Boats and Buoyancy

This week as I was reviewing for Physics Quizzes I realized that I didn't remember much about buoyancy, so I've decided to use this topic for this week's blog. This is a picture of a boat sailing in Pearl Harbor. This boat is obviously floating, which, in other words, means that the buoyant force pushing up on it from the water is equal to the weight of the water that the boat displaces. Buoyant force can be calculated by calculating the weight of the displaced water by using the density formula (density of water is 1000 Kg/s and the volume is the volume of the boat beneath the water) and then multiplying this mass by 9.8 m/s^2 (gravity).

To calculate what percent of the boat is underwater using the fact that the weight of the displaced water and the buoyant force are equal. Density times volume can be substituted for the mass and then a ration between volume and density can be found, telling what percent of the boat is underwater.

Stage Band Fair Performance

This Friday at the Iolani Fair the stage bands performed in the entertainment tent. Typically, during concerts, each or every other saxophone, one trombone, one trumpet, and the singer get microphones so they can be balanced by the sound crew and be heard while they solo. Microphones use the properties of diodes to amplify sound as it runs from the instrument to the microphone, and eventually to the speaker.

A microphone and speaker system consists of a transistor which has an n-zone filled with "holes" and a p-zone filled with electrons. These two areas are connected with an n-channel that allows electrons to flow and a current to flow. In a transistor that is attached to a microphone, when there is no sound, such as when a singer is quiet, there is no potential difference running through the transistor and a depletion zone is created where electrons cannot flow. On the other hand, if a loud sound is played, the potential difference causes electrons to flow readily through the n-channel and a large current is produced, thus causing an amplified sound to be produced at the speaker.

Rainbow Projector

This rainbow projector that I used to watch when I was younger uses properties of reflection to create a rainbow that spans across a bedroom wall. The projector emits a rainbow of light from the top. This light is shone upon a convex mirror which enlarges the image (in this case projection) and also creates an arc shaped image. Convex mirrors magnify images and are often used for store security as they allow a person to see a wider range of objects as they gather light from an angle larger than concave or planer mirrors.

The rainbow image that is produced by this device is projected because the light source is placed slightly behind the mirror so that the angle of incidence is great. The angle of incidence equals the angle of refraction so the image is projected out of the device and onto a wall. The arc-shape of the rainbow is created because the mirror is convex so the different light rays intersect with the mirror at slightly different angles causing them to be reflected in the shape of both the mirror and a traditional rainbow.

Winter Ball Snow Globe

In this cool snow-globe we got at Winter-Ball, you can see a great example of refraction. In the picture you see the picture, or object, and the picture "magnified" through the globe, or the image. This refraction occurs similarly to how the object refracted in our Cheese-box experiment. The picture refracts because the index of refraction of water is greater than the index of refraction of air, about 1.33 to 1. Using Snell's Law we can determine the angle of refraction of the object. Snell's Law is n2sin(theta)=n2sin(theta) where the first theta is the angle of incidence of the light hitting the object. Because the snow-globe is round the light refracts only once and because the picture in the snow-globe takes up most of the globe, it each point on the picture refracts equally and the picture appears to be magnified.

Also, if you turn the snow-globe there is a point where you can no longer see the image. This is where total internal refraction occurs. Total internal refraction occurs at a critical angle as found by the equation Sinc=n2/n1, so in this case it is about 49 degrees from the center of the picture.