Contents of The Universe and Deforming Solids

Transcription

1 Skyscrapers in the 2011 Japan Earthquake Contents of The Universe and Deforming Solids For most of this course, we ve talked about physics we ve known about for > 100 years. Today, we ll discuss some physics we are still trying to figure out!

2 Today The contents of the WHOLE UNIVERSE! You should be able to make small talk about Plasma and Dark Matter Matter we can interact with: Stretching and squeezing forces. Pushing atoms together. What kind of materials make up the Universe? Part of my goal for today is to introduce you to the really major change in human self-understanding that astronomy has given us in the past years. The first half of this lecture will be all conceptual and then we ll move back to some discussion about physical principles of solids.

3 Light travels at finite speed. vlight = c = 3 x 10 8 m/s 150 million km (1.5x10 8 km) t = Δx/v = 8 minutes for Sun s light to reach us The first If the sun disappeared suddenly, we d take 8 minutes to know about it. So we see the sun as it was 8 minutes ago.

4 you are here km So if we look at things further and further away, we are seeing into the more distant past: light from across OUR OWN GALAXY takes 30,000 years to reach us. So we re seeing those objects as they were 30,000 years ago. But as we look at things further and further away in the sky, we see older and older stages of the Universe. It s a little like going through the photo album of your life backwards.

5 The Universe as we see it Once you get through the astronomically local environment to the really old stuff, the universe starts to change how it looks. Now, we have such sensitive telescopes we can look further and further and further away. Now if you think of further away as seeing older and older light, you think: if I look far enough, I should be able to see through the development of stars and galaxies, right out to just about the very beginning of the Universe. I find I m often the person who is the first to tell you this, but we have actually done this. We have imaged the sky at the earliest phase of the Universe that we can possibly see, when the Universe is almost pure radiation.

6 The visible edge of the (infinite) Universe, as we see it. Here s what it looks like. This is the furthest point we can see in the Universe. This is a projected temperature map of the whole sky. You see some hot areas in red and colder areas in blue. Again, everything was basically all just radiation back then. We call this radiation wall the cosmic microwave background. Based on how far it is, we can say it s light from around 13.7 BILLION years ago. The baby Universe. From our observations of this edge of the visible universe, everything at this point was basically very hot and dense, no coherent structures formed yet. But there were the seeds of them: you can see these as temperature ripples on the sky. These eventually, over time, will form into the galaxies and structures we see today.

7 Make-up of the Universe From observations of this background, and of the galaxies across the Universe s history, we can map how the Universe is evolving with time. This has told us a few key things: - The Universe is expanding (galaxies look like they re speeding away from us!). - This expansion is accelerating. So things are getting further apart more rapidly with time. The cause of that is something we don t know, and refer to as DARK ENERGY. Bear with me.

8 The Cosmic Budget Dark Energy is a repulsive force : pushes things away from each other. } Matter has gravity: an attractive force. We can see from the accelerated expansion of the Universe that there s something pulling space to get larger and larger. But we also know that gravity is an attractive force: it wants to pull things together. So there are opposing forces acting on the large scale, one pushing and one pulling. The pushing matter, the dark energy is winning: we can see therefore that the fabric of the Universe is made up of mostly dark energy.

9 The rest of this chapter: Solids, liquids, gasses, plasma. What never ceases to both amuse and terrify me, is that this little wedge, this 4%, what we refer to as baryonic matter is what we as humans interact with. And this is what we ll be spending the rest of the chapter discussing. In particular this material exists as four more familiar states of matter: Solid, liquid, gas, and plasma.

10 First: states of regular, baryonic matter (non-dark-energy and non-dark-matter). FOUR States of Regular Matter

11 What if we apply more energy? Plasma: 4th state of regular matter (and 99% of the 4% of our interactions). Plasma is a cloud of atoms with its electrons ripped off. Now if we apply MORE energy to gas, we get what we call a plasma, which is basically a cloud of atoms with some of its electrons ripped off. Making an ion: apply energy to overcome that force and rip the electrons away from the atom.

12 Familiar Locations of Plasma Also 3rd floor of White Hall :) All stars are plasma, fluorescent lights, plasma TVs, those plasma globe things. It s also a big field of study of people here at WVU.

13 And now back to more familiar things You don t need to know anything more for the test about these things. Just to have a general sense of the Universe s make-up and how we know what it is.

14 The rest of today: Deforming Solids What does it take to change the shape or volume of a solid? An external force! The shape of a solid will return if a small force is applied. Large forces might break/deform object. Fdoor Area of cat head Ffloor Rest of today, we re going to talk about compressing solids. There are three things to consider.

