Fun Definition and 428 Threads

Here's the project: You have a 60x60x60cm box, and a marble (the material of the marble could be steel, glass, plastic, etc.). There are 2 holes in the side(s) of the box that are 20cm vertically apart. The marble must start from the lower hole with basically no velocity, and by any...

Hey all, This is a just for fun question, as I am sure there is no definitive correct answer. But here it goes Blackholes to my knowledge, generate the strongest gravitational fields in the known universe. While thinking about gravitational time dilation, and the sheer magnitude that black...

The Problem: A plane is dropping supplies to a clearing in the forest. The plane will approach the clearing at an altitude of 150 m while flying level at 40 m/s. Why can't the plane drop the supplies while directly over the clearing and at what distance should it release them to arrive to...

Homework Statement Found a pretty fun question on power from one of my friends old physics exams just wanted to see if I was doing it right so far.The Attempt at a Solution So the first thing I did was draw a free body diagram and used Newtons Second law so ƩFx: F - (250 + 0.7v^2) - mgsin10 =...

Homework Statement A barrel of fun consists of a large vertical cylinder that spins about the vertical axis. When it spins fast enough, any person inside will be held up against the wall. http://i.snag.gy/Wh1B9.jpg Question: If you double the angular speed (i.e., \omega _2=2\cdot \omega _1)...

Evaluate the given sum: S_n=\sum_{k=0}^n\left(\frac{1}{k+1}{n \choose k} \right)

. . . . . . . . Mondegreens - 4Children are unfamiliar with phrases like "which art" and words like "hallowed". .Hence, they recite: . . Our father, Richard in heaven, Harold be thy name.Shirley, good Mrs. Murphy shall follow me all the days of my life.Jose, can you see by the donserly light...

Homework Statement 1. You drop a rock down a well and hear a splash 3 s later. How deep is the well assuming that air resistance is negligible and the time needed for sound to travel up the well is also negligible? 2. The acceleration due to gravity on the Moon is about 1/6 that on Earth...

I've been programming for fun as a hobby for years, but with math, I have to put in so much effort and I get exhausted so easily. Why is that?

Background: This is my first post here on physics forums. I have perused for quite a while. I am a Chem Eng. student at University of Houston and this question is from my Thermodynamics class. I have enjoyed working on this problem (for hours) but am certain i have made a mistake...

Please compute the following sum: S_n=\sum_{k=1}^{n}\frac{n!}{(k-1)!(n-k)!}

There are 111 people in a competition. The competition has 4 boxes and 4 jewels. Each box is identical and is completely opaque (i.e. you cannot see inside the box once it is closed). The jewels are all different: diamond, ruby, emerald and topaz. Everyone in the competition knows this. The host...

The curve in the figures above is the parabola $y=x^2$. Let us define a normal line as a line whose first quadrant intersection with the parabola is perpendicular to the parabola. Five normal lines are shown in the figures above. For a while, the $x$-coordinate of the second quadrant...

If you are having difficulty figuring out the percentage of an item and don't have a calculator, you may utilize this trick (which i still don't know how it came to be in my mind). Let: ##a## be a fractional number (percentage) and ##b## a whole number. If you make ##a## be a whole number...

I hope I'm in the right section. This part is not important but this is thought behind the program. If you have n-mathematicians and each has a secret number. How many phone calls have to be made for all mathematicians to know all numbers? In this brute force approach I, hypothesize that you...

Show that: \sum_{k=1}^n\left(\frac{(-1)^{k-1}}{k+1}{n \choose k} \right)=\frac{n}{n+1} Hint:

My boyfriend is into magic, and he has a device that sends a small current through his body. His shoe has an electrode that is activated by a magnet in his other shoe; a wire runs up to a battery. As long as he is standing and grounded, it allows him to channel a small amount of electricity...

Here is a fun exercise to prove \int^1_0 \frac{\log(t) \log(1-t)}{t} \, dt = \zeta(3)

I'll go right to the point. I'm trying to get someone interested in physics (and relieve physics of adjectives like boring) . All I'm asking for is a clear, fun and kind of insightful way for looking at physics and how it relates to our daily lives and how it helps us understand our...

Hi, so I have a little background in biology. I took AP bio in HS and got a 5 and really enjoyed it along the way. I got a microscope for my own amusement and also to maybe spark an interest in my little brother. What I'm having trouble with is finding good densities of moving microorganisms...

I gave away the answer in the title, but still, this is a pretty cool demonstration of what happens when you wring-out a washcloth in space: https://www.youtube.com/watch?v=lMtXfwk7PXg

Hi all, I've had an itching lately to dive into something new. Currently, I am a professional computer programmer but have always been interested in astronomy. I took an astronomy course (as well as a lab for it) when I was in college and I remember enjoying it all immensely. I want to get...

I'm not sure if these have been looked into extensively (they probably have, I just have a hard time finding them), but I was just wondering about a couple conjectures I thought up and tested by hand for a bit. Matlab can't run it for very long. Let me know if anyone finds a contradiction or if...

To all those who have studied metric spaces, take a look here. It's a fun little exercise, if you have a hour or two.

Homework Statement I'm trying to see if I can prove that any non-square number's square root is irrational. I'm using only what I already know how to do ( I like trying to prove things myself before looking up the best proof), so it's going to be round-about. Attempt#1 Eventually required me...

Homework Statement As a prank, your friends have kidnapped you in your sleep, and transported you out onto the ice covering a local pond. Since you're an engineer, the first thing you do when you wake up is drill a small hole in the ice and estimate the ice to be 6.7cm thick and the distance...

