PHY111: Summer 201253

Lesson 11: Linear Mechanics I

- Types of forces- Inertia (Galileo)- Newton’s Laws of Motion

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Y:\David_LaFazia\Physics Courses\PHY111_2

Types of ForcesBelow I have made a simple tree of forces. It leaves out some (pun intended, get it?), certainly,

but for you these are the ones most likely to come up. I will briefly go through each one and discuss their basic natures.

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Types of ForcesDistance forces versus Contact forces

These are two very important force categories. It is necessary for you to know that some forces require contact between two objects in order to act, while some can act over long distances (through empty space, essentially). It is usually useful to demonstrate how distance forces can act when two objects are not even in contact. Here are two examples:

1) Drop a ball. Why did it drop (what force caused this ball to change its motion)? The force due to gravity caused the ball to change its motion.

2) Rub a balloon across your hair to produce a state of static electricity. Hold the balloon above (but not touching) your arm-hairs or the head-hair of a peer (or even a small piece of paper). You will observe a change in motion of the hair (or small piece of paper). Why did the object move (what force caused this object to move)? An electric force was acting on the hairs/paper.

In this last experiment, it is sometimes interesting to note that the electric force had to first overcome the gravitational force in order to lift up on the object (this is most easily discussed when the object is that small piece of paper). I have emphasized that the piece of paper should be SMALL because of this very same "tug-of-war" between the two forces in this vertically-oriented experiment.

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If you think THAT was a mouthful, you ain’t seen nothin’ yet.

Types of ForcesGravitational force

Gravity is. We do not know WHY gravity exists, but we can certainly study its effects. Basically, anything at all that has mass has some "gravitational field" associated with it. Even the particles of air that we breathe or that zoom by us exert a gravitational force on all other objects. The closer two objects are, the stronger the "Weight" (or force because of gravity) between them (and vice versa for being further away).

[For our purposes, this is governed by a "complex" instead of a "simple" relationship...in other words the relationship between distance and gravity is non-linear].

Usually in the classroom experience we talk about gravity acting "downward," but of course since EVERY object has its own gravitational attraction then gravity acts in whatever direction the mass occupies. The reason we identify "down" as being toward the center of the Earth is because the Earth's mass "trumps" the masses of any other in the area. All of the other gravitational force sources are incredibly weak compared to the Earth (again, simply because gravity is associated with mass, and the Earth is rather massive).

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Types of ForcesElectromagnetic forces

People tend to have fun with magnetic forces very early on in life (generally speaking). We usually divorce magnetism from electric concepts, but the two by nature go hand in hand. It is usually sufficient, however, to simply say that the two are very closely related and then consider them two separate ideas on their own. Both electricity and magnetism are related to charges. Charges make up the basics of matter. I am not going to go into a long explanation of how magnets work (or how to make a magnet). Instead, I simply want to point out that the Electric Force is key to understanding what is happening on the SMALL SCALE. The Electric Force acts very much like a spring between particles.

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Types of ForcesTension

Tension is basically the "I WANT TO STAY AS I AM!" force. If you pull on a rope, the material of the rope resists stretching. This allows a force applied at one end to "translate" through the rope to the other end. You can see how important it is to use rigid materials by simply using a weak rubber band and attaching a heavy mass to the end. Then, bob the mass up and down on the end of the rubber band. There is a definite delay in the motion due to the ability of the rubber band to stretch. Although this IS an example of tension, for materials like rubber bands we more correctly consider this to be a "spring force" (see an upcoming slide). Tension can be summed up as the resistance of any material to undergo a change in its [dimensional] characteristics. In other words, the rope did not want to lengthen (or become thinner). If you pull on someone's hair, the same thing is seen. The strand of hair resists a change in its dimensions and the root of the hair feels the same force as that which was applied at the other end.

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Types of ForcesFriction

Friction is a broad category, but I typically like to break it up into two: kinetic (or sliding) and static. Friction is most definitely a contact force. Friction exists because of microscopic interactions between two objects' surfaces. With static friction, there must be some applied force for these interactions to resist. If there is no force applied to try to get the object moving, then there need be no friction! Friction's "job" is to prevent slipping (as best it can), so if there is no danger of slippage (no force applied to resist) then a frictional force cannot exist at that time. However, once you try to move something (applying a force), then a frictional force because of these microscopic interactions between the two surfaces will exert itself in the opposite direction.

