The following article was taken from the "What If?" section of the website XKCD. The original article can be found at the address given below. but it has been reproduced on the following pages for ease ofaccess: httpszl [what-ixkcdcom/ 21 f To earn bonus credit equal to 1 in-class quiz grade, read the article and then answer the following questions. i will allow hand-written submissions, as you will need to show me some solved equations for proof of your work. Please write neatly! A. The author makes several comparisons to the Saturn V rockets used during the Apollo NASA missions [the ones that landed astronauts on the moon). The thrust force of the Saturn V rocket was about 34,000 kN during take off. Use this and the information presented in the article to determine the mass of the rocket. " , B. The number you found in part A should be large enough to have no real meaning to you. Let's convert it into a different unit. Assume one standard elephant has a mass of 5,000 kg. What is the mass of the Saturn V rocket in elephants? C. What is the approximate minimum number of AK-47s a 150 lb. person would need to strap to their back to be able to lift off the ground. according to the author's weight and thrust estimates? Assume the Alt-47 starts off fully loaded. D. The author claims that the GAU-B Avenger \"res up to 60 one-pound bullets per second\" and produces 5 tons of thrust force. Assume he means metric tons, which is equivalent to 1,000 kg: the thrust force would be equal to the weight of this much mass on Earth. Knowing this. use the thrust equation given in the article to estimate the bullet velocity ("speed of ejection") for this gun. E. The mass of the GAU-B Avenger is 280 kg. A typical car has a mass somewhere in the range of 1500 kg. The author claims that ifhe mounted this gun to the hood of a car and red it while the car was in neutral. the thrust from the GAU-B Avenger would allow it to break interstate speed limits within 3 seconds. Using your kinematics equations and assuming the car starts from rest, determine what acceleration the thrust from this gun would give the car. and then determine how fast it would be moving after 3 seconds. is the author correct? Now that I've ruined it for you with math, enjoy the article! Note: We discovered a few estimates that appear in this article that are somewhat different from published values. Use those found in the article for this assignment. Do not be alarmed ifyour answers are as much as 50% off from published ones. Finally. it may be useful to recall that one pound [lb.] is equal to 4.45 Newtons (N). Machine gun letpack Is it possible to build a jetpock using downward ring machine guns? Rob 3 By: Randall Munroe I was sort of surprised to nd that the answer was yes! But to really do it right, you'll want to talk to the Russians. The principle here is pretty simple. If you re a bullet forward. the recoil pushes you back. So ifyou re downward, the recoil should push you up. The rst question we have to answer is "can a gun even lift its own weight?" If a machine gun weighs ten pounds but only produces eight pounds of recoil when ring, it won't be able to lift itselfoff the ground. let alone lift itselfplus a person. In the engineering world, the ratio between a craft's thrust and the weight is called, appropriately, thrust-to-weight ratio. [1' it's less than 1, the vehicle can't lift off. The Saturn V had a takeoff thrust-to-weight ratio of about 1.5. Despite growing up in the South. I'm not really a rearms expert, so to help answer this question. I got in touch with an acquaintence in Texas. [Judging by the amount of ammunition they had lying around their house ready to measure and weigh for me. Texas has apparently become some kind of Mad Max-esque post-apocalyptic war zone.) 5am V W lib/ll As it turns out, the AK-47 has a thrust-to-weight ratio of around two. This means if you stood it on end and somehow taped down the trigger (Note: Please, PLEASE do not try this at home) it would rise into the air while firing. This isn't true of all machine guns. The M60, for example, probably can't produce enough recoil to lift itself off the ground. The amount of thrust created by a rocket (or firing machine gun) depends on (1) how much mass it's throwing out behind it, and (2) how fast it's throwing it. Thrust is the product of these two amounts: Thrust = Mass ejection rate x Speed of ejection If an AK-47 fires ten 8g bullets per second at 715 meters per second, its thrust is: 10 bullets x 8 grams bullet X 715 meters second second = 57.2 N ~ 13 pounds