Here's a nice challenge that I made up thinking about compressing data one night... Print out a number that you can read within it: The numbers 1 to 20(easier) or 1 to 99(very hard) Rules: →Can be read forward or backwards and use same numbers eg. 123 you can read...

Homework Statement Homework Equations The Attempt at a Solution Honestly no idea where to start, I don't even know what this means.

Here's a nice geometry problem, not hard at all if you can see what's really going on. https://lh3.googleusercontent.com/-qqF-3y81rvI/UQjt7jishKI/AAAAAAAAAII/gP8G0dgKCmc/w497-h373/cercles.gif Solution (don't click if you want to work it out yourself!):

My friend bought a new chair for the living room. He says I sit in it with too much force and claims I basically free fall into the chair (padded chair, like a one person loveseat) and we tried to calculate the pounds per second against the chair but I don't know much about material science and...

Hey folks. I've been interested in physics for awhile and would like to expand my knowledge. I'm not looking to enroll in college courses, but I would like some good readings to gain more knowledge specifically in the areas of particle physics, dark matter and energy, and string theory. I've...

Hi, i know I've posted similar threads before but here it goes: im a second year university student studying biochemistry. Now in theory its ok, and some of the courses are fun but i have no passion for studying biochemistry. i thought organic chemistry would cheer me up but its pretty dull...

Homework Statement A ski-jumper comes off the bottom of the slope going horizontally at a speed of 20 ms. It starts off 3 m above a slope going downwards at an angle of 45 degrees. How far along the slope does it land. Homework Equations 1) y= Vsinθ - (.5)gt^2 2) x= Vcosθt 3) tanβ =...

Fun physics activity! Homework Statement Under the conditions of normal activity an adult inhales about 1.1l of air during each inhalation. Using a stopwtch, determien the time for one of your own inhalations (avg several to get two significant digits) and hence estimate the volume flow in...

I recently had fun on another forum solving a variation of this problem: Consider the region within a square containing the points which are closer to the center of the square than to any of the sides. What portion of the square is this region? I am curious to see what other methods may be...

I've made a few efforts to learn to program in the past, but I've never lasted more than a few days. What are ideas on ways to make it fun? Websites maybe? Or forums? For learning science/engineering principles, this forum is great. Do you guys have suggestions for ways to make...

Hello, I am a freshman EE/CompE (Hardware) major seeking a math minor. Since I have already arrived to university with Calc III and ODE's completed, I would still like to dedicate about 4-7 courses of mathematics. I would like some math classes to be applicable to my major as well as others to...

Q1: If every atom has to adjust their energy levels according to every other atom in the universe, does that mean that any given single atom has its interior invaded by a catalog of energy states from every other atom in the universe? And only after accounting for all the energy states that...

Let H be a house with only one entrence. Assume that between any two rooms in the house there can only be at most one door. The owner's of this house, keen on selling to an American buyer, decide to place a TV set in every room with an odd number of doors. Prove that the the American will be...

Homework Statement I'm trying to figure out how to use Ito's Lemma, but all I have are notes and proofs. It would help if someone could go through one actual example with me: Use Ito's Lemma to solve the stochastic differential equation: X_t=2+\int_{0}^{t}(15-9X_s)ds+7\int_{0}^{t}dB_s and...

Hey everyone! Ok, this summer I am self-studying Alg II so I can test out of it in August for my high school. I was also planning on learning a lot of pre-calc/calc from a friend, but I'm somewhat skeptical about it because he seems to not have that much time on his hands and I don't want to...

could it be possible to use sf6 (sulfur hexafluoride) + photosynthetic bactera + hydrogen to transform mars's atmosphere into a breathable atmosphere that is also warm enough for survival? If somone could produce ozone efficiently, would it be possible to create some kind of radiation shield on...

I run Windows machines at the moment, but I have always had a soft spot in my heart for Linux and the open source philosophy. So I decided to start learning hard-core Vim. It's fun to see how powerful Vim is. I think I'm going to switch from TextPad to Vim for $\LaTeX$ editing now. Cheers.

I am by no means in the same stratosphere as Jameson and others on this forum when it comes to chess, but I do enjoy the game. Here's a fun little chess problem. White to play and mate in 2.

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I think the video is clear enough: http://www.youtube.com/watch?feature=player_embedded&v=qHrBhgwq__Q. Looks like a nice game.

More "fun"? mechancial vs. electrical I am currently a student at a university finishing my last semester completing a BS in mathematics and a concentration in physics (engineering emphasis). After I graduate, I am going to pursue a BS in engineering before going to graduate school for...

Homework Statement I need to find the distribution of A Homework Equations A|B\sim \text{Poisson}(B) B\sim \text{Exponential}(\mu) The Attempt at a Solution \displaystyle P(A=k)=E[P(A=k|B)]=E\left[e^{-B}\cdot\frac{B^k}{k!}\right]=\ldots Not sure how to calculate this...

I'm a 2nd year math student. I'm taking 5 courses, but only 2 are math courses (differential equations and linear algebra). The rest are just 1st year electives I never did earlier (first year psychology and first semester biology). In short, I hate things like midterms, final exams, the idea of...

Fun Problems! Evaluate the following: 1. \( \displaystyle \sum_{n=1}^{\infty}\frac{\left( 1+\dfrac{1}{1!}+\dfrac{1}{2!}+\cdots +\dfrac{1}{(n-1)!} \right)}{2^{n-1}}\) 2. \( \displaystyle \sum_{n=1}^{\infty}\frac{1+2+2^2+\cdots+2^{n-1}}{n!}\) 3. \( \displaystyle...