If you push (or pull) hard enough, then you break those microscopic interactions between the two surfaces and the object begins to move. The interactions are still present, but in a weakened form. They will not return to their original strength again unless the object stops moving across the surface (even if only for the briefest of moments). This friction while two objects are sliding across each other is called, appropriately, sliding friction (or kinetic friction).

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Types of ForcesSpring force

A spring (or a piece of elastic, or an air-filled ball, or a rubber band, &tc.) will resist a change in its shape. However, it's generally not all that good at it. The force required to stretch or compress an elastic material increases "simply" (i.e., "linearly") the further you stretch or compress it! For instance, let us say that I take a spring. I stretch it 2 cm and I note (with a scale) that this requires 8 Newtons of force. I then stretch it to 4 cm and note that this requires 16 Newtons of force. My prediction is that if I stretch it to 8 cm, then it would take 32 Newtons of force to do so.

[Note that, in reality, there is always an "elastic limit." In other words, materials have an extreme point which shows that they are actually breakable...but within the reasonable range for any material, this "simple" relationship holds true very well].

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Actual Guiness World Record

Winner for Most Elastic Mouth!

Types of ForcesAir Resistance

I will be brief with air resistance. Basically, air resistance is a complicated set of interactions...but for our purposes it can be simplified. Assume that all air is made of tiny bowling balls. As an object moves through the air, it is continually colliding with these extremely small bowling balls. Yes, the balls are moved out of the way or around the edges of an object, but they take their toll on the kinetic energy. In fact, they receive some of the kinetic energy of the moving object. That is air resistance in a nutshell.

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Types of ForcesSupporting Force

The Support force (or "Normal force," if you prefer) is the "STAY OUT OF MY SPACE!" force. As has already been stated, materials do not like to change their characteristics. If you stand on a floor, you are trying to compress (or at least displace) the material of the floor. However, because of the properties of the material of the floor, it is able to resist any significant change in its shape. This resistance is the "support force.“ The same thing is true of leaning against a wall, or banging your head against a test paper (or desk, if you prefer). We are very fortunate that objects can exert this support force. How well an object (or surface) does this depends on the microscopic characteristics of the materials of which it is made.

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Types of ForcesApplied Force

This list would not be sufficient if I left out "Applied Force.“ This pretty much covers any other push or pull force for which your situation might call. There is not much to say about this type, except that it is convenient to use the name. This is a very versatile force type--almost a category of its own that can (let's be honest) get you out of many "jambs" in your work.

It is similar to me saying “Force-LaFazia” to mean “Force applied by Mr. LaFazia.”

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Galileo Galilei on Inertiaa MrLaFazia.com original snapshot

SOURCE: http://www.cartoonstock.com/newscartoons/cartoonists/bro/lowres/bron1636l.jpg

NOTE: Galileo lived from 1564 to 1642… NOT 1489!

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Introduction & Overview

• Galileo’s life teaches us many things– (not the least of which is—DON’T STARE AT THE

SUN THROUGH A TELESCOPE!)• For today, however, we will discuss his ideas

on MOTION1) the Leaning Tower of Pisa2) defining Force and the role of friction3) Inertia (ramp experiments)

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IMPORTANT NOTE: You will only be able to view the embedded videos by (instead) going to the appropriate folder in the Course Documents section on Blackboard. You may have to save the videos to your computer in order to view them.

The Leaning Tower of Pisa• This tower portion is considered “legend,” of course…but...• Wherever he dropped the objects, Galileo showed that less

massive objects fall at the same rate as more massive ones– air resistance must either be equal or eliminated

SOURCE: http://improbable.com/airchives/paperair/volume15/v15i3/v15i3-web-images/KIM-Galileo_of_the_lem_opt.jpeg

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VIEW VIDEO CLIP HERE:http://mrlafazia.com/studentaccess/PHY111_temp/leaning_tower.wmv

Defining “Force”• Forces are most simply defined as

– A PUSH– Or A PULL

• It was once believed that forces were needed to KEEP objects in motion.– People believed this because life taught them that objects slow down

and eventually stop (like your car not moving) unless a force keeps them going.

• Galileo showed that objects need no force to maintain their motion. – What people originally had not realized was the fact that friction is a

FORCE as well!• The fact is: Forces that aren’t balanced out will ALWAYS cause a

change in any object’s motion (whether speeding up or slowing down or changing direction)!

