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1. ## Fun with Shapes in the Universe!

Or more like shape OF the universe! The only book I read anymore is The Cosmic Cocktail by Katherine Freeze, and one topic she came upon was the shape of the universe. This topic is a very hard one to think of in your head, because its hard to imagine a universe in which we live in expanding! Yet as I showed in another blog post, Hubble himself showed that it must be expanding since galaxies are growing farther away from us! So then what just shape are we expanding from?? Or Into??? Well there are three options we have. If the density of the universe is less than the critical mass density (found in proportion to the square of Hubble's constant then we are left with a negatively curved geometry, like a saddle. If it matches the mass found from Hubble's constant than we are left with a flat geometry like a piece of paper. But if the density is greater than the one we expect, we are left with a spherical geometry. Flat geometry is the one Einstein preferred because is it easiest to work with a flat axis instead of a curved one. The effects of these different geometries are interesting though. For example, if the universe was spherical than there would not be enough mass (and density) so after expanding a "Big Crunch" will occur after the Big Bang and the universe will collapse on itself. The other two options are not AS sad though. The flat and hyperboloid geometries on the other hand will continue to expand forever! This will lead to a big chill since the universe will be so expansive and will never stop. I did say as. The obvious evidence points to flat, the simple answer. It has good evidence behind it though, if the universe was spherical the "Big Crunch" would have happened extremely soon after and there would not have been enough time for the galaxies and such to form! Also a hyperboloid geometry would have led to a much faster expansion than seen a the "Big Chill" would have lead to the same result. The numerical evidence behind flat geometry is iffy at best though, and is also very complicated, so stay tuned for next time when you can decide for yourself if our universe is like a pancake or a basketball!
2. ## The Life of a Star (Not my autobiography)

The life of a star is a long and interesting one, I read about this process in the one and only book The Cosmic Cocktail by Katherine Freeze. The main sequence of a star (which are sun is now in) is when the fusion of four hydrogen atoms to a helium atom releases heat and energy. This type of fusion is hard to even imitate here on earth because we don't have enough energy to make it happen. As this fusion takes place more inert helium is built up until finally all the hydrogen is gone and we are left with a helium filled star. Without any fusion taking place the pressure in the star is not enough from keeping it from collapsing. When it does collapse from gravitational effects, the helium will start to be burned and fused together to make carbon! This is when the red giant stage starts and the sun increases in size by massive proportions. At this time our earth, and other close planets, will be consumed in this expanding sun and burn to a crisp . But no worries, that's in about 5 billion years! Once all the helium fuel is gone to, literally NOTHING is left to burn or fuse, which means gravity can work its magic and collapse the star like it has been trying to for 10 billion years. When it does contract it becomes a white dwarf, the Pauli exclusion principle explains the pressure inside the star, which basically says that two electrons cannot be in the same place at the same time which creates a pressure inside the star that sustains it. The density at this point is extremely great because you would have a blue dwarf with about half the mass of our sun but the size of our earth. This is where the paths diverge though, for heavier stars like ones 20 times bigger than our sun, the star will collapse into a black hole since its density is so great and creates so much gravitational pull. For Stars a little bigger than our, say 3 times, they collapse to neutron stars, where the same principle used for white dwarfs applies except with neutrons now! Two neutrons cannot be in the same place so the star is stabilized and continues to shine. These 3 outcomes, white dwarf, neutron star and black hole are pretty amazing to think about and have massive effects on the structure of our whole universe.
3. ## Hubble's Bubble Constant (The expansion of the Universe)

