walsh416

Analog mice are markedly simple devices, essentially motion sensors that perform vector addition to calculate a change in position. At the heart of a mouse you'll find ventricles and aortas... (sorry, wrong kind of mouse). At the heart of a computer mouse a rubber ball rubs against two or more rolling bars. This ball is designed to be rather heavy, and have a high coefficient of static friction. These two attributes combine to form a ball that rolls instead of slides (heaviness increases normal force, and high coefficient of static friction increases the value for mu, multiply them together and one ends up with a high maximum static friction force). When the mouse is moved along a horizontal surface, the ball will roll underneath it. This rolling is registered by two or more small cylinders within the mouse that are in contact with the ball. Because the radius of the cylinders and the radius of the ball is known, it is easy to figure out how far each roller has moved (essentially, how far the mouse has moved in each axis). The mouse then performs some form of vector addition of of this information (if there are just two rollers at ninety degrees to each other, it would be a simple Pythagorean identity, if there are three or more things get tougher). The mouse then transmits these vectors to the computer via USB, and the computer moves the cursor on screen accordingly.

Now it's time, To start a rhyme. A rhyme of physics, No, not metaphysics. Newton was 'neath an apple tree, When an apple cometh falling free. "Ow" he shouted, As his thoughts unclouded. A great invisible force, must be! Perhaps we shall call it... gravity! Soon publishing the "Principia Mathematica," He gave the academic world a heart attacka. Within this massive tome, Newton drove just three points home. Now numbered one, two, and three, Newton finally set physics free. Number one, a classic! We know your jar of Vlasic Shall never move, Unless 'tis kicked by a horse's hoove. Then on to number two, With a constant mass, it's always true! F=ma, that's all. This is Regents stuff, y'all. Finally, we come to the third, Always seen and often heard. For all actions, each and every, The opposite reaction is just as heavy.

I really really like the fact that we both put up posts about driving in the snow on the same day. I also like that yours said "So stay safe and follow those road signs" and mine said "In the end, maximum slide is achieved by going around a corner and then pulling the handbrake." A more representative pair of sentences has never been written. ()

When it comes down to it, your basic mechanical pencil really is a remarkably simple device. A plunger is used to depress the entire inner sleeve. A spring keeps the plunger under tension and draws it back after it has been pushed. The inner sleeve contains a lead holder with the end split into two 'pincers' that are held together by a collar. This collar is moved by depressing the plunger, which pushes the inner sleeve down while keeping the collar in the same place. Perhaps the most critical part of the apparatus is the 'exit tube', located on the outer sleeve. This tube is the last thing the lead comes into contact with before being used, and functions as a way to retain the lead as it is pushed out by the pincers. Because the tube is functionally the same diameter as the lead, they are in complete contact and therefore exert a normal force on each other. Because neither of them are frictionless, this normal force combines with their coefficient of friction and forms a frictional force. It is this frictional force that holds the lead in place when one presses the plunger and opens the pincers. Incidentally, the work one on the plunger by the operator is converted into both spring potential energy that is released when the plunger is released, and heat due to the sliding of the lead through the 'exit tube.' As such, Al Gore has suggested that we all "be kind to the great mother earth, and stop global warming by using fewer mechanical pencils." He always was an odd duck...