of force Since the AK-47 weighs only 10.5 pounds when loaded, it will be able to take off and accelerate upward. In practice, the actual thrust turns out to be up to around 30% higher. The reason for this is that the gun isn't just spitting out bullets-it's also spitting out hot gas and explosive debris. The amount of extra force this adds varies by gun and cartridge. The overall efficiency also depends on whether you eject the shell casings out of the vehicle or carry them with you. I asked my Texan acquaintences if they could weigh some shell casings for my calculations, but for a while they couldn't find a scale anywhere in the house. I helpfully suggested that given the size of their arsenal, really they just need to find someone else who owned a scale. (Ideally someone with less ammo.) So what does all this mean for our jetpack? Well, the AK-47 can take off, but it clearly doesn't have the thrust to spare to lift anything weighing much more than a squirrel.We can try multiple guns. If you fire two guns at the ground, it creates twice the thrust. If each gun can lift five pounds more than their own weight, two can lift ten. At this point, it's clear where we're headed: If we add enough rifles, the weight of the passenger becomes irrelevant. It's spread over so many of them that they don't notice. As the number of rifles increases, since it's effectively many individual rifles flying in parallel, the craft's thrust-to-weight ratio approaches that of a single, unburdened rifle: ALONE THRUST WEIGHT 2 RATIO WITH 60 kg RIDER 100 1000 10,000 100,000 NUMBER OF AK-47s But there's a problem: Ammunition. An AK-47 magazine holds 30 rounds. At ten per second, we'll get a measly three seconds of acceleration. We can improve this with a larger magazine-but only up to a point.It turns out there's no advantage to carrying more than about 250 rounds of ammunition. The reason for this is a fundamental and central problem in rocket science: Fuel makes you heavier. Each bullet weighs 8 grams, and the cartridge weighs over 16 grams. lfwe add more than about 250 rounds, the AK-47 is too heavy to take off. This suggests our optimal craft comprises a large number of AK-47s [a minimum of 25 but ideally at ieast 300) carrying 250 rounds of ammunition each. The largest versions of this craft could accelerate upward to vertical speeds approaching 100 meters per second, climbing over half a kilometer into the air. [If you want to work through the math on that in more detail, there's a good primer hm.) So we've answered Rob's question. With enough machine guns, you could y. But our Alt-47 rig is clearly not a practical jetpack. Can We do better? My Texas friends suggested a series of machine guns, and I ran the numbers on each one. Some did pretty well; the MIG-42 a heavier machine gun, had a marginally higher thrust-to-weight ratio than the AK-47. Then we went bigger. The Wm res up to sixty one-pound bullets a second. It produces almost ve tons of recoil force. which is crazy considering that it's mounted in a type of plane [the M11932] whose two engines produce only four tons of thrust each. If you put two of them in one aircraft. and fired both guns forward while opening up the throttle, the guns would win and you'd accelerate backward. To put it another way: If] mounted a GAU-B on my car, put the car in neutral, and started ring backward from a standstill, I would be breaking the interstate speed limit in less than three seconds. DDWKWM-IYI m. Rut-:Dirw OVER? \\- 3,014 ( As good as this gun would be as a rocket pack engine, the Russians built one that would work even better. The Gryazev-Shipunov GSh-6-30 weighs half as much as the GAU-8 and has an even higher fire rate. Its thrust-to-weight ratio approaches 40, which means if you pointed one at the ground and fired, not only would it take off in a rapidly expanding spray of deadly metal fragments, but you would experience 40 gees of acceleration. This is way too much. In fact, even when it was firmly mounted in an aircraft, the acceleration was a problem: [The recoil ... still had a tendency to inflict damage on the aircraft. The rate of fire was reduced to 4,000 rounds a minute but it didn't help much. Landing lights almost always broke after firing ... Firing more than about 30 rounds in a burst was asking for trouble from overheating ... But if you somehow braced the human rider, made the craft strong enough to survive the acceleration, wrapped it in an aerodynamic shell, and made sure it was adequately cooled ... ... with a GSH-6-30, you could jump mountains