[The Tenth Blog] Electrostatic.

Today I went to a first birthday party for my mother's co-worker's daughter. Her name is Leura (after the city in Australia) and she's really cute. :] But anyway, since it was a birthday party, there were lots of balloons, which of course reminded me of...physics!

Objects can become charged by friction if they are rubbed together. I would not have done this at the party (sorry, not even for physics) because I would have looked ridiculous as well as made my hair all frizzy and such, so I'll just speak theoretically. If I had rubbed the balloon against my hair, both my hair and a balloon would have become charged. Since the rubber balloon has a greater electron affinity (Yay for chemistry. :P) than hair, it would pull electrons away from my hair (It is always the electrons that move! :]), making the balloon negatively charged and my hair positively charged.  Also, since charge is conserved, the net charge would be constant throughout the process. The balloon and my hair were both neutral at the beginning, and since electrons are simply transferred to make one object positive and the other negative, the total number of electrons and protons remains the same (equal), so the net charge is still zero. Now that we have created two objects of opposite charge, guess what? They'll attract! Because opposites don't only attract in real life; opposites attract in physics too. :] We would actually be able to calculate the electrostatic force that my hair would exert on the balloon using the equation 
F = kQ₁Q₂ /r² where k is equal to 8.99 x 10⁹ N • m²/C², Q₁ and Q₂ are the charges of my hair and the balloon, and r is the distance between them. I actually recall doing this as an experiment back in elementary school, but only now do I actually know the physics behind it (after, like, six years... Haha.)

[The Ninth Blog] Thermodynamics.

Since finals ended, I haven’t really thought about school. At all. Even though it’s only been, like, five days since we’ve been in physics class, I’ve basically forgotten everything. Well, not everything, but quite a bit. I’m forgetful, what can I say? :] 

I baked some pumpkin muffins this weekend. For Christmas, one of our neighbors gave us a jar of pumpkin bread/muffin mix with raisins in it that I finally decided to use on Saturday. They actually turned out to be pretty good. And the process involved physics, so all the better, right?

From the very beginning, physics was at play: when I set the oven to 350°, heat was added to the system in order to bring it up to temperature. Such a process is isochoric, as the volume of the oven cannot be changed. According to the ideal gas law PV = nRT, as temperature rose, so too did pressure. Also occurring due to the added heat was an increase in the system’s entropy.

Once the oven had reached 350°, it was time to put in the muffins. Since heat readily flows from hot to cold, heat was transferred from the surrounding air to the muffins, causing them to undergo a temperature and phase change. At this point, the muffins were taking part in an isobaric process. As the temperature of the muffins increased, it caused them to rise as they baked, with temperature and volume varying but pressure constant. Once the muffins were brought up to the same temperature as the oven, they finished baking in an isothermal process. [I think...] The muffins dropped slightly in height (volume decreased) as they continued to cook, since pressure was increasing as the batter became more dense, completing its change from a liquid-like substance to a solid, and temperature was being held constant.

And voila! The result: delicious pumpkin-raisin muffins and a nice lesson in physics. :]

 

[What Was Supposed To Be...The Eighth Blog] Sound.

Wow, it’s been a while... So here’s the response on sound from December that I just never got around to posting:

Values/Calculations

Instrument

Violin

Properties

Chosen string: D

- Frequency: 294 Hz

- Vibrating length: 0.32 m

- Mass density: 9.375 x 10^-4 kg/m [mass = 0.30 g]

- Tension: 33.191 N

      

Frequencies Of Next Highest Harmonics

- Second harmonic: 588.00 Hz

- Third harmonic: 882.00 Hz

    

Analysis

Fingering Positions

The fingering positions correspond to where the frequencies for the next notes can be found.  When you press the string down with your finger, it decreases the vibrating length of the string.  This shorter length results in a higher frequency.  When placed in the correct position, the new frequency is that of a new note.  For example, in first position, placing your first finger on the D-string gives the note E while your second finger can give either the F♮or F#, depending on where it is placed.

To play an E on the D-string, the vibrating length is reduced by about 0.03 m, making the new length 0.29 m.  So when the new frequency is calculated, it comes out to 324.412 Hz (which is fairly close to the established 329.63 Hz...).

Plucking/Bowing Location

The plucking/bowing location is close to the bottom (by the bridge) node of the string.  At this location...all (or most of...many of...) the harmonics are likely to be heard! :]

Plucking Versus Bowing

When a string is plucked, energy is only applied for an instant so the sound diminishes quickly.  When it is bowed, energy is constantly applied so the note can be heard for a longer period.  After the initial sound of a plucked note is heard (with all of its frequencies), some of the higher frequencies are lost so only lower and fundamental frequencies can be heard until the sound is stopped altogether.  However, when a note is bowed, all frequencies are being heard together continuously, giving it greater depth.  

[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)! :]