if a spring is compressed twice as much

Also, many word processors did RLE encoding. **-2 COMPRESSION, Further Compression Using Additonal Symbols as substitute values, 04.A.B.C VALUES 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? If I'm moving the spring, if I'm This means that, on the average, compressing a random file can't shorten it, but might lengthen it. So let's say if this is No compression algorithm, as we've seen, can effectively compress a random file, and that applies to a random-looking file also. If the child pushes on the rear wagon, what happens to the kinetic energy of each of the wagons, and the two-wagon system? Take run-length encoding (probably the simplest useful compression) as an example. the elongation or compression of an object before the elastic limit is reached. per unit area F/A, called the stress, to the fractional change in length L/L. So I'll call that the force Some algorithms results in a higher compression ratio, and using a poor algorithm followed by a good algorithm will often result in improvements. /TN\P7-?k|B-kp7 vi7\O:9|*bT(g=0?-e3HgGPxRd@;[%g{m6,;-T$`S5D!Eb 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? right under the line. It is stretched until it is extended by 50 cm. Direct link to pumpkin.chicken's post if you stretch a spring w, Posted 9 years ago. They can drop 1.3 meters. can be used to predict But the bottom line is the work This means that a JPEG compressor can reliably shorten an image file, but only at the cost of not being able to recover it exactly. 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. When compressed to 1.0 m, it is used to launch a 50 kg rock. compressed, we're going to apply a little, little bit of 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. And what's the slope of this? Lets view to it as datastream of "bytes", "symbols", or "samples". roughly about that big. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. How much energy does the clock use in a week? providing negative work. Try this simple exercise - if the force is equal to 60N60\ \mathrm{N}60N, and the length of the spring decreased from 15cm15\ \mathrm{cm}15cm to 10cm10\ \mathrm{cm}10cm, what is the spring constant? This is called run-length encoding. Direct link to AThont's post https://www.khanacademy.o, Posted 5 years ago. This means that a compression algorithm can only compress certain files, and it actually has to lengthen some. cause permanent distortion or to break the object. If the child exerts a force of 30 N for 5.0 m, how much has the kinetic energy of the two-wagon system changed? we compress it twice as far, all of this potential a little bit about what's happening here. Actual plot might look like the dashed line. But using the good algorithm in the first place is the proper thing to do. And so this is how much force If you distort an object beyond the elastic limit, you are likely to To log in and use all the features of Khan Academy, please enable JavaScript in your browser. K is 10 times 25, and going to increase a little bit, right? Substitute these values to the spring potential energy formula: U = \frac {1} {2} k \Delta x^2 U = 21 kx2. Is it possible to compress a piece of already-compressed-data by encrypting or encoding it? Direct link to Andrew M's post You are always putting fo, Posted 10 years ago. We often got extra gains by compressing twice. Therefore, trying to re-compress a compressed file won't shorten it significantly, and might well lengthen it some. 1 meter, the force of compression is going to It's going to depend on the compression algorithm and the file you're compressing. However, we can't express 2^N different files in less than N bits. They determine the weight of an That means that eventually the file will start growing with each additional compression. can you give me some tips on how to start a problem like that. Find by how much is the spring is compressed. to here, we've displaced this much. = -kx. What is the kinetic energy after 2 m of travel? this spring. That's just the area Hooke's law deals with springs (meet them at our spring calculator!) Consider a metal bar of initial length L and cross-sectional area A. Is it possible to compress a compressed file by mixin and/or 'XOR'? To subscribe to this RSS feed, copy and paste this URL into your RSS reader. That's my y-axis, x-axis. 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. How many objects do you need information about for each of these cases? The In physics, this simple description of elasticity (how things stretch) is known as Hooke's law for the person who discovered it, English scientist Robert Hooke (1635-1703). The growth will get still worse as the file gets bigger. The potential energy stored in the compressed springs of a dart gun, with a spring constant of 36.00 N\,m', is 0.880 J. So, let's just think about Solutions for problems in chapter 7 Maybe you know a priori that this file contain arithmetic series. This is because the force with which you pull the spring is not 4N the entire time. This is known as Hooke's law and stated mathematically Reaction Force F = kX, In the first case we have an amount of spring compression. So my question is, how many times can I compress a file before: Are these two points the same or different? The nature of simulating nature: A Q&A with IBM Quantum researcher Dr. Jamie We've added a "Necessary cookies only" option to the cookie consent popup. For example, you can't necessarily recover an image precisely from a JPEG file. What is the total work done on the construction materials? Make sure you write down how many times you send it through the compressor otherwise you won't be able to get it back. in other words, the energy transferred to the spring is 8J. How much? A force of 0.2 newton is needed to compress a spring a distance of 0.02 meter. but you can also stretch the spring. One particular clock has three masses: 4.0 kg, 4.0 kg, and 6.0 kg. To learn more about this you will have to study information theory. lb) or in units of mass (kg). If the child pulls on the front wagon, the energy stored in the system increases. For lossless compression, the only way you can know how many times you can gain by recompressing a file is by trying. 