In my last blog I briefly described how red-shifting has proven the existence of the expansion of the universe but there is much more to it than that as Dr. Freeze describes in her book The Cosmic Cocktail and I try to explain here. Edwin Hubble was the scientist brave enough to disagree with Einstein, but also the one smart enough to prove Einstein wrong. The debate at the time was on the subject of what the universe was actually doing, scientists had already established the fact that the universe was homogenous (looks the same at every point) and isotropic (looks the same in every direction), but Einstein also believed that the universe was static or always looked the same. That's where Hubble came in, he observed light from many different galaxies and noticed that the rays of light were red-shifted, a term I have already described in my last blog post (PSA: Our Galaxies going to collide with another...), which basically states that a longer wave length of light shows that the source is increasing in distance from us. Imagine it like this, if you went to your local candy store, purchased some Hubble Bubble Gum, and began to blow the gum into a giant bubble it could be a model of our universe! Say there were large specks of pink sugar in your gum, as the bubble expanded the specks of sugar would increase in distance from each other even though they are in no way changing in size or placement really. This is just like our universe, although the distance of us from other galaxies is increasing, we are unaffected by the expansion. This again proves the two cosmological observations stated earlier, the universe looks the same at every point, or every sugar speck, since everything is expanding from each speck, and it also looks the same in every direction, because the bubble is increasing in size everywhere. Another common analogy for this idea is the "raisin bread model", where the universe is the bread expanding, and the unaffected galaxies the raisins, it serves the same purpose but in no way highlights the point that Hubble's name sounds like a bubble gum brand. Anyways back the real point, Hubble was able to apply this law into an equation known as Hubble's Law which stated v (speed) = d (distance) times H (Hubble's constant of universal expansion). This equation finally convinced people that the universe was expanding and a static universe was just a silly notion, sorry Einstein. Furthermore, the equation has been applied to find the age of the universe (14 billion years) since the constant measure the stretching of the universe and we can then use it in reverse to find when the distance was 0 and the universe had just began! All this and more came from a guy who's name now resides on the most powerful telescope in the universe ...and the tastiest gum of all the galaxies.
4. ## Newtons 3rd law vs lifting

Nice job stealing my blog post idea
5. ## PSA: Our galaxy is going to collide with another...

...in 4 billion years. Yea I got you, you were probably really afraid for a second and frantically clicked this blog to find out if you really HAD to do your physics homework tonight or if it would all be pointless since the end of humanity could be just over the horizon. Well sadly for you it is not, but since you're already reading you might as well find out what will happen when it does. I was of course reading The Cosmic Cocktail again by Katherine Freeze, since that is all that I do now, and came across this little tid-bit while reading about red-shifting. Red-shifting is a term used by really smart people to prove that the universe is expanding. You see since we know that the frequency of light equals c (the speed of light) times wavelength. Since we know that the speed of light is constant (3 x10^8 meters per second) if we see light with a different frequency we know that the wavelength must have changed. Think of it like this, if you see a fire truck as it approaches the pitch of the siren is deeper, this is because the speed of sound is constant but the wavelength is being pushed closer and closer together as the fire truck approaches you making a shorter wavelength and deeper pitch. When the fire truck passes you on the other hand the wavelength is being stretched out so the pitch is higher. The same principle applies to light waves and galaxies! When we examine the light waves reaching earth we find that almost all of them have a low frequency and shift more to the red spectrum of light, therefore they have a longer wavelength, showing that these galaxies emitting light are getting farther from us proving the universe is expanding!! I did say almost. The one exception is the Andromeda Galaxy, the light from this galaxy is actually blue shifted, it has a higher frequency and a shorter wavelength than normal. This means, like the fire truck approaching us, that the Andromeda Galaxy is actually getting closer! Even the Fire Department can't save us from this apocalyptic event though. Luckily for us the space inside our galaxies is so great that the Earth would probably not even be affected by the galactic wrestling match going on around it. Also on the positive side, this battle won't be taking place for almost 4 billion years! Even better, by that time our sun will have reached the red dwarf stage by then and already engulfed Earth! So do not fret Earth dwellers, our planet is safe for now! Maybe not 4 billion years from now though...
6. ## The Hunt for Dark Matter ft. Rotational Speeds of Galaxies

