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A Physics Lesson from a Ketchup Bottle

8/31/2016

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It happens to all of us. We reach into the fridge and pull out the ketchup bottle only to that find the remainder of ketchup is clinging for dear life at the bottom of the bottle. There are two well known practices of getting the remainder of the ketchup out of the bottle. Either you place the bottle on its head and wait for gravity to do its job, or you shake the ketchup down. But, I'm here to tell you there is a third and more efficient way to get that last bit of ketchup out of the bottle.
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Hold the bottom of the ketchup bottle and make sure the lid is secured tightly. Then swing your arm around in a quick circle a few times. When you stop all of the ketchup should be at the top of the bottle. How does this work? Centripetal and centrifugal forces!
Centripetal force is plainly defined at the force exerted on an object towards the center when moving in a circular motion. Centrifugal force is the opposing force exerted on an object to move it away from the center. Both of these forces are required to understand what is happening in our ketchup bottle.
It is helpful to break the bottle and the ketchup into their own force diagrams while maintaining the rotating reference frame. Since you are holding onto the bottle, your hand is exerting the centripetal force necessary to keep the bottle on its circular path. However, there is nothing holding onto the ketchup. Therefore, the centripetal force acting on the ketchup is zero. 
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This causes an unbalanced force to act on the ketchup. Remember what Newton's First Law states? "An object at rest tends to stay at rest and an object in motion tends to stay in motion in the same direction and speed unless acted upon by an unbalanced force." Therefore, the ketchup accelerates away from the center of circular motion until it hits the lid, which subsequently exerts the centripetal force towards the center of the circular motion to stop the flow of ketchup.

Give this technique a "whirl" the next time you need to get the remaining bit of ketchup out of the bottle and impress your friends and family with your knowledge of Physics!
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The Anatomy of a Successful Student

8/24/2016

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What makes a student successful? Is it natural ability or well-developed study skills? The first place to begin answering this question is to define success. Merriam-Webster defines success as "the correct or desired result of an attempt" [1]. Therefore, success does not mean a straight-A student. Success is a measure of whether or not your attained your personal goal. The standard you create for yourself may not necessarily be explicit in the letter grade you obtain.

While attending college for my bachelor's degree in Chemical Engineering, I met three types of students. They all had the same definition of success: they wanted to complete the coursework and be awarded their degree. Each student's journey to success was a little different:

The Late Bloomer: didn't push themselves in high school but became more engaged in coursework once they entered college.
The Overcomer: had a learning disability but didn't let that limit their passion.
The High Achiever: always excelled in academics and continued to do so in college.

I graduated alongside all three of these students, and each of our academic journeys varied greatly. Some of us graduated with honors, some of us got a few C's, but ultimately we were successful because we graduated. Now, academic success is not exclusive from your actual academic efforts. All three of these students had to work hard in their pursuit of success, but that success was not solely dependent on the letter grade they obtained. Letter grades are important, since they couldn't have graduated if they were below college expectations, but they didn't all need A's either. So what did they need?
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Despite their differences, each student had certain characteristics to help them achieve their version of academic success:
  • Motivation
  • Grit
  • Discipline

Motivation is a culmination of your desires and passions that guides you behaviors. This is what draws you to learn more about a subject and to work towards mastery.
Grit is not letting obstacles get in your way. You become creative and dig deep to find ways to be successful despite challenges. This is what makes you try a new study method after failing a test.

Discipline is the ability to focus your motivation and grit on a specific objective. You know what you want and what you need to do to get there. This is what makes you ensure you have the foundational pieces to achieve your goal.

Work on these behaviors if you want to become a successful student. Find you motivation, and develop your grit and discipline. If you focus on that there is nothing to stop your from reaching your goals.
[1] Merriam-Webster. Web. Accessed 22 Aug 2016
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New School Year, New You

8/17/2016

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On New Year's Eve, many people have a list of goals they want to accomplish throughout the new year. The First Day of School offers students the same opportunity. Notebooks are empty, teams and groups need members, and there are new people to meet. How do you even begin to distill down all of the possibilities into an achievable list of goals?

It is commonly recommended to have no more than three to five yearly goals. It's natural to want to create a long list of goals, but in reality, you only have time for a few. So don't set yourself up for failure! Instead, invest the time into well-defining a few goals and continue to improve from there.
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The most popular approach to goal-setting is to create SMART goals. The SMART acronym stands for: Specific, Measurable, Attainable, Relevant, and Time-Bound. The anatomy of a great goal contains all of these features.

For example, last semester you got a B in your math course and this semester you want to get an A. To make this goal SMART, you would write:

"To obtain an A in math class (what/outcome) by the end of the fall semester (when/time) as evaluated by tests and homework (how) so that I can apply for academic scholarships (why). This can be achieved by building on my knowledge from the previous math course (means)."
 This doesn't seem entirely helpful. You may be thinking, "That just says what I want, but not what I need to do everyday to get there." That's an accurate observation. A goal is the end result, it doesn't talk about the journey. To plan the journey, you need to break that goal into smaller pieces. Anna Akana's video, "How to Level Up Your Productivity," gives some advice on how to achieve your goals. She explains that defining your goals and breaking them into steps is the easy part. The hard part is staying accountable to the plan. Akana recommends making to-do lists with only tasks that help you reach your goal, creating a "not-to-do list," and creating a daily routine [1]. So what would this look like with our example above?
  •  Read chapter before class.
  • Complete the weekly homework in advance of the due date.
  • Study 3 nights a week for at least an hour.
  • Complete all study guides (if given).
  • If not on track, seek extra help from teacher, peer group, or tutor.

