. When the mass is being pulled downward by Earth's gravity, the acceleration is called g which Newton figured out to be 32.2 ft/s².

In this PTOA Segment #143, PTOA Readers and Students will learn the differences and interrelationships between mass, force, and weight.

When your body is standing on a scale, the force that is created by Earth's gravity pulling down on your mass is called your weight.

Weight is a force that is used to infer ...or measure ... a quantity of mass.

 

 

Believe you me there are A LOT of Process Operators walking around blissfully unaware of how the relationship between a mass and the weight force created by the mass when gravity pulls it downward is fundamental to understanding the PV Pressure.

And all these Process Operators are living  fine lives.

So don't stress if you don't "get it."

 

POUNDS OF MASS (lb_m) DEFINED

The PV Pressure does not exist without some amount of mass.

That's because the PV Pressure is determined by the magnitude of a force that is spread over an area ...

And one of the two components that make up a force is mass:

F = m*g

PTOA Readers and Students who are reading the PTOA Segments in the intended sequential order were first introduced to Stuff/Matter/Mass in PTOA Segment #60 which was entitled "I Am The Walrus."

Mass can be super small ... like dust mites ...

or super big like elephants and whales and buildings.

Mass can have a lot of space between it ... like air particles.

 

A container that is 1 foot high and 1 foot wide and 1 foot long ...

aka a cubic foot (which is written 1 ft³) ...

 

has the same volume as 7.48 gallons and 28.3 liters.

 

If that container is in a dry area that is held at 70 °F and the atmospheric pressure is at sea level ...

14.97 lb_f per square inch...

 

well there's 0.075 pounds of air mass (lb_m) in that container ... even though you can't see it!

The point Your Mentor is trying to make is that ...

Anything you can visually see is mass.

And even some very tiny stuff you can't see is mass.

Some folks use a fancy name for small particle mass ...the word is "matter".

Your Mentor tends to just say "Stuff."

Whatever!

The English units used to measure all types of Stuff/Matter/Mass in the PTOA are "pounds of mass" aka lb_m.

 

HOW TO INFER THE AMOUNT OF MASS (lb_m)
FROM THE AMOUNT OF WEIGHT FORCE (lb_f)

So ...

If the end goal is to get around to quantifying the PV Pressure in its various industrial applications ...

We must first quantify how much mass is involved with creating the force that is spread out over an area.

How do we determine how much mass we are both talking about?

This is not a trivial problem!

Let's say we all live in regions that have barter and trade economies. No coins or currency exist.

How do I know for sure that I am getting a 1 lb_m of apples from you in exchange for 1 lb_m of grain from me?

And nowadays ...

How do I know that the 3 lb_m bag of apples (aka1.36 kg_m) in the modern grocery store truly is 3 pounds of apple mass for the advertised price?

 

Whether we are talking about mass in units of nanograms, pounds, kilograms or tons ...

How can I be sure we are talking about the same quantity of mass?

This is how:

The mass in question is inferred from the weight force that is created by gravity acting on a standard, calibrated mass.

Clarification, please!

Ok!

PTOA Readers and Students just learned in PTOA Segment #142 that gravity creates forces by pulling a mass downward ... which is exactly what happens when you step on a scale

In the USA, the vast majority of teenagers grow into 100 lb_m (aka 45.5 kg_m) around the age of 13.

It's kind of a big deal to look down on the scale and notice the pointer is hovering around 100 pounds (45.5 kilograms)!

But guess what?

That scale reading of a weight is actually reading 100 pounds of force ... lb_f!

 

Each of us infers our body mass from a scale that reads in pounds of force ... aka a weight.

One more chorus ...

A body weight is determined from gravity pulling the mass of the body downward as the body stands on the scale surface.

 

Since the acceleration of gravity is universally constant on the surface of Earth, the weight force reading output infers the magnitude of the mass that created the weight force in the first place.

Aha!

That means...

A pound of mass (lb_m) is not impacted by gravity ...

but a pound of force (lb_f) is!

So what happens when you step on a scale that is located on the Moon?

The Moon has 1/6th the surface gravity that Earth has.

 

Oh! There's another rule from the Universe that must be squeezed in at this point.

Unless we are traveling at the speed of light (and we are not) ...

