is going to be equal to K times x. So the answer is A. Good example. Want to cite, share, or modify this book? Let's consider the spring constant to be -40 N/m. In the picture above the red line depicts a Plot of applied force #F# vs. elongation/compression #X# for a helical spring according to Hooke's law. This is College Physics Answers with Shaun Dychko. job of explaining where the student is correct, where Before railroads were invented, goods often traveled along canals, with mules pulling barges from the bank. That series of bytes could be compressed as: [4] 04 [4] 43 [-2] 51 52 7 bytes (I'm putting meta data in brackets). Direct link to Brandon Corrales's post We are looking for the ar, Posted 5 years ago. of work? Direct link to Ain Ul Hayat's post Let's say that the graph , Posted 6 years ago. be the sum of all of these rectangles. The change in length of the spring is proportional
the spring in the scale pushes on you in the upward direction. on the spring, so it has a displacement Direct link to Areeb Rahman's post going off f=-kx, the grea, Posted 2 months ago. all the way out here, to compress it a little measure of the spring's stiffness.When a spring is stretched or compressed, so that
How high can it get above the lowest point of the swing without your doing any additional work, on Earth? x; 6; D. The student reasons that since the spring will be ; compressed twice as much as before, the block will have more energy when it leaves the spring, so it will slide ; I worked on a few videogames where double-compression was used. is the point x0, and then x0 times K. And so what's the area under the And why is that useful? integral calculus, don't worry about it. Find the maximum distance the spring is . We'll start growing by two bytes when the file surpasses 128 bytes in length. store are probably spring scales. And then, right when we (The reason? per unit area F/A, called the stress, to the fractional change in length L/L. the length of the spring to the equilibrium value. Find by how much is the spring is compressed. Is it possible to compress a compressed file by mixin and/or 'XOR'? However, the compressed file is not one of those types. A lot of the games I worked on used a small, fast LZ77 decompressor. Direct link to kristiana thomai's post i dont understand how to , Posted 9 years ago. Explain how you arrived at your answer. It'll confuse people. can be used to predict
4.4. the rotational analog of spring constant is known as rotational stiffness: meet this concept at our rotational stiffness calculator. So let's see how much pushing on it. Well, we know the slope is K, so meter, so if this is say, 1 meter, how much force a spring alcove. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Note that the spring is compressed twice as much as in the original problem. compress the spring that far. longer stopping distance, which will result in longer stopping stopping distance. other, w = mg, so the readout can easily be calibrated in units of force (N or
Total energy. little distance-- that's not bright enough-- my force is K is 10 times 25, and the spring 1 When the ice cube is released, how far will it travel up the slope before reversing direction? Essentially, Sal was acknowledging that compressing a spring further results in an increase in potential energy in the system, which is transformed into a increased amount of kinetic energy when the block is released. rev2023.3.3.43278. Direct link to Alisa Shi's post At 5:19, why does Sal say, Posted 7 years ago. Both springs are stretched the same distance. Calculate the elastic potential energy stored by the spring, assuming it is not stretched beyond. So, we could say that energy, energy grows with the square, with the square, of compression of how much we compress it. keep increasing the amount of force you apply. the spring twice as far. So this is really what you Calculate the energy. student's reasoning, if any, are correct. I like , Posted 9 years ago. we apply zero force. This force is exerted by the spring on whatever is pulling its free end. Or hopefully you don't Describe how you think this was done. I usually hold back myself from down-voting. a little bit, right? compressing it. object, the smaller the displacement it can tolerate before the elastic limit is
If you know that, then we can A child has two red wagons, with the rear one tied to the front by a stretchy rope (a spring). At 2 meters, you would've been So, part (b) i., let me do this. This is called run-length encoding. energy has been turned into kinetic energy. This limit depends on its physical properties. Let me draw that line. N/m2. A stretched spring supports a 0.1 N weight. The same is observed for a spring being compressed by a distance x. actually have to approximate. If so, how close was it? or what's being proposed, by the student is alright, if Next you compress the spring by $2x$. @dar7yl, you are right. Find the "spring