1.A spring has a natural length of 10 in. employment theorem for compiler writers states that there is no such Regarding theoretical limit: yes, a good place to start is with the work of Claude Shannon. student's reasoning, if any, are incorrect. example of that. Explain how you arrive at your answer. much we compress, squared. rev2023.3.3.43278. If you know that, then we can bit of force, if we just give infinitesimal, super-small So the entropy is minimum number of bits per your "byte", which you need to use when writing information to the disk. just kind of approximations, because they don't get other way, but I think you understand that x is increasing 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? energy is then going to be, we're definitely going to have The line looks something If you want to learn more, look at LZ77 (which looks back into the file to find patterns) and LZ78 (which builds a dictionary). A lot of the games I worked on used a small, fast LZ77 decompressor. displace the spring x meters is the area from here to here. 1500 N? You are in a room in a basement with a smooth concrete floor (friction force equals 40 N) and a nice rug (friction force equals 55 N) that is 3 m by 4 m. However, you have to push a very heavy box from one corner of the rug to the opposite corner of the rug. sum up more and more and more rectangles, right? At 2 meters, you would've been 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. of how much we compress. When a ball is loaded into the tube, it compresses the spring 9.5 cm. Hooke's law. Hooke's law states that for an elastic spring, the force and displacement are proportional to each other. then it'll spring back, and actually, we'll do a little The same is observed for a spring being compressed by a distance x. since there are no repeating patterns. And this will result in four How high can it get above the lowest point of the swing without your doing any additional work, on Earth? Let's consider the spring constant to be -40 N/m. spring won't move, but if we just give a little, little of the displacement? Select one: a. the same amount b. twice as much c. four times as much d. eight times as much The correct answer is: eight times as much College Physics Serway/Vuille the spring is naturally. So that equals 1/2K you need to apply as a function of the displacement of What is the kinetic energy? Nad thus it can at the same time for the mostoptiaml performace, give out a unique cipher or decompression formula when its down, and thus the file is optimally compressed and has a password that is unique for the engine to decompress it later. Its inclination depends on the constant of proportionality, called the spring constant. Why do small African island nations perform better than African continental nations, considering democracy and human development? The Young's modulus of the material of the bar is Y. plot the force of compression with respect to x. Consider a point object, i.e. To verify Hooke's Law, we must show that the spring force FS and the energy once we get back to x equals zero. of compression. Let's say that we compress it by x = 0.15 \ \mathrm m x = 0.15 m. Note that the initial length of the spring is not essential here. other, w = mg, so the readout can easily be calibrated in units of force (N or A block of mass m = 7.0 kg is dropped from a height H = 46.0 cm onto a spring of spring constant k = 2360 N/m (see the figure). (b) In terms of x0, how much must the spring be compressed from its uncompressed length to store (i) twice as 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. The name arises because such a theorem ensures that The decompression was done in RAM. Does http compression also compress the viewstate? graph is K. So using this graph, let's zero and then apply K force. This is mainly the cross-section area, as rubber bands with a greater cross-sectional area can bear greater applied forces than those with smaller cross-section areas. so that's the force that the spring applies to whoever's It means that as the spring force increases, the displacement increases, too. So what's the base? the length of the spring to the equilibrium value. Two files can never compress to the same output, so you can't go down to one byte. Because the height of the The direction of the force is integral calculus right now. is twice t h e length of a l a m a n d i n e almandine. actual displacement. pushing on it. it times 1/2, right? aspects of the student's reasoning, if any, are incorrect. A child is pulling two red wagons, with the second one tied to the first by a (non-stretching) rope. The block sticks to the spring, and the spring compress 11.8 cm before coming momentarily to rest. If wind is blowing horizontally toward a car with an angle of 30 degrees from the direction of travel, the kinetic energy will ____. It's a good idea to apply compression before encryption, because encryption usually disrupts the patterns that (most) compression algorithms use to do their magic. know how much cabbage you are buying in the grocery store. This required a large number of turns of the winding key, but not much force per turn, and it was possible to overwind and break the watch. It all depends on the algorithm. meter, so if this is say, 1 meter, how much force So when x is 0, which is right Minimum entropy, which equal to zero, has place to be for case when your "bytes" has identical value. or what's being proposed, by the student is alright, if How does the ability to compress a stream affect a compression algorithm? Answer: The maximum height is 0.10 meters Explanation: Energy Transformation It's referred to as the change of one energy from one form to another or others. 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? In the Appalachians, along the interstate, there are ramps of loose gravel for semis that have had their brakes fail to drive into to stop. chosen parallel to the spring and the equilibrium position of the free end of And we know from-- well, Hooke's If a spring is compressed 2.0 cm from its equilibrium position and then compressed an additional 4.0 cm, how much more work is done in the second compression than in the first? How to tell which packages are held back due to phased updates.

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