Goals are a great way to refine our focus on what's really important. Give it a try! Think of one or two academic and personal goals and try to reach them by the end of the school year. You never know what you may accomplish!
[1] Akana, Anna. "How to Level Up Your Productivity." Online video clip. You Tube. 10 Mar 2016. Web. 17 Aug 2016.
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Music to Your Ears

8/5/2016

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Have you ever wondered what causes your favorite instrument to create sound? The answer is rooted in the physics of waves. There are many different types of waves: transverse, longitudinal, and standing. Transverse waves move perpendicular to the direction of the wave, longitudinal waves move parallel to the direction of the wave, and standing waves appear stationary in space. 
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Basic elements that define a wave are its wavelength, period/frequency, and speed. A wavelength (w) is the distance over which a wave repeats itself. The period (T) is the time required for a single wavelength to pass a defined point. The frequency (f) is inversely related to the period. Finally, speed (v) is the same as if we were referring to the speed of a car: the amount of distance covered over time.
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​Instruments produce sounds via standing waves. Standing waves are composed of nodes (the point at which the wave appears to have zero displacement) and antinodes (the point at which the wave appears to have maximum displacement). The frequency - otherwise known as a harmonic for standing waves - is determined by the fundamental (first) harmonic. Consider part of the derivation shown below.
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So what does any this have to do with instruments? Consider a guitar. It is composed of strings of varying weight, length, and tension. In a string, the wave speed (v) is dependent on the mass per length (m) and tension (F), as shown in the equation at right. ​
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Substituting the equation for the speed of a wave in a string into the equation for the frequency of a standing wave, you find that the frequency of a standing wave depends on the weight, length, and tension of the string, as shown at right. Higher frequencies cause higher pitches. Likewise, lower frequencies cause lower pitches. Therefore, the frequency of the string plucked changes when you adjust string tension when tuning a guitar, or changing the length of the string by moving your finger along the neck.
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So, at your next jam session you can impress your friends with both your musical skills and Physics knowledge.
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How Caffeinated is Your Coffee?

8/3/2016

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When morning rolls around an important element to starting the day on the right foot is a cup of coffee. But, did you know that every time you brew a cup of coffee you are essentially performing an extraction experiment? In this case, the extraction process is more specifically referred to as leaching. Leaching is a technique used to isolate a substance of interest from a solid by dissolving it in a liquid.

Coffee grounds (inert solid) contain caffeine molecules (solute). The coffee grounds are submerged in water (solvent) to obtain the caffeine molecules. In water, the coffee grounds are insoluble while the caffeine molecules are soluble.  Over time the caffeine molecules dissolve and diffuse into the water.​ When brewing coffee, a filter captures what remains of the coffee grounds but allows the caffeine and other molecules that have dissolved into the water to pass through.
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There was a study conducted to understand how time and water temperature affect the amount of caffeine obtained. The following charts were produced from data produced in the study for Coffea arabica beans[1]:
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Notice that the amount of dissolved caffeine in a solution increases over time and increasing temperature. Therefore, if completely disregarding taste, the longer and hotter you brew your coffee the more caffeine you will obtain.

[1] Nhan, Pham Puoc, and Nguyen Tran Phu. "Effect of Time and Water Temperature on Caffeine Extraction from Coffee". Pakistan Journal of Nutrition. 11. 2. (2012): 100-103. Web.
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Estimating Your Way to a Jelly Bean Victory

8/1/2016

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A popular fundraiser is to guess how much of a certain object are in a container. Often this object is sweet, sweet candy. The person with the closest guess wins the candy-filled container. Increase your odds of winning by making an educated guess! An educated guess is simply an estimate.

Let's say there is a jar filled with jelly beans. How many jelly beans does the jar contain?

First, estimate the size of the jar to determine its volume. You pull out the cell phone in your pocket that you guess is about six inches tall. Using it to estimate the dimensions of the jar, you determine the height is about one-and-a-half cell phones and the diameter is one cell phone. Using the volume of the cylinder you calculate the volume of the jar to be about 254 cubic inches. Using the same logic you intuitively estimate that a jelly bean has a diameter of 0.5 inches and a length of 0.75 inches. Estimating the volume of a jelly bean using a cylinder you find the volume of a single jelly bean to be 0.15 cubic inches.
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Then it is a simple matter of dividing the volume of the jar by the volume of a single jelly bean to find that about 1,693 jelly beans could fit in the jar. But what about the gaps between the jelly beans? Great point! Various sources estimate the jar contains 20% air by volume [1][2]. Use proportions to calculate how many jelly beans would take up 80% of the jar by volume.
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How sweet is that? Give this technique a whirl at your next fundraiser. Who knows, your math wizardry may help you walk away with a jar full of jelly beans!

[1] "How to win a guess the number of jelly beans contest". How Tutorial. WordPress. 18 April 2011. Web. 31 July 2016.
[2] "How to Win a Jellybean Guessing Contest". Cleverness: Getting Diggy with It. WordPress. 07 March 2007. Web. 31 July 2016.
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