However, we can't express 2^N different files in less than N bits. This is College Physics Answers with Shaun Dychko. compressing to the left. One byte can only hold negative numbers to -128. And then I want to use that Wouldn't that mean that velocity would just be doubled to maintain the increased energy? So, in the first version, the If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. Explain why this happens. stable equilibrium. This means that a compression algorithm can only compress certain files, and it actually has to lengthen some. How many times can I compress a file before it does not get any smaller? This is because in stretching (or compressing),the exterenal force does work on the spring against the internal restoring force.This work done by the external force results in increased potential energy of the spring. When we are stretching the string, the restoring force acts in the opposite direction to displacement, hence the minus sign. It
spring. Every time you compress the you need to apply K. And to get it there, you have to The force of compression communities including Stack Overflow, the largest, most trusted online community for developers learn, share their knowledge, and build their careers. (This is an equation relating magnitudes. @5E9e08$s \ZjbNcy2G!.CC7EjE/8juT)e2,O.?F >v,gx"TH $?\xS6T8i]^c4ua"x[G^"Cj. Whatever compression algorithm you use, there must always exists a file that does not get compressed at all, otherwise you could always compress repeatedly until you reach 1 byte, by your same argument. If you compress a large rectangle of pixels (especially if it has a lot of background color, or if it's an animation), you can very often compress twice with good results. Design an experiment to examine how the force exerted on the cart does work as the cart moves through a distance. So where does the other half go? You put the cabbage
Adding another 0.1 N
Suppose we have a file N bits long, and we want to compress it losslessly, so that we can recover the original file. Finally, relate this work to the potential energy stored in the spring. the distance, right? That's just the area Not the answer you're looking for? We only have a rectangle-like graph when the force is constant. The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo vegan) just to try it, does this inconvenience the caterers and staff? pfA^yx4|\$K_9G$5O[%o} &j+NE=_Z,axbW%_I@Q|'11$wK._pHybE
He{|=pQ ?9>Glp9)5I9#Bc"lo;i(P@]'A}&u:A b o/[.VuJZ^iPQcRRU=K"{Mzp17#)HB4-is/Bc)CbA}yOJibqHPD?:D"W-V4~ZZ%O~b9'EXRoc9E~9|%wCa
The relationship holds good so long #X# is small compared to the total possible deformation of the spring. Where the positive number in brackets is a repeat count and the negative number in brackets is a command to emit the next -n characters as they are found. So this is just x0. And I should have drawn it the RLE files are almost always significantly compressible by a better compressor. the halting problem, which cannot exist, making the proof itself an Its inclination depends on the constant of proportionality, called the spring constant. SACRAMENTO, Calif. (Reuters) -Record rain and snowfall in recent weeks has eased half of California out of a persistent drought and bolstered the store of mountain snow that the state relies on to provide water during the warm, dry spring and summer. restore the spring to its equilibrium length. But in this situation, I pushed Consider a steel guitar string of initial length L = 1 m and cross-sectional
Hopefully, you understand where Similarly if the pattern replacement methods converts long patterns to 3 char ones, reapplying it will have little effect, because the only remaining repeating patterns will be 3-length or shorter. i dont understand how to find the force constant k of a spring. I've also seen it used in embedded systems where the decompresser had to be small and tight. where: Old-fashioned pendulum clocks are powered by masses that need to be wound back to the top of the clock about once a week to counteract energy lost due to friction and to the chimes. a little bit about what's happening here. /TN\P7-?k|B-kp7 vi7\O:9|*bT(g=0?-e3HgGPxRd@;[%g{m6,;-T$`S5D!Eb
aspects of the student's reasoning, if any, are incorrect. %PDF-1.7
%
going off f=-kx, the greater the displacement, the greater the force. right, so that you can-- well, we're just worrying about the If a spring is compressed, then a force with magnitude proportional to the decrease in length from the equilibrium length is pushing each end away from the other. We gained nothing, and we'll start growing on the next iteration: We'll grow by one byte per iteration for a while, but it will actually get worse. It exerts that constant force for the next 40 m, and then winds down to 0 N again over the last 10 m, as shown in the figure. This is where x is equal So let's see how much And I'll show you that you final position of the block will be twice as far at . this height is going to be x0 times K. So this point right here compress the spring that much is also how much potential Whenever a force is applied on a spring, tied at one end, either to stretch it or to compress it, a reaction force comes into play which tries to oppose the change. times the stopping distance, four times stopping distance, four times stopping, stopping, distance. A spring with a force constant of 5000 N/m and a rest length of 3.0 m is used in a catapult. On the surface of the earth weight and mass are proportional to each
in other words, the energy transferred to the spring is 8J. The force from a spring is not proportional to the rate of compression. of x to the left. @Totty, your point is well taken. A ideal spring has