Katherine Freeze continues her description of the hunt for dark matter in The Cosmic Cocktail describing how the rotational speeds of galaxies, or at least the hypothesized ones, provide more evidence for the phenomena. In short, some very smart people applied a 300 year old equation to data that Mr. Newton himself couldn't have imagined. The equation was Newton' gravitational force equation which says F = (GMm)/r^2 which then would equal centripetal force or F = (mv^2)/r giving you the speed of a body to be v = ((GM)/r)^(1/2). They took this simple equation and applied it to the speeds of nearby galaxies. But what they found was quite intriguing. It is simple to understand based on the equation stated above that as r increases the velocity should decrease. But the data they found was contrary to this understanding for the speed of multiple galaxies. They noticed that there was a small bump in the beginning of the graph which was expected since much of the mass in a galaxy is not in the center. They expected the velocity to drop off after that, however it did not and was still quite large very far away from the center of the galaxy. How could they explain this increased speed? Well M would have to be much bigger, and since they had already calculated the visible masses of these galaxies, they knew that the mass must be invisible, such as dark matter is inferred to be. The speed of the galaxy would require more mass to make it go faster, dark matter explains why even as r increases v does not drop off. The graph below shows this idea as the observed velocity is much lower than the observed one, and a line showing dark matter is also included to account for this. Something surely is out there propelling these galaxies, and it sure is interesting that an equation learned by high school physics students was so integral in providing one answer for it!
7. ## Double Vision with Gravitational Lensing

I have begun reading a book called The Cosmic Cocktail by Katherine Freeze and was immediately interested into one of the first topics she discusses that helps prove the existence of dark matter. A long time ago, or at least before I was born, Albert Einstein made his Theory or Relativity which stated many things including the fact that light will always travel at the same speed, about 3 x 10^8 meters per second, but he also stated that the gravitational pull of a planet can affect light, or bend it! This phenomena became known as Gravitational Lensing since the planets acted almost like a lense by bending the light. The major difference though was that the light is bent most closest to the body pulling it, and least farther away. One might ask, why do I care about some bent light in space? But the impacts go a long way. For one it gives the mirage of multiple sources of light as the light path is bent in multiple directions. So one far off star may appear as 2 or even more if there happens to be another celestial body in between the telescope and it. Since it is predicted that there are over 100 billion galaxies on the universe it would not be out of place for there to be a large enough body to affect our views of the universe. So how does this apply to dark matter? Something we can't even see? Well that's where MACHO's come in. MACHO stands for Massive compact halo object, or in high school terms, a big glob of dark matter. Lets explain, since scientists already know the affects of gravitational lensing they applied that knowledge to examples in the universe where they knew it was occurring. They then found a few strange cases where they knew light was being bent but no celestial bodies were in between the light emitting body and the scientists telescope. SO how could they explain this shift? DARK MATTER! Scientist knew that something was bending the light, and if they couldn't see it, the only explanation they could come up with was the existence of dark matter, a form of matter that is invisible but still has the pull of regular matter. This discovery and application of science helped scientist find another way to prove the existence of dark matter which is important since it is so hard to prove something that you can't even see! On my next post I will talk more about evidence of dark matter, this time in the rotational velocity of the galaxies!
8. ## Boy Scout Physics Swag

I happen to both be a Boy Scout as well as a physics student which I believe to be probably the coolest combination ever. Sooooooo, I decided to apply my physics knowledge to my Boy Scout skillz! On a recent campout to the Pennsylvania Grand Canyon I decided to bring a hammock as a lighter alternate to a tent since I would be hiking around 10 miles. When I packed my things I decided to just grab some random rope from my garage for my hammock... which could have been a bad idea! Luckily the rope held up but I decided to find just how strong the rope had to be! Now the hammock was strung up between 2 trees with knots on each side and me in the middle. I weigh about 170 pounds or 77.1 kg which will be very important in finding tension or "T". Since the hammock is in equilibrium we can use Newton's 2nd Law to find T. The net force in the x direction on the right is equal to the net force on the left. Since both ropes were at about a 30 degree angle we can then say the Tensions are equal so -Tsin30 + Tsin30 = 0. Then since ups must equal downs we can say 2Tsin30 = mg or rewritten T = (mg)/(2sin30) which gives us T! Now lets plug in numbers T = (9.8x77.1)/(2sin30) or T = 755.8 Newton's. That was the tension in the rope of my super comfortable hammock. Maybe in a future blog post I will determine just how strong that rope was... or maybe not that could be quite challenging... The average strength of say paracord is about 250 pounds or 1107.4 Newton's and what I was using was certainly not as strong as paracord! So I guess this times I can count my lucky stars I wasn't sleeping on the ground, and maybe next time I should BE PREPARED with some stronger rope!
9. ## Lifting Bro's Use Physics Too!

ayyyyyye you know it lol
10. ## Lifting Bro's Use Physics Too!

