Instructions
Complete the following problems as best as you can. There are no ''right'' or ''wrong'' answers here.
All of these questions are designed to give your brain some practice with a certain type of thinking used by physicists as they analyze the world around us.
The most important thing is to show your work. ChatGPT, Wikipedia, and other online sources will provide answers for some of these questions, but we are interested in how you think.
All of these questions are designed to give your brain some practice with a certain type of thinking used by physicists as they analyze the world around us.
The most important thing is to show your work. ChatGPT, Wikipedia, and other online sources will provide answers for some of these questions, but we are interested in how you think.
1. Estimation
The great pyramid of Giza (above, image from the Encyclopedia Britannica) was constructed by the Egyptian pharaoh Kufu sometime around 2600 BC. Its purpose is to serve as Kufu's burial chamber.
At the time of its construction it was the tallest human-made structure in the world, and remained the tallest structure for almost four thousand years until being surpassed by the Lincoln Cathedral in England in the year 1311.
The pyramid stands at 138.5 meters high (without its limestone casing stones) atop a square base. Each side of the square base measures 230.3 meters.
At the time of its construction it was the tallest human-made structure in the world, and remained the tallest structure for almost four thousand years until being surpassed by the Lincoln Cathedral in England in the year 1311.
The pyramid stands at 138.5 meters high (without its limestone casing stones) atop a square base. Each side of the square base measures 230.3 meters.
(a) Make an "order of magnitude" guess as to the number of blocks in the pyramid. We'll call this your "wild guess."
(b) The pyramid is constructed of individual stone blocks. What is your estimate for the length, width, and height of a single block?
(c) Given your estimate of the block size, how many blocks do you think are in the pyramid? How does this compare to your "wild guess?"
(d) Can you think of why your quick estimates might be different from the estimates of archeologists, who have visited the pyramid?
(e) It has been estimated that it took 20 to 30 years to construct the pyramid. Certainly, it would not have taken of order hundreds of years, because it was commissioned by Kufu as his burial site and needed to be completed before his death. (Most adults in ancient Egypt lived to roughly age 40 -- a pharaoh might or might not live longer for a variety of reasons.) Given your estimate in part (c), and that blocks were being placed 24 hours a day, 365 days a year, what is the average length of time between block placements? (i.e., "they would have to place a block every X minutes" -- find X).
(f) Estimate the weight of a single block. It will be helpful to know that most of the blocks are made of limestone, which has a density of 2900 kg/m^3. How many adults would it take to move a block of that weight?
(g) How many adults do you think worked on the pyramid project?
(b) The pyramid is constructed of individual stone blocks. What is your estimate for the length, width, and height of a single block?
(c) Given your estimate of the block size, how many blocks do you think are in the pyramid? How does this compare to your "wild guess?"
(d) Can you think of why your quick estimates might be different from the estimates of archeologists, who have visited the pyramid?
(e) It has been estimated that it took 20 to 30 years to construct the pyramid. Certainly, it would not have taken of order hundreds of years, because it was commissioned by Kufu as his burial site and needed to be completed before his death. (Most adults in ancient Egypt lived to roughly age 40 -- a pharaoh might or might not live longer for a variety of reasons.) Given your estimate in part (c), and that blocks were being placed 24 hours a day, 365 days a year, what is the average length of time between block placements? (i.e., "they would have to place a block every X minutes" -- find X).
(f) Estimate the weight of a single block. It will be helpful to know that most of the blocks are made of limestone, which has a density of 2900 kg/m^3. How many adults would it take to move a block of that weight?
(g) How many adults do you think worked on the pyramid project?
2. Essays
Every question asked by every university, scholarship program, or school is being asked for a very specific reason. Each question is being asked to determine whether you have parts of your personality that is valued by the faculty, students, and administration at that college.
For example, a college where most students major in science may ask "What field of STEM interests you most, and why?" They are trying to determine whether your interest in STEM is real, or if deep down inside your heart, you are not interested in science.
Here are essay prompts from the 2025 Common App for admission to US universities:
- (1) Some students have a background, identity, interest, or talent that is so meaningful they believe their application would be incomplete without it. If this sounds like you, then please share your story.
- (2) The lessons we take from obstacles we encounter can be fundamental to later success. Recount a time when you faced a challenge, setback, or failure. How did it affect you, and what did you learn from the experience?
- (3) Reflect on a time when you questioned or challenged a belief or idea. What prompted your thinking? What was the outcome?
- (4) Reflect on something that someone has done for you that has made you happy or thankful in a surprising way. How has this gratitude affected or motivated you?
- (5) Discuss an accomplishment, event, or realization that sparked a period of personal growth and a new understanding of yourself or others.
- (6) Describe a topic, idea, or concept you find so engaging that it makes you lose all track of time. Why does it captivate you? What or who do you turn to when you want to learn more?
For each of the personality traits listed below, write the number (or numbers) of the question(s) trying to uncover that trait:
(a) self-understanding -- how well do you know yourself and your own interests?
(b) understand others' interests and perspectives
(c) willingness to contribute to a community
(d) creativity
(e) willingness to see things from someone else's point of view
(f) a true, genuine deep interest in one field of study
(g) ability to accept criticism
(h) ability to stick with a tough project or solve a tough problem
(i) willingness to ask for help
(j) being thankful for the help of others
(b) understand others' interests and perspectives
(c) willingness to contribute to a community
(d) creativity
(e) willingness to see things from someone else's point of view
(f) a true, genuine deep interest in one field of study
(g) ability to accept criticism
(h) ability to stick with a tough project or solve a tough problem
(i) willingness to ask for help
(j) being thankful for the help of others