Energy Project:
This project showed us the different ways that energy is looked at and used in the world. In the energy project we learned the main concepts behind how energy is created, distributed, and used in every day life. We also learned the humanitarian side as well as the political challenges that oil, coal, and natural gas give to communities that reside near these power plants. In math we learned the different equations that are used to understand the resistance, current, and voltage of and electrical current.
Reflection:
During the energy project in math, we learned the fundamental math principles of what is involved in the generation and transmission of our energy. We started learning how we measure electricity using volts, amps, ohm’s, watts, and coulombs. And then divided into ohm’s law which looks at the relationship between voltage, current, and resistance. And then we looked at series and parallel circuits and how they differ. The overall goal of this unit in math was to learn about efficiency and relating to energy. Efficiency can be thought of as be able to conduct the most amount of electricity with the least amount of loss. We this with Transmission by stepping up voltage and lowering the current so that we do not lose energy due to heat loss. We step down the voltage that goes into our home to make electricity safe to use. As the future approaches we will be consuming more and more energy at an encressing rate that we cant keep up with in the resources that we currently use to generate our electricity. so efficiency and how we generate, transmit, and consume our energy is becoming increasingly more important.
During the energy project in math, we learned the fundamental math principles of what is involved in the generation and transmission of our energy. We started learning how we measure electricity using volts, amps, ohm’s, watts, and coulombs. And then divided into ohm’s law which looks at the relationship between voltage, current, and resistance. And then we looked at series and parallel circuits and how they differ. The overall goal of this unit in math was to learn about efficiency and relating to energy. Efficiency can be thought of as be able to conduct the most amount of electricity with the least amount of loss. We this with Transmission by stepping up voltage and lowering the current so that we do not lose energy due to heat loss. We step down the voltage that goes into our home to make electricity safe to use. As the future approaches we will be consuming more and more energy at an encressing rate that we cant keep up with in the resources that we currently use to generate our electricity. so efficiency and how we generate, transmit, and consume our energy is becoming increasingly more important.
Cookies Project:
Project Reflection: In what ways has the cookies project helped you gain perspective on doing real-world mathematics?
I liked this project because it related math to a real-world situation. I have an interest in being an entrepreneur and this was interesting to see how businesses develop products and maximize profits. The cookie project helped me think as a business person where my end goal was to determine which of my products would have the best return. Going into this project I knew in order to generate a price for my product, I would need to know the cost of each ingredient that went into making the product. I understood the concept of marking my product up to create a profit. However, learning about how constraints affect my product was something I did not understand going into this project. The constraints I considered in this project were time (because baking can be time-consuming and there has to be an amount earned for the time it takes to produce a product), storage capacity (because I need to think about once the product is produced, where am I going to put it that doesnt cost me additional money for storage), and lastly eggs (because eggs are becoming super expensive and hard to get). Expressing the constraints as inequalities allowed me to graph them and see how they would affect each another. I was able to find the points at which I could sell the most amount of batches while taking into consideration all three constraints at the same time. I feel like I can apply this knowledge to other products. For example, I want to start a business of 3D printing gaming miniatures. I thought I had already figured out how to price them based on the cost of the resin, paint ect. However, now I realize that I need to also think about the constraints associated with 3D printing such as the time it takes to print, the availability of the resin, and the time it would take to paint each miniature. I could use the principles I learned in this project to better determine a sales price for my work.
I liked this project because it related math to a real-world situation. I have an interest in being an entrepreneur and this was interesting to see how businesses develop products and maximize profits. The cookie project helped me think as a business person where my end goal was to determine which of my products would have the best return. Going into this project I knew in order to generate a price for my product, I would need to know the cost of each ingredient that went into making the product. I understood the concept of marking my product up to create a profit. However, learning about how constraints affect my product was something I did not understand going into this project. The constraints I considered in this project were time (because baking can be time-consuming and there has to be an amount earned for the time it takes to produce a product), storage capacity (because I need to think about once the product is produced, where am I going to put it that doesnt cost me additional money for storage), and lastly eggs (because eggs are becoming super expensive and hard to get). Expressing the constraints as inequalities allowed me to graph them and see how they would affect each another. I was able to find the points at which I could sell the most amount of batches while taking into consideration all three constraints at the same time. I feel like I can apply this knowledge to other products. For example, I want to start a business of 3D printing gaming miniatures. I thought I had already figured out how to price them based on the cost of the resin, paint ect. However, now I realize that I need to also think about the constraints associated with 3D printing such as the time it takes to print, the availability of the resin, and the time it would take to paint each miniature. I could use the principles I learned in this project to better determine a sales price for my work.
Chi-Squared Project:
The Rocket Project:
Cover letter -
Laws of Motion -
1. Newton’s First Law, the Law of Inertia, includes inertia, net force, and support (normal) force.
2. Newton’s Second Law, the Law of Force and Mass, includes the idea that force causes acceleration, friction, and mass vs. weight.
3. Newton’s Third Law, the Law of Action and Reaction, includes forces and interactions, what a “system” is, and action and reaction on different masses.
Kinematics -
Dynamics -
- Linear motion is motion along a straight line.
- Speed is the rate at which distance is covered. It is how fast you are traveling (for example 20 mph). It is a scalar quantity.
- Velocity is the speed in a given direction (20 mph going east). It is a vector quantity.
- Acceleration is how velocity changes over time. It is the rate of change of velocity with time. (speed increases, decreases, or changes direction).
- G is the abbreviation for gravity and gs- is a measure of acceleration or deceleration (change in speed over time)- gs are experienced with sudden changes in velocity like a car making a tight turn). One g is 9.81 m/s^2.
- Our frame of reference is the ground that we are launching from.
- Free fall is falling through the air with no forces other than gravity acting upon you. Two objects with the same mass, but different weights will fall at the same time.
