[The Seventh Blog] Fluids.

     Well it's been a while since we've done a blog and I honestly forgot about it till not too long ago, but that's okay because I still have ample time to finish it.  And luckily I found something to write about while scavenging through old trip photos, otherwise who knows what I'd be doing right now (maybe shooting my brother with a water gun or something...).  So anyway, here is the lovely picture that I came across of a pirate-y looking boat (in Japan, which just makes it all the better. :]).  

     
     Why is it that an object that seems so heavy can float on water?  I can understand rubber duckies floating in a bathtub, but gigantic ships floating on the ocean? I think not. But it's possible (anything is possible if you just believe. ^_^) and the explanation lies in PHYSICS, of course!  Contrary to what seems logical, it is really not the weight of an object that determines whether it will sink or float; it is the object's density as compared to the fluid's density that matters.  If an object's density is less than the fluid's density, it will float, and if it is greater than the fluid's density, the object sinks.  This must mean that the ship's average density is lower than the density of sea water. 
     Also, all objects placed in liquids have this thing called buoyant force acting on them.  This force counteracts the object's weight, pushing up on it from below.  Buoyant force is equal to ρVg (density of the liquid x volume submerged x gravity), also stated as the density of the liquid multiplied by the weight of the fluid displaced.  When buoyant force is greater than or equal to an object's weight, the object floats, and when it is less than the object's weight, the poor object sinks to the bottom.  And good thing there is physics to explain why the boat floats instead of sinking to the bottom of the ocean as would be expected if we didn't know any better, because I don't think the people on it would appreciate if it sank - who knows what creepy things are hidden far far below the ocean's surface...

[The Sixth Blog] Circular Motion.

Circular motion can be observed in many instances of everyday life, such as in the blades of a ceiling fan as they spin or as a car makes a rounded turn.  However, today I will be discussing circular motion regarding something that generally can't be as commonly observed - a ferris wheel (this one was in Japan ^_^).  

There are several forces at work as the ferris wheel moves.  There is mg, which is always directed downward, F_N, which is perpendicular to the surface in contact (directed upward since people in the individual carts are sitting down...), and there is F_C, which is directed toward the center of the ferris wheel.  

Even though velocity (instantaneous velocity, tangent to circle) is unchanging, there is acceleration because the direction of motion is constantly changing.  Centripetal acceleration is equal to v²/r.

Since there is acceleration, we know that there must be some sort of unbalanced net force causing it, and that special force is known as centripetal force, which points toward the circle's center, as I have mentioned above.  At the top, F_C is equal to (mg - F_N), whereas at the bottom, it's equal to (F_N - mg).  We can also derive the equation for F_C because we know that 

F_net = ma and therefore F_C = m(v²/r).

We can even find angular values by knowing linear ones, 

ω = v/r (velocity) or α = a_T/r (acceleration). There is so much to learn from just a few values (plus all of these lovely physics equations, of course)! :]

[The Fifth Blog] Momentum.

       Yesterday I attended the UH versus New Mexico State football game – my first live UH football game, might I add, and only my second time sitting in Aloha Stadium.  Honestly, the (unnecessarily) loud, screaming fans and blinding bright lights don’t do much for me, but that’s okay because at least I got to experience some physics while I was there. 

I didn’t take any pictures of my own, but this one will do:

       I will refer to the UH player as A, the other as B, and assume that they were running toward each other from opposite directions prior to the collision.  The collision that these two players experienced was a perfectly inelastic collision, so momentum was conserved but kinetic energy was not, and the two players ended up “stuck together” (Hmm, what if it had been an ordinary inelastic collision and they had bounced off of each other instead... o_O). Anyway...if we give the two players random masses and initial velocities... (A has a mass of 110 kg and was moving at a velocity of 5 m/s and B has a mass of 90 kg and was moving at a velocity of -5 m/s) we can solve for the common final velocity of the two players upon impact because we know that momentum is conserved. 

                                                                            

                                                                             

[The Fourth Blog] Work, Energy, & Power.

When we hear the word work, we usually think of that place where our parents go while we're in school or, much more likely (being that we are such studious 'Iolani students), homework. To a physicist, though, work can be defined as displacement times force in the direction of displacement (W = FcosθΔx) or as a change in energy (W = E_f - E_i).