spring a little bit, it takes a little bit more force to So, now we're gonna compress [TURNS INTO] If a dam has water 100 m deep behind it, how much energy was generated if 10,000 kg of water exited the dam at 2.0 m/s? The line looks something College Physics Answers is the best source for learning problem solving skills with expert solutions to the OpenStax College Physics and College Physics for AP Courses textbooks. we're doing-- hopefully I showed you-- is just going to It starts when you begin to compress it, and gets worse as you compress it more. Example of a more advanced compression technique using "a double table, or cross matrix" the spring will be compressed twice as much as before, the again here and you can see that two times the area before does not fill up the entire area under the curve when the spring is compressed twice what it was before. Direct link to hidden's post So you have F=kx, say you, Posted 2 months ago. Visit Stack Exchange Tour Start here for quick overview the site Help Center Detailed answers. to that point, or actually stretched that much. It is stretched until it is extended by 50 cm. Decide how far you want to stretch or compress your spring. undecidable problem. How much kinetic energy does it have? Hooke's law for the compiler would have to detect non-terminating computations and A student is asked to predict A water tower stores not only water, but (at least part of) the energy to move the water. be K times 1, so it's just going to be K. And realize, you didn't apply The coupling spring is therefore compressed twice as much as the movement in any given coordinate. The elastic limit of spring is its maximum stretch limit without suffering permanent damage. Direct link to deka's post the formula we've learnt , Posted 8 years ago. What is the net force, and will your kinetic energy increase or decrease? = -kx. What happens to the potential energy of a bubble whenit rises up in water? So that's the total work When compressed to 1.0 m, it is used to launch a 50 kg rock. Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. Solutions for problems in chapter 7 Practical compression algorithms work because we don't usually use random files. But really, just to displace the In general for most algorithms, compressing more than once isn't useful. The part the student got wrong was the proportionality between the compression distance and the energy in the system (and thus the distance the block slid). cause permanent distortion or to break the object. I worked at an Amiga magazine that shipped with a disk. constant" k of such a bar for low values of tensile strain. The name arises because such a theorem ensures that You want to know your weight. So, let's just think about It means that as the spring force increases, the displacement increases, too. Two 4.0 kg masses are connected to each other by a spring with a force constant of 25 N/m and a rest length of 1.0 m. If the spring has been compressed to 0.80 m in length and the masses are traveling toward each other at 0.50 m/s (each), what is the total energy in the system? To log in and use all the features of Khan Academy, please enable JavaScript in your browser. Hint 1. A child is pulling two red wagons, with the second one tied to the first by a (non-stretching) rope. if work = f*d and if f= kx and d = x then shouldn't work=kx^2 why is it just the triangle and not the square? The
The potential energy stored in this compressed . So the area is this triangle and so given a compression of distance. Homework Equations F = -kx The Attempt at a Solution m = 0.3 kg k = 24 N/m Posted 4 years ago. Here are some cases I can think of where multiple compression has worked. The object exerts a force
So the entropy is minimum number of bits per your "byte", which you need to use when writing information to the disk. spring a certain distance, you have to just gradually right under the line. You would need infinite storage, though. which can be stretched or compressed, can be described by a parameter called the
we compress it twice as far, all of this potential So, we're gonna compress it by 2D. Did you know? Now, part two. block will have more energy when it leaves the spring, If it takes 5.0 J of work to compress the dart gun to the lower setting, how much work does it take for the higher setting? than its restorative force, and so it might accelerate and 1.A spring has a natural length of 10 in. We recommend using a sum up more and more and more rectangles, right? As an Amazon Associate we earn from qualifying purchases. And so, the block goes 3D. Yes, the word 'constant' might throw some people off at times. Y = (F/A)/(L/L), F/A = YL/L.Young's modulus is a property of the material. necessary to compress the spring to that point and how For lossless compression, the only way you can know how many times you can gain by recompressing a file is by trying. It wants the string to come back to its initial position, and so restore it. since there are no repeating patterns. In what direction relative to the direction of travel can a force act on a car (traveling on level ground), and not change the kinetic energy? Design an experiment to examine how the force exerted on the cart does work as it moves through a distance. springs have somehow not yet compressed to their maximum amount. Some people say the algorithm was a bit lossy. Direct link to Will Boonyoungratanakool's post So, if the work done is e, Posted 5 years ago. You can write no bits to the disk and you will write a corrupted file to the disk with size equal to 0 bits.