"Mass/Matter/Stuff cannot be created nor destroyed ... although it's okay to change forms."

That statement means a quantity of mass determined to be 100 pounds on Earth will still be 100 lb_m on the Moon!

But a weight determined to be 100 lb_f on earth is just 16.6 lb_f on the Moon.

 

Hey! That makes sense because the weight force that would be created by the Moon's weaker surface gravity would be just 1/6th of the weight force created by the same mass with Earth's gravity.

You know what this means ...

No matter how much less you weigh on the Moon ... you still won't be able to button those jeans that didn't fit on Earth!

However it will be a lot of fun bouncing around in 1/6th g!

Sooo...

What would happen on Jupiter if a mass of 100 pounds that weighed 100 pounds force on earth were reweighed on Jupiter?

According to the above chart, the gravity of Jupiter is 2.53 times the gravity experienced on Earth's surface.

A 100 lb_f on Earth would weigh 253 lb_f on Jupiter.

But the 100 lb_m would be the same amount on both planets ... it would just feel a lot more crushed on Jupiter!

 

LET'S GO TO THE MOVIES:  APOLLO 13

The 1995 Movie Apollo 13 featured the true story of NASA's finest days and hours guiding three American astronauts safely back to earth after their mission to explore the Moon was interrupted by an oxygen tank explosion (root cause: damaged electrical wire insulation).

The trajectory of the returning Command Module was just one of the many challenges of the suddenly redefined mission.

The original trajectory had been calculated with the assumption that a mass of collected moon rocks (lb_m) would be on board.

As the Command Module was pulled toward Earth by Earth's gravitational field, the missing weight (lb_f) of the moon rocks influenced the intended trajectory of the Command Module.

 

HOW ARE YOU DOING FRED?

Fred ...

Do you understand the difference between mass and weight?

 

Check!

 

 

Great, Fred!

Do you understand that weight is a force?

 

Check!

 

 

Fantastic, Fred!

Do you understand that we Earthlings infer the amount of mass we're talking about by determining the weight force created by the mass and the Earth's surface gravity ... which is indicated via a weight scale of some type?

 

Check!

 

 

Magnificent, Fred!

Do you understand that mass is not impacted by gravity but that a weight force is?

 

Check!

 

 

Super, Fred!

So you're good, right?

 

OMG, FRED!
What's troubling you now?

 

 

 

Fred doesn't understand why Newton's definition of force does not match up with respect to the units of the two components that create the force.

Good for Fred for remembering that consistency of units is A BIG DEAL when defining things with mathematical expressions!

And Fred is correctamundo!

The units on both sides of Newton's force definition are not compatible.

F= m*g does not end up with equivalent units!

Let's say that one pound mass of apple (1 lb_m) falls down and hits Newton in the head with the 1 lb_f that is created by Earth's gravity:

F= m *g

So let's plug-in what we know on both sides of the mathematical expression that defines Force:

1 lb_f = 1 lb_m * 32.2 feet/sec²

No way are the units the same on both sides of the mathematical expression that Newton developed to define force!

And why isn't the force determined to be 32.2 lb_f since 1 * 32 = 32?

The next PTOA Segment will demonstrate how the problem of English unit inconsistency between Force and its contributing components ... mass and the acceleration caused by gravity ... are fixed.

 

TAKE HOME MESSAGES: The intent of this PTOA Segment was to clarify the definition and interrelationships between: 

• "Pounds of Mass" ... measured in lb_m. The magnitude of a Mass is not dependent upon a gravitational field.
• "Pounds of Force" ... measured in lb_f. The magnitude of a Force is dependent upon a gravitational field.
• "Weight" ... a force created by gravity acting upon a mass ... and which is likewise measured in lb_f. The sole purpose of determining a weight is to infer the magnitude of the mass that is creating the weight force.

The PV Pressure is created when a Force is spread over an Area.

Figuring out the magnitude of a Pressure depends upon quantifying the amount of mass that is contributing to the Force component of Pressure.

The English units of measurement require a little magic to make the units of F = m*g consistent.

©2016 PTOA Segment 0143
PTOA Process Variable Pressure Focus Study Area
PTOA Introduction to PV Pressure Focus Study

 

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