Waves and Sound

Last week, we studied waves, sound, and music as it relates to math and physics. Two types of waves we studied are transverse and logitudinal. They differ in that the movement of the medium in a transverse wave is perpendicular to the direction of energy transport. However, the movement of the medium in a longitudinal wave is parallel to the velocity of the wave. These are both forms of mechanical waves, which require a medium to travel, as opposed to electromagnetic waves, which can travel in space due to electric and magnetic fields. Sound waves are also mechanical waves. Standing waves, or "stationary waves," occur when a wave remains in a constant position, at certain frequencies called harmonics. Music is made up of a blend of harmonics.

Standing waves occur in stringed instruments, like the guitar displayed above, that are tied down at both ends. The first harmonic of a stringed instrument is the lowest frequency at which at standing wave will occur. The second harmonic is the two times the fundamental frequency, the third harmonic is three times the fundamental frequency, and so on. The first harmonic is one half of the wavelength, as opposed to woodwind instruments where the first harmonic is one fourth of the wavelength. Woodwind instruments are those where the pipes are closed at one end. These instruments only have harmonics of odd numbers such as the first harmonic, third harmonic, fifth harmonic, and so on. For both types of instruments, air molecules come together at the nodes, where there is no air movement. In between the nodes, however, there is high air movement. Sound, in fact, is the movement of air molecules that move our ear drums. Thanks to harmonics and physics, this sound appears as music!

Light and Optics

Refraction:
Light follows the "Path of Least Time" to get to a destination in the quickest way possible. This involves 2 different mediums and a "bend." This bend is otherwise known as refraction. Refraction is when light passes through a medium and changes its path. It follows the principle of Snell's Law, where n1(sin1) = n2(sin2). In Snell's Law, n1 is the index of the angle of incidence, angle 1 is the angle of incidence, n2 is the index of the angle of refraction and angle 2 is the angle of refraction itself.

Real World Connection:

The image above depicts refraction through a pencil in a container of oil. The upper half of the pencil remains in air, where the index of refraction is 1. The lower half of the pencil  is submerged in oil, where the index of refraction is 1.47. Because the pencil is moving at a faster velocity in the air, it will slow down in the oil, making the angle if refraction smaller than the angle of incidence. If we plugged these numbers into Snell's Law, we would find the angle of refraction, which would explain the "bend" in the image shown above. A "bend" is necessary in order for light to achieve the path of least time.

Magnetism

Explain how objects like the earth and metals can be permanent or temporary magnets.

When it comes to magnets, a domain is a cluster of atoms that are magnetically aligned. A permanent magnet has domains that are all lined up in the same way. The three most common magnets are iron, nickel, and cobolt. Some objects have magnetic material and the potential to become magetic, however, are not always magnetic. They have domains, but they are not always lined up. Other objects are made of non-magnetic material. They have domains but these domains can never be lined up. In these types of objects, there are magnetic fields but no magnetic domains. In conclusion, all objects have domains. If these domains are lined up, the object is magnetic or has potential to become magnetic. If the domains are not lined up, the object cannot become magnetic.

iPad Battery Connection

http://www.mahalo.com/ipad-battery/

     The article talked about the voltage of batteries when they are fully charged. Because of last week’s lesson, these terms are much more familiar. The charge of an atom is generally neutral. When an atom looses electrons, it becomes positive. However, when it gains electrons it becomes negative

Fields of charged objects make up voltage. Voltage is the separation of charges. The lithium poylmer batteries are used because they separate the charges for a long period of time.

Voltage and charge combined make up electric potential energy. However, voltage alone is supplied by a battery. In our lemon battery lab, the lemon supplied a voltage. With a current, resistor, and voltage, a simple circuit is made and electric potential energy can be transferred.

Projectile Motion

For this week's lab, we went down to the gym and played some basketball while measuring the projectile motion of the basketball. We used the Video Physics app to create motion maps from the video of the shot at the basket. Then, we created graphs for the x and y components, the position over time and a velocity over time graph in the horizontal direction (x) and the vertical direction (y). 

The graph to the left on top shows the x position over time.  The change in position over the change in time represents the slope, which is is constant.  The change in position over the change in time is also velocity, which is constant. The graph below to the left shows the x velocity over time.  The change in velocity over the change in time is acceleration.  Because the slope of the line in this graph is 0,  there is no acceleration and no net force.

The top graph to the right shows the y position over time. The change in position over the change in time is the slope and velocity. The slope is not constant--therefore, the object is accelerating. The bottom graph to the right shows the y velocity over time. The decreasing line crosses the x-axis, and at that moment the object has a velocity of 0, which means it is at its peak. The rest of the time it is decreasing.

Forces in 2D and Circular Function

In our first lab of the second semester, we used the kick discs to test the nature of normal, gravitational, and tension forces. We measured the x and y values and used SOH CAH TOA to find the magnitude. These x-components and y-components are independent from one another. By adding up the x-components and the y-components, we can calculate the net force to analyze these forces in 2D. By spinning the disc, we created a centripetal force.  For an object to move in a circle, you need to apply one force toward the center--this motion causes acceleration. To orbit means to travel in a circular path. Satellites and even other planets orbit the earth through the centripetal force of gravity.

Newton's Laws of Motion

Lab #1: Hover Disc:

In the Hover Disc Lab, we went down to the gym foyet and discovered what gives rise to a change in motion. We observed the disco at rest, in motion, and while it was being pushed. Then, we took note of the change in motion and documented it in an interaction diagram and a free body diagram.

When the disc was at rest and in motion, there was a gravitational and normal force between each person and the earth and the disc and the earth. The normal force was going upward and the gravitational force downward in the free body diagram. When the disc was being pushed by either person, there was a gravitational and normal force between each person and the earth and the disc and the earth. There was also a normal force between the disc and the person pushing it. In the free body diagram, there was a normal force going upward and to the right, and a gravitational force going downward.

Newton's 3rd Law of Motion:

This lab allows us to act upon Newton's 3rd Law of Motion, which states that when two objects interact, they exert equal and opposite force on each other.These objects are equal magnitude, opposite in direction, and the same type of force.

Lab #2: Fan Cart:

In our Fan Cart Lab, we discovered the relationship between mass, force, and acceleration. First, we found our slope, or constant force of .15 N. Then, we added mass to our fan cart to observe the affect on the acceleration. Below is an image of our data:

Newton's 1st and 2nd Laws of Motion:

From our data, we derived the equation: force= mass x acceleration. This equation happens to be Newton's 2nd Law of Motion. This affects Newton's 1st Law of Motion, which states that an object at rest or traveling at a constant speed will continue to do so, unless a net force acts on it. 

Real World Connection:

Below is a video, which describes Newton's three laws of motion, and involves connections to our everyday life:  http://www.youtube.com/watch?v=UVdqxYyFRKY