Let's just get this out of the way first: if it doesn't have three pedals and require both hands to drive, it's simply not a car. It's a sad, sad excuse for transportation. A manual transmission lets the driver select which gear they would like to be in, and control how they shift. By depressing the clutch (operated by one's left foot), the engine is disconnected from the wheels. One can now use the gear shift lever to select an appropriate gear. The gear shift lever typically operates a set of selector forks in the transmission. These forks engage different gears, depending on the position of the gear shift lever. One a gear is selected, one slowly lets the clutch out while increasing the amount of gas given to the engine. The clutch is essentially a plate connected to the engine and a plate connected to the wheels that mesh together. When the clutch pedal is to the floor, the plates are completely separated. By letting the clutch out, one slowly brings the plates together. It is incredibly important to let the clutch out slowly: when the clutch is in, the plates are likely rotating at different speeds. By bringing them into contact slowly, one allows slippage between them before full engagement takes over, which means that they can accelerate each other until they are rotating at the same speed. Increasing the amount of gas given to the engine while letting the clutch out makes one less likely to stall. Stalling occurs when the engine isn't producing enough power to continue to rotate, and so it simply seizes. This is deeply embarrassing, especially when it occurs at a busy red light (ask me how I know...). In letting the clutch out one is engaging a gear, and therefore increasing the load on the engine. Pushing the gas pedal in more lets the engine produce the power the transmission is now calling for.

First, let us bow our heads and give brief thanks: "We thank thee, creator of roads and corners. Bringer of snow and handbrakes. You alone make driving fun." And now, lets talk about driving in the snow! Effectively, snow lowers the coefficient of static friction between the tires and the road surface. This means that for the same weight of car and contact patch with the road, The road can provide less "push" against the tires, so they're more likely to spin instead of roll. This effect is increased in corners, due to the added force applied to the tires. Rather than simply being asked to provide force in the plane of the wheel, they're now also being asked to provide force in a plane perpendicular to the wheel. Vector addition tells us that if we add two perpendicular vectors, the resultant is the square root of the individual vectors squares (Pythagorean theorem). This spinning instead of rolling is also 'helped along' by using the car's brakes. Fortunately for safety, but unfortunately for someone who actually enjoys skidding, modern cars are equipped with antilock brakes (ABS). This means that if a wheel starts to slide under braking rather than continue to roll, the car automatically pulses the breaks, working to find the point where maximum breaking force is applied to a wheel without causing it to skid. As evidence that there really is a divine being, most cars are equipped with a hand-operated emergency brake. This brake has a direct connection to the wheels, and is therefore unaffected by the antilock braking system. In the end, maximum slide is achieved by going around a corner and then pulling the handbrake. This ensures that the tires are under maximum load, and then knocks them loose by locking them up. As always, be safe, don't wreck any lawns or mailboxes, past results do not guarantee future success, don't drink and derive, and don't share needles.

First seen as a relatively mature product in the 1910s, the typewriter quickly became an indispensable part of the 'modern' office and home. An entirely mechanical, analogue device, the typewriter uses a complex series of metal levers to raise 'typebars' (longer levers with characters on the ends). These typebars strike an ink ribbon and press it against the page. This impulse transfers some of the ink from the ribbon onto the page. At the end of a line of text, a typist must press the carriage return; a bar which moves the paper over and up to prepare for the next line to be entered. A truly classic example of mechanical advantage, typewriter keys only need to be depressed half an inch or so to cause one of the type bars to swing up many inches and strike the ink ribbon and paper. This conversion lessens the force the type bars can exert at the end of their radius, but means this point moves very quickly. Because momentum is equal to mass multiplied by velocity, the end of the typebar builds up a great deal of momentum. This momentum is then used as an impulse to compress the paper and ribbon against the character and actually 'type' something.

Ahh, the keyboard. Platter of choices. Pallet of Arabic characters. Based on the QWERTY layout introduced in 1867, the keyboard is our portal to the world. But just how do they work? First, it is important to note that this article centers on modern, computer keyboards. Check back later for the physics of a typewriter. Modern computer keyboards feature upwards of 70 keys (I just counted, mine has 84) which take a consistent and relatively small magnitude of force to depress and register as a keystroke. On my keyboard, this consistent force is provided by a small synthetic spring and series of two levers. The spring is formed through a molded piece of what appears to be silicone, with small "humps" where each of the keys are located. These humps compress in a manner where the first millimeter or two of displacement requires most of the total force, and the rest of the displacement requires very little force. Practically, this means that the keys can support quite a bit of force (say, the weight of one's fingers), while still being relatively easy to compress. I believe that the two small sliding levers function only to keep the keys oriented correctly, as they are sprung but very, very lightly. If one had far, far too much time on one's hands and wanted to the spring constant of a key over its displacement, one could set up a range finding system to measure the acceleration of the key when a constant force is applied. This graph could then be examined to determine the change of net force and, therefore, variation in spring constant across the displacement. Let's not do that though, because that's the sort of thing only done by thirty year old guys named Ted who live in their mothers' basements.