     I normally don't think much about walking up the stairs at home because it's something I do every day, but I thought twice about it today since such an action can be related to physics.  When I am standing at the bottom of the stairs, kinetic and potential energy are both zero (no velocity and no h). When I reach the top, though, both my kinetic and potential energy have changed and thus I have done work - little as it may be. To calculate my work, I find my total energy at the bottom (0 J) and subtract it from my total energy at the top (612 J), resulting in 612 J of work. Not much work, but work nonetheless...  (And probably a greater value than that representing the amount of homework I have accomplished thus far. Not good.) From this I can calculate my power (P = W/t), which comes out to be 266 W (or 0.357 hp).  Physics has redefined the meaning of work for me and has taught me about the relationship between work, energy, and power.   

         

I made it to the top. :]

                

[The Third Blog] Force.

       This afternoon, as a break from homework, I decided to clean my room.  After folding my clothes and putting some things away, I was in the mood to rearrange the little bit of furniture that I have...yet again. My room is the smallest in our house (why, I ask?), so I'm always trying to find an arrangement that uses the space I have most effectively.  As I was moving things around, I realized that physics could be applied to what I was doing. Amongst other things, my little Sunday afternoon project demonstrated Newton's third law of motion - for every action, there is an equal and opposite reaction: as I pushed forward against my bed to move it, it was also pushing back against me with the same force. Thanks to physics, I was also aware of the specific forces that were acting on my bed throughout the process. When at rest, the bed experienced forces of gravity & normal force (which counteract each other) as well as static friction. As I began to push on the bed, though, while gravity and normal force were still being applied, the force of my push was also added, and static friction became kinetic friction, which worked against my applied force. I also learned that the force of static friction is greater than that of kinetic friction, which is why it was harder to get my bed to move initially than it was to keep it moving. Well, without further ado, here is the result of my physics-filled project (not very exciting, I know, but that's okay.):

I should have done a before/after type of thing, but that thought didn't
really occur to me until everything was moved - whoops.

[The Second Blog] Projectiles.

     This week, we extended our knowledge of position, velocity, and acceleration into two (and even three) dimensions with the lesson on projectiles.  A projectile is an object projected, for lack of a better word, into space that, once released, is only influenced by the force of gravity. The motion of a projectile can be seen as my brother shoots a basketball. Today he just so happened to be doing so—in the living room (but at least he didn’t hit anything).  I don’t generally pay attention to him when he’s practicing – he wouldn’t want me to, anyway – but since I could relate it to our physics concepts, I decided to observe for a second.

[General graphs depicting
projectile motion]

     Being that it is a projectile, when the basketball is shot into the air, it moves in a parabolic path. This is due to the fact that the only force acting on the ball, assuming no air resistance, is gravity. Therefore, in the y-dimension, because of the acceleration of gravity – a constant –9.8 m/s² – acting on the ball, position follows a curved path, increasing initially then decreasing to form the shape of a parabola, with velocity decreasing (in the positive direction) from the time the ball is released until the time that it reaches the peak of its trajectory and increasing (but in the negative direction) on its way back down after reaching the peak. In the x-dimension, though, because there are no forces, position increases at a constant rate, velocity remains constant, and thus acceleration is zero. 

   

[The First Blog] Kinematics.

       Yesterday, as I took a break from taking history notes, I stopped to think about what to write for this blog (yes, simple as this first concept may seem, I had to think about it). But nonetheless, I eventually got somewhere. I knew that I would be attending the UH versus UCLA volleyball match in the evening, so as a newly "physics-literate" person, I began thinking about the movement of the ball - and the physics behind it - as it makes its way around the court. I tried to focus on applying physics during a serve because that seemed easiest to capture in a picture, but after several failed attempts, I concluded that I am not a good photographer, and hopefully my application of physics proves more successful. So here it goes:
       As the ball is tossed into the air, even though it is moving in the positive direction, it experiences decreasing velocity because the force of gravity, -9.8 m/s², is pulling it down. When it reaches the top of its trajectory, the ball has a velocity of 0.0 m/s before it begins to make its way back toward the earth. As it comes back down, the ball’s speed increases at the same rate at which it was decreasing on its way up (since acceleration, which is gravity in this case, remains constant).  However, even though speed is increasing, the direction in which the ball is traveling is negative, and thus, since velocity is a vector, the ball is still experiencing decreasing velocity. [Yay! The first blog -- completed. :)]