Laws of Motion -
1. Newton’s First Law, the Law of Inertia, includes inertia, net force, and support (normal) force.
- “An object that is still will stay still until an outside force makes it move.”
2. Newton’s Second Law, the Law of Force and Mass, includes the idea that force causes acceleration, friction, and mass vs. weight.
- “Force is = to mass times acceleration”
- When the force is greater the acceleration is greater and when the mass of an object is larger the acceleration is less.
3. Newton’s Third Law, the Law of Action and Reaction, includes forces and interactions, what a “system” is, and action and reaction on different masses.
- “Every action has an equal and opposite reaction”
- When one body pushes on a nether body they push back on each other.
Kinematics -
- Average acceleration during takeoff
- Average velocity of the rocket on the descent
- Average deceleration on landing
Dynamics -
- Average force of thrust during takeoff
- Forces acting on the rocket during descent.
- Average force on the rocket during landing
Takeoff -
Descent -
Landing -
- Rocket starts on the ground and remains stationary until an outside force acts on it. This is a representation of Newton's First Law of Motion.
- The lighter your rocket is the easier time that the rocket will have during flight. Less mass = more acceleration. This is a representation of Newton's Second Law of Motion.
- The rocket pushes out the water making it fly because the water is also pushing on the rocket. This is a representation of Newton's Third Law of Motion.
- The more water you have (mass) the more that will push out the rocket and force the rocket to go higher. This is a representation of Newton's First and Second Laws of Motion.
Descent -
- Drag affects the rocket when it is flying and falling because the wind resistance is pushing down on the rocket. This is a representation of Newton's First Law of Motion.
- When the rocket falls through the air (the medium) it falls at a constant rate because the medium prevents the rocket from moving any faster until it reaches net 0 (Hitting the ground). This is a representation of Newton's First Law of Motion.
- A heavier rocket will generate a higher constant acceleration during its free fall until it reaches terminal velocity that prevents it from further acceleration. This is a representation of Newton's Second Law of Motion.
Landing -
- The rocket will stay on the ground unless an outside force makes the rocket move. This is a representation of Newton's Law First of Motion.
- When the rocket lands on the ground it will push on the ground and the ground will also push on the rocket with the same force. This is a representation of Newton's Third Law of Motion.
- If the rocket moves higher with more force then a similar amount of force will be applied to the rocket when it hits the ground. This is a representation of Newton's Second Law of Motion.
Reflection:
How did you and your partner(s) function as a team? Were there conflicts or issues, and how did you overcome them? If you had no conflicts or issues, what did you do to enable this?
In what capacity were you a leader in your group? How about a follower? Did you support your partner’s strengths and fill in for their weaknesses? Explain.
Identify where in the seven steps of the Engineering Design Process you were successful and where you struggled. Give concrete examples of your application of the process.
(The seven steps: Ask, Research, Imagine, Plan, Create, Test, Improve)
Pick one lesson you reflected on above, or something new that you learned during this project, and discuss how this lesson will aid you in your future goals beyond the fields of physics, engineering, and mathematics (or in them, if you are considering a career in STEM).
How did you and your partner(s) function as a team? Were there conflicts or issues, and how did you overcome them? If you had no conflicts or issues, what did you do to enable this?
- Cassidy and I worked together by splitting up the work and talking to one another about issues and challenges that the project held. We worked well together with no conflict because we communicated with each other every step of the way.
In what capacity were you a leader in your group? How about a follower? Did you support your partner’s strengths and fill in for their weaknesses? Explain.
- I had the opportunity to be a leader when I generated ideas and implemented them into our rocket design. Cassidy brought to our team level-headedness and initiative to get the job done on time and with quality. I tend to stress out about deadlines and meeting expectations and she was able to help me stay grounded and finish the work when I got frustrated.
Identify where in the seven steps of the Engineering Design Process you were successful and where you struggled. Give concrete examples of your application of the process.
(The seven steps: Ask, Research, Imagine, Plan, Create, Test, Improve)
- Where I feel like we were the most successful in the engineering design process was in the improvement process. Each time we tested our rocket we found ways to improve our design and we did not get frustrated with minor errors in the design. We saw that it was an opportunity to improve and learn from our mistakes. For example, during one of our test launches, we decided that a sharper nose cone and a sleeker design would improve the aerodynamic quality of our rocket. We got advice from Julian, who agreed that a sleeker design would generate more height. As a result, we streamlined the body of the rocket by adding a sleeve to the neck of the bottle to smooth out the drag and we added a pointed nose cone. This design change was very successful. Where I think we struggled the most in the engineering design process was in the creation process. We struggled at first to build the rocket design that we had researched and planned. We had decided to try and build a body that spliced together two bottles in order to increase the water and air pressure capacity. This was really tricky to do because we could not figure out how to give the design the integrity it needed so that it would not explode. We kept brainstorming and working together to come up with a solution that would work. This was frustrating at times because we wanted it to work right away so that we wouldn’t explode our rocket and have to start over.
Pick one lesson you reflected on above, or something new that you learned during this project, and discuss how this lesson will aid you in your future goals beyond the fields of physics, engineering, and mathematics (or in them, if you are considering a career in STEM).
- The most important thing I learned from this experience was how to work well with a partner during a group project. I have had struggles with this in the past. Often times I feel like I don’t work well with groups. I get frustrated when I feel like others are not doing what they are supposed to. Last year I had some bad experiences working with people and ended up doing all the work myself. I was nervous to work with a friend because I didn’t know if it would improve this mindset I had and I did not want it to ruin our friendship. I feel like I had a lot of success working with Cassidy. They were engaged in the project the entire time and we were able to produce a really good project. I think having this success will help me navigate future group projects at school and in life outside of school.