SOURCE: http://goozydumps.files.wordpress.com/2008/09/galileos_experiment.jpg

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Inertia

• Galileo did a number of experiments to test his theories of forces and motion:

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VIEW VIDEO CLIP HERE:http://mrlafazia.com/studentaccess/PHY111_temp/Galileo_ramps.wmv

SOURCE: http://www.cartoonstock.com/cartoonview.asp?catref=mhen235 17/33

Inertia

• Imagine if a ball were allowed to roll down a ramp and roll right onto a level ramp.– Without a force to slow it down or speed it up,

what would happen to its motion?• THIS is the concept of “inertia.”

– What would be needed to speed up the ball?– What would be needed to slow down the ball?– ______________ slow down the ball in the real

world. This does NOT violate the concept of Inertia, but rather justifies it!

Frictional Forces

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The Law of Inertia

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VIEW VIDEO CLIP HERE:http://mrlafazia.com/studentaccess/PHY111_temp/Law%20of%20Inertia.wmv

Forces…Motion…& Energy?• Do the results of the ramp experiments (see page

32, Figure 3.4 of Conceptual Physics) match up with our understanding of the Conservation of Energy (“Total Energy is Boring”) Principle?

• Perhaps you have heard the formation of these concepts attributed to Sir Isaac Newton or another scientist, before. There is a someday-famous poem which describes this misconception quite well. I will read it to you during our next class…

• STAY TUNED! 20/33

A Final Bit of Humor

SOURCE: http://emdashes.com/assets_c/2010/04/Galileoroll2-thumb-182x224.png

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Newton’s Laws of Motion- an introduction -

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First off, we must ask…“What ARE Forces”??

• Put simply, a Force is “a push or a pull”.

• Looking at the BIG PICTURE, a Force is defined as “a way to transfer Energy”.

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Vector or Scalar??

• Strictly speaking, Forces are VECTORS

• For this reason, we represent Forces with arrows. The longer the arrow, the greater the magnitude (number-value), and the angle of the arrow tells us the direction of the Force!

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F.B.D.-ing

• This is best seen by drawing a Free-Body Diagram (as important as Dimensional Analysis!)

• A Free-Body Diagram (or FBD) is a tool that takes an object all by itself and shows ONLY the Forces acting on THAT OBJECT!

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An Example of FBD-ing

fk

Fg

N

Fpush

Box being pushed along rough surface:

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Why do we need to know about Newton’s Laws of Motion???

• Newton’s 3 Laws of Motion help us to understand WHY an object moves (or why one doesn’t move).

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Law # 1

• The Law of Inertia– What is inertia??

• Bill Nye says…? • Definition (the tendency of….)

• So…what IS Newton’s 1st Law of Motion??– “An object in motion will tend to stay in motion,

and an object at rest will tend to stay at rest, unless acted upon by an outside, unbalanced Force.”

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Inertia is a property of mass.

The tendency of an object to resist a change in its motion.

Law #2

• “The acceleration an object experiences is directly proportional to the overall Force acting on it and inversely proportional to the object’s mass.”

• This is hard to picture, so let’s just remember it as an equation:

F = m a∙

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Law #3

• …often known as the “action/reaction” Law

• “For every action there is an equal and opposite reaction.”

– Examples: “Normal” force from floor, pushing against a wall, letting air out of a balloon, &tc.

• Note: “Normal” means “Perpendicular” or “Orthogonal”. Never think of it as the “regular” force.

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Sometimes it is useful to refer to this as a “Support” force. The two are interchangeable.

Video Clips• Watch Julius Sumner Miller Inertia mini-lecture

Part 1http://www.youtube.com/watch?v=BwkUNrSCNMg

• Watch Julius Sumner Miller Inertia mini-lecture Part 2

http://www.youtube.com/watch?v=Hyw9uNF4nmE&feature=related

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Grades/Assignments:Read Sections 3.8-3.10; 4.6.

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Looking Ahead:Lesson 12 will take place in-class (Room 144, this time, remember). We will continue our discussion of Linear Mechanics.

I will be updating both Blackboard and MrLaFazia.com for the remainder of the semester, so that no one is inconvenienced by the switch if they preferred Blackboard. For everyone else, however, I will continue to develop our alternative form (as I plan to use this full-time starting in the Fall).

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