"Bruh do you even lift?", is now a common phrase often heard in our modern world. And while many people think lifting is just a bunch of knuckleheads throwing around weights, in reality it a strenuous exercise that demands perfect technique and lots of practice. So I decided to look into the physics behind lifting to prove my point. I started with benching one of the most well known exercise. A basic workout for me would consist of a warm-up of 10 reps at 135 pounds, then 10 reps at 185, 8 reps at 185 and then 10 reps at 165. If you look simply at the force required for each set you find some impressive results. The force that would first have to be exerted just to lift the bar in the first set would be the weight in kg times the acceleration due to gravity. Warm-up: 600.103 Newton's/rep Set 1: 822.36308 Newton's/rep Set 2: The same as set 2 Set 3: 733.45846 Newton's/rep This is of course assuming that the lifter is using good form and therefor bring the bar down and up at a near constant velocity to get the most out the workout. If we are to change our view though and instead look at energy involved in "repping" the weight we find some more interesting results. You would find the energy required in each rep most easily by finding the change in potential energy of the bar as each rep is performed. Potential energy is found with the equation mgh, or mass times the acceleration due to gravity times the height of the bar. The mass of the bar is constant for each set and so is the acceleration due to gravity, so the change in potential energy would be those constants times the change in the y-plane. The change for me when my arms are extended to bench is around 20 inches, or .508 meters. The energy for each rep and then for each set are shown below. Warm-up: 304.85 Joules/rep AND 3048.52 Joules total for this set Set 1: 417.76 Joules/rep AND 4177.6 Joules total for the set Set 2: 417.6 Joules/rep AND 3342.08 Joules total for the set Set 3: 350.02 Joules/rep AND 3500.15 Joules total for the set This comes to a whopping total of 14068.35 Joules expelled for the entire workout! This would be about enough energy to power a light bulb for around 2.3 minutes, which may seem not like a lot but compared to the little amount of effort people usually believe lifting takes it shows you a lot. Also to consider, this is only just one exercise of a workout that would surely include many more and obviously use more energy. So don't look down at those lunkheads clunking around your local gym as you jog on the treadmill, because they're working hard just like you. Picture from www.yiddishecup.com
11. ## TI Selfie Challenge

I turn up in science with my TI Calculator
12. ## Getting to Know Me!

My name is Robert Campbell German, but I go by Campbell, a name often related to the soup brand, and it doesn't help that my hair shares the same color as Tomato Soup... I am a student, a musician, a leader, a Boy Scout, a wrestler and much more. Even though now I'm just a puny high school student one day I have much higher dreams for myself, that would include the military, business and maybe even politics one day, vote for President Campbell! I am currently enrolled in AP Physics C, I took the course because I enjoy the challenge that physics provides. Also I love the practicability of physics, unlike most other classes Physics is linked to almost every action we take. The different topics we learn are used in everything around us and also they are still leading to new discoveries one of the most amazing parts. I hope to get out of AP Physics C a better foothold in physics so that I can apply this knowledge to engineering, a major I may be interested in as I head off to college. Since I plan on going into the military I know engineering and physics will be something that will be highly demanded and will help me serve my country better. This year I am most excited for wrestling season. Wrestling is a large passion of mine, I have spent 5 years perfecting and working on my technique and my senior year will be the last opportunity for me to prove that I my work hasn't been in vain. It is an exciting sport which challenges me every day and I can't wait to get back on the mat. I am most anxious this year about applying to colleges. I am currently in the process of applying to the United States Naval Academy, I have spent months working on my application as well as on getting a nomination to the academy and hopefully everything will turn out for the best and I could reach my goal of going to the Academy.
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