Does anybody have any great ideas for how to do parts b-d? It seems like there should be a way to integrate the force of the spring, subtract the force of friction, do some math-o-magic, and pop out an answer. Or maybe look at the Uspring and work (hehe, puns) from there? It's (obviously) the fact that friction is non-conservative that makes the whole thing tough. Also- Kerbal Space Program makes doing homework really hard...

I mean, there is a super slim chance that I am, in fact, over thinking it...

Some super-intense, deep rooted hatred coming out here. (there must be a joke in here somewhere about not being concerned about gym teachers actually reading a physics blog, but I'm not finding it.)

This is literally the single best and most sarcastic blog post ever. Well done.

2013. San Francisco Bay. The 34th America's Cup. Race 8. Emirates Team New Zealand is neck and neck with Oracle Team USA, headed upwind (the slow point of sail; the 72 foot catamarans might only hit 30mph). In a typical race with typical boats, this would be a run of the mill maneuver. Do your best to stay in front of the other guys, don't lose ground, and find the perfect balance between outright speed and sailing as close as possible to the wind. However, nothing about racing the AC72 is typical. One of the biggest (pun intended) reasons behind their ability to attain mind-boggling speeds is the 132 foot wing. Most sailboats have, well, a sail. When writing the rules for the 34th America's Cup, Larry Ellison decided, in all his infinite (eg nonexistent) wisdom that the boats would have wings rather than sails. This means that instead of a piece of cloth propelling the boat, a rigid, adjustable wing is used, almost like taking a wing off of an airplane and mounting it vertically. Each time the boat turns, the wing's trailing edge must be adjusted, as must the angle of the curve in its midsection. These adjustments are made with hydraulic pumps, pressurized by the grinders onboard the boat. Now, back to race 8. New Zealand tacks (turns, pointing the bow [the front of the boat] into the wind as it does so) to avoid Oracle, but seems to lack the hydraulic pressure required to "pop" its wing. The boat has now turned but the wing remains convex to the wind, when it should be concave. This causes their boat to lean near 45 degrees for a heart-stopping 10 seconds before it returns to a normal angle with the water. In the end, always remember Bernoulli's Principle! If the pressure has not been provided initially, there is no ability to create a pressure differential to properly execute the action.

Since his meteoric rise to fame on the back of "Born to Run" (without a doubt one of the best albums ever released), The Boss has remained a fascinating physics problem. Let us look closely at the second track on "Born to Run," "Tenth Avenue Freeze Out." Here, Springsteen tells us that 'the big man joined the band.' One may obviously assume from his use of 'big' that he is referencing the Big Bang. Thusly, he is telling his audience that one night on Tenth Avenue, a human representation of the Big Bang joined the E Street Band. How could this be so? Rather simply, in fact. If one completely ignores all rules and conventions of physics created or discovered past roughly 1500 AD, it becomes clear that on the famed night a second Big Bang occurred (henceforth referred to as the Medium Bang). This Medium Bang created a second universe, filled with burly, afroed men demonstrating godliness on the saxophone. However, a single large error with the so-called Medium Bang theory exists. Since was a "Tenth Avenue Freeze Out," it can clearly be assumed that Springsteen was referencing a moment where absolute zero came to fruition on Tenth Avenue. Since this is the case, the Medium Bang can't possibly have created a second universe because absolute zero is defined as the point where entropy reaches its minimum value. While inspirational, this second, saxophone playing universe would increase entropy, not lower it to an absolute minimum. In all, one is forced to determine that either The Boss lied to us, or he was simply telling a story and not referencing non-existent and often nonsensical physics concepts. The nerve of some people.