15 Pressure/Stress Force over Area. Damage depends more on pressure than force! Pressure or Stress = F / A SI units: Pascal (Pa) N m 2 Pressure (liquids/gases) or Stress (solids) tells you over what area the force is spread. In particular, what if we deform them or apply pressure? Recall PRESSURE AND STRESS REFER TO THE SAME THING.

16 Types of deformation Length (tensile stress) Pushing atoms together Shape (shear stress) Bending or breaking bonds Volume (bulk stress)

17 Pressure, Force per Area Deforming solids stress = modulus x strain higher implies stiffer material How squished it gets while stressed Small modulus (easy to deform) Large modulus (hard to deform) All of these relations are of similar format They relate the force you re applying over some area to how deformed it gets when you hold it with that force. And they depend very much on the object s modulus, which defines the material s stiffness. As an example If I lean on a rock, it doesn t deform very much. Because it has a large stiffness (large modulus). Jello has very low stiffness (small modulus) and deforms a lot more under the same pressure, or stress, from my hand. Materials also have what s called an elastic limit, where it can only take so much stress before permanently deforming, or breaking.

18 Deforming solids If you strain something beyond its elastic limit, it will not spring back. If you strain something beyond its breaking point, it will break! Clay has a low modulus but also a very low elastic limit. My ball has a low modulus but a high elastic limit (it springs back). But push too hard and it WON T!

19 Strain in your life Ex: roads, airplane wings, medical inserts, building materials, etc. What are the applications of this? There are TONS the main issue is, we need to know how much force materials can stand before they PERMANENTLY BEND or BREAK. Strain/Stress analysis in comparing different materials can tell us that.

20 Elasticity in Length Tensile stress = Perpendicular F A = Y ΔL Lo stress = modulus x strain ΔL = L f L 0 Y = Young s modulus TensileStrain = ΔL L o Force is perpendicular to the surface over which the force is applied.

21 Find the Young s Modulus of JELLO! Tensile stress = F A = Y ΔL Lo ΔL L o F = mg The book has a list of Young s modulus for various materials, including steel, aluminum, etc. But you can calculate it yourself for softer things: you could easily calculate Youngs modulus for JELLO! Some of the problems you see will be simply calculating the modulus, or how far something will be squashed given a modulus.

22 Example Problem The total cross-sectional area of the calcified portion of the two forearm bones is approximately 2.4 cm 2. During a car crash, the forearm is slammed against the dashboard. The arm comes to rest from an initial speed of 80 km/h (22 m/s) in 5.0 ms. If the arm has an effective mass of 3.0 kg, what is the compressional stress that the arm withstands during the crash? a = Δv Δt F Stress = = A ma A [did on light board]

23 Elasticity in Shape Example: bending or cutting something. Shear stress = F Acs = S Δx h stress = modulus x strain Parallel S = Shear modulus ShearStrain = Δx h In shear stress, the applied force is parallel to the crosssectional area. (In tensile stress, the force is to the CS area.) Push on book down (young s modulus) vs. parallel (shear modulus). To push parallel I use the friction between my hand and the book.

24 Elasticity in Shape Example: bending or cutting something. Shear stress = F Acs = S Δx h What is the shear cross-sectional area of the missing paper? Q90 r t (thickness) A. πr 2 B. πr 2 t C. 2πr D. 2πrt ANSWER: D. To get you to wrap your head around this I want you to think about a hole punch. You had to punch through all that paper to make a hole. This is a shear stress applied to the paper: it deformed the paper s shape beyond what the paper could take. What I want to ask you is: over what area is the force acting to break all the bonds across the thickness of this paper?

25 Elasticity in Volume The shape stays the same, only volume changes. Volume stress = ΔP = - B ΔV Vo stress = modulus x strain B = Bulk modulus VolumeStrain = ΔV V o Notice the negative sign. Makes sense: Increasing the pressure on an object, decreases it volume and vice versa. NOTE THE NEGATIVE SIGN!

26 Elasticity in Volume The shape stays the same, only volume changes. Volume stress = ΔP= - B ΔV Vo Think of how you feel deep underwater. The bulk modulus characterizes how easy it is to uniformly squeeze a material in all directions.

27 Two rods are made of the same kind of steel and have the same diameter. F F length L length 2L F F A force of magnitude F is applied to the end of each rod. Compared to the rod of length L, the rod of length 2L has A. more stress and more strain. B. the same stress and more strain. C. the same stress and less strain. D. less stress and less strain. E. the same stress and the same strain. Q91 Answer: E First, what kind of stress is this? Tensile, so what area are we interested in?

28 Two rods are made of the same kind of steel. The longer rod has a greater diameter. F F length L length 2L F F A force of magnitude F is applied to the end of each rod. Compared to the rod of length L, the rod of length 2L has A. more stress and more strain. B. the same stress and more strain. C. the same stress and less strain. D. less stress and less strain. E. the same stress and the same strain. Q92 Answer: D