Honking the hooter. Emptying the schnozz. Launching the snot rocket. Everybody blows their nose, but how exactly does it work? First, you create positive pressure in your lungs by tensing your diaphragm. Since initial PV/T must equal final PV/T, when a larger pressure is created it will result in an increase in the velocity of air exiting the lungs. This fast moving air is then guided up to the nose and out the nostrils. As the air passes through your nostrils, it must pick up the snot clinging there and carry it out. It does this through drag due to air resistance. As soon as the force on a snot particle is greater than the maximum adhesive force holding it to your nose, the piece of snot will be blown off and carried away. Thus, it follows that there must be a 'terminal blowing velocity' -- a velocity at which blowing faster will not result in the purging of any additional snot. This author encourages all readers to grab a pack of kleenex, a wind speed gauge, a family member with the flu, and experimentally determine said terminal blowing velocity!

As we learned from Professor Goho, friction due to air resistance is equal to .5c[ROW]Av^2. In bicycle racing, one's goal is to minimize this value as much as possible. Manufacturers spend millions of dollars each year lowering frontal area of their components and increasing making them more aerodynamic. As an individual cyclist, one lowers aerodynamic drag by drafting; the practice of following as closely behind another rider as possible to catch their slipstream, essentially lowering the local density of the surrounding air. This is done by riding down the road at 25mph behind someone you've never met, keeping your front wheel no more than half an inch to an inch behind their rear wheel, and praying they don't swerve or stop. Fun, right? By following so closely behind, you are taking advantage of the zone of low density air behind them and lowering your friction due to air resistance. The practical effect of this is absolutely huge; in the middle of a well-developed peloton (large clump of riders), your effort can decrease by 25% or more. That is to say that if the leading rider is outputting 500W to ride at 30mph, you need only 375W to stay in the pack. In a race, this creates a curious paradox: you want to remain close to the front of the group to avoid the “yo-yo” effect caused by the reaction times of individuals braking to avoid collisions, but leading the group is the very last thing you want to do, as you are burning energy you'll need later to keep up with the breaks or contest the final sprint.

"The following is a recreation of the real world events of a late October day in two thousand eleven, anno dominae." T-10sec: Timothy is riding along on his bicycle, and comes across a group of walkers blocking the roadway. Being the amiable gentleman he is, he decides to go around them, swerving onto the sidewalk. T-1sec: Disaster seems ready to strike our hero, for as he prepares to dive back into the street he strikes a pedal on the driveway, lifting his rear wheel up and reducing its frictional force from relatively high to null in a matter of milliseconds. T-0sec: Our hero hits the deck! Due to a sudden and catastrophic loss of the rear wheel's frictional force, the bike's forces are no longer balanced (centripetal force is no longer opposed by the static/rolling friction of the rear wheel) and the bicycle/cyclist system rotates about the z and y axes, throwing our hero to the ground. T+.5sec: Our hero hit the pavement with a momentum in the z-plane roughly equal to 422 Newton seconds, and is now sliding along the asphalt. T+1sec: After sliding on the asphalt for ~1 second, Timothy comes to rest. This decrease of speed was (pun alert!) forced by a force imbalance. Kinetic friction was retarding forward motion and no force was causing forward motion, so our hero slowed to a stop. T+5sec: Timothy says a small prayer that no one he knows saw any of the previous six seconds, pulls himself to his feet, and rides off. He swears to never again strike a pedal (that promise lasted a depressingly short amount of time).

A bicycle's drivetrain includes the pedals, cranks, bottom bracket, gear rings, chain, sprockets, freewheel, and derailleur. With all of those parts working in harmony, it takes the power provided by a human pedalling at 90rpm and uses it to turn a 27.75" diameter wheel at 20mph, all with an efficiency upwards of 95%. The drivetrain is, essentially, a system of levers and adjustable pulleys, working together to convert torques and forces. A typical crank is 175mm, measured from the center of the bottom bracket hole to the center of the pedal hole. This means that the downward force supplied to the pedals by the rider is instantly converted into a torque .175 times as great. This torque is altered again by whichever chainring is selected, and then travels via the chain to the back of the bike. Here the torque is again changed by the selected sprocket (the series of smaller gears at the back of the bike), where it is then transferred along the rigid spokes to the outside of the rear wheel. Here it is finally appropriate to talk about it in terms of a force again (instead of a torque, as it was throughout the drive train),at least when one is thinking about it relative to the road surface. In all, the torque/force relationship is repeatedly altered throughout the drivetrain, all to allow the most efficient input of human power for a given output of force by the rear wheel.

Golly gee biking (cycling) is hard. Perhaps the hardest part of all is mastering high speed cornering. You see it all the time in the Tour de France; pros carving graceful arcs as they fly down mountainsides at 100kph. How do they do it? By maintaining an incredible awareness of where their center of mass is relative to their bike at all times, and adjusting it so that they can achieve the right angle of cornering. By far the most common mistake any new cyclist will make is to turn their handlebars in the direction they wish to go. At low speeds this works to steer the bicycle, but at anything above a walking pace, all this does is cause one to eat asphalt. Instead, one must "counter steer," especially when beginning a corner. Counter steering is the act of pushing the handlebars in the direction opposite the one you want to go. This causes the bike to lean into the corner, moving your center of gravity lower and towards the inside of the corner.

But the langleys, man, the langleys!

So we launched catapults on Friday, that was pretty intense. In theory, ours was utterly perfect. We optimized it mathematically, and built it with the strongest $1.99 2x4s in all the land. What we didn't account for was wind. Not wind's effect on our projectile, but on the catapult itself. When cocked, our catapult had 135 pounds roughly four feet in the air (about 700 joules of potential energy, for those keeping score). During one launch our catapult, well, fell on me. If it fell two feet before hitting me, it was moving at (super rough mental math) ~1.5m/s. More interestingly, the piece of rebar I was hit with was half inch diameter, or .00051 square meters. This becomes an average of 690371 Joules/square meter of my flesh. In turn we can convert this measure to Langleys, we see I was hit with the equivalent of 16.51 ly of solar radiation, a dose surely considered hazardous in any reasonable scientific culture.

So I went to see Gravity this weekend. Overall, it was pretty good! Unfortunately, Sandra Bullock was truly brain dead throughout much of the film. In one memorable scene, she's trapped inside the International Space Station, alone, and fighting a massive fire. Panicking, she grabs a fire extinguisher off the wall and aims it. Now, before we get to what happened, it is important to understand a few things. The character she is portraying is an MD Ph.D, with years upon years of education. Unfortunately, it appears she never learned about a dead guy named Isaac Newton, who taught us that "any action will have an equal and opposite reaction." Poor Sandy believed that she would be able to float in zero gravity, firing a fire extinguisher, and remain in the same position. That was stupid. As it happened, she flew backwards and smashed her head on a metal pipe, something that definitely wasn't helpful as she tried to navigate her way back to earth.

The other two build on that concept, except instead of Vox = Voy straight up, you need to get triggy with them.

break it up into x components and y components. You know that Vox and Vfx are equal and Ax is zero, and that Ty equals Tx (times are the same..duh). You also know that Vox=Voy because the angle is 45deg. Do some kinemagic equation stuff and find x=.5(Vo+Vf)T, which becomes 618=Vx(T) for the x component and y=VoyT+.5aT^2, which becomes -3=Vx(T)-16T^2 for the y components. (Vx is interchangeable for Vox, Vfx, and Voy because they're all the same. Doe some systems magic and you'll get your answer (140.287 f/s, I hope).

Thanks!