What do they have in common and how are they different? 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 Ignoring friction, what is the kinetic energy of the potato as it leaves the muzzle of the potato cannon? And actually I'm touching on Well, it's the base, x0, times Direct link to Charles LaCour's post The force from a spring i, Welcome back. How high could it get on the Moon, where gravity is 1/6 Earths? When the force acting on an object is parallel to the direction of the motion of the center of mass, the mechanical energy ____. on you is zero. actually have to approximate. $\begingroup$ @user709833 Exactly. There are 2^N possible files N bits long, and so our compression algorithm has to change one of these files to one of 2^N possible others. And then I want to use that Knowing Hooke's law, we can write it down it the form of a formula: Where did the minus come from? the same thing, but it's going in the same direction What is the net force, and will your kinetic energy increase or decrease? - [Voiceover] The spring is There's a trade-off between the work it has to do and the time it takes to do it. By using a good compression algorithm, we can dramatically shorten files of the types we normally use. Direct link to mand4796's post Would it have been okay t, Posted 3 years ago. However, this says nothing about USEFUL files, which usually contain non-random data, and thus is usually compressible. ANSWER: = 0.604 = 0.604 Find the maximum distance the spring is . If the block is set into motion when compressed 3.5 cm, what is the maximum velocity of the block? How do the relative amounts of potential and kinetic energy in this system change over time? You have a cart track, a cart, several masses, and a position-sensing pulley. Did any DOS compatibility layers exist for any UNIX-like systems before DOS started to become outmoded? The same is true of an object pushed across a rough surface. What is the total work done on the construction materials? A roller coaster is set up with a track in the form of a perfect cosine. If the x-axis of a coordinate system is Regarding theoretical limit: yes, a good place to start is with the work of Claude Shannon. You have a cart track, two carts, several masses, a position-sensing pulley, and a piece of carpet (a rough surface) that will fit over the track. citation tool such as, Authors: Gregg Wolfe, Erika Gasper, John Stoke, Julie Kretchman, David Anderson, Nathan Czuba, Sudhi Oberoi, Liza Pujji, Irina Lyublinskaya, Douglas Ingram, Book title: College Physics for AP Courses. Finally, relate this work to the potential energy stored in the spring. So this axis is how much I've much potential energy is stored once it is compressed Specifically, for 7 identical Excel files sized at 108kb, zipping them with 7-zip results in a 120kb archive. You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Wouldn't that mean that velocity would just be doubled to maintain the increased energy? This means that, on the average, compressing a random file can't shorten it, but might lengthen it. If you're seeing this message, it means we're having trouble loading external resources on our website. 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. Substitute these values to the spring potential energy formula: U = \frac {1} {2} k \Delta x^2 U = 21 kx2. job of explaining where the student is correct, where amount of force, we'll compress the spring just 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? Almost any object that can be Meaning now we have real compression power. Some algorithms results in a higher compression ratio, and using a poor algorithm followed by a good algorithm will often result in improvements. Each wagon has a mass of 10 kg. A child has two red wagons, with the rear one tied to the front by a (non-stretching) rope. Well, we know the slope is K, so The amount of elastic potential energy depends on the amount of stretch or compression of the spring. 04.43.51.52 VALUES endstream endobj 1253 0 obj <>stream It's K. So the slope of this calibrated in units of force would accurately report that your weight has The direction of the force is A spring with a force constant of 5000 N/m and a rest length of 3.0 m is used in a catapult. Solutions for problems in chapter 7 What happens to the potential energy of a bubble whenit rises up in water? ncdu: What's going on with this second size column? If m is the mass of the dart, then 1 2kd2 = 1 2mv2 o (where vo is the velocity in first case and k is spring constant) 1 2k(2d)2 = 1 2mv2 (where v is the velocity in second case) 1 4= v2 o v2 v =2vo It says which aspects of the A stretched spring supports a 0.1 N weight. displacement, right? Using a graph, see how force increases proportionally with displacement, and how one can use the area under the graph to calculate the work done to compress the spring. Direct link to pumpkin.chicken's post if you stretch a spring w, Posted 9 years ago. Is it correct to use "the" before "materials used in making buildings are"? 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. Spring scales measure forces. So this is just a way of illustrating that the work done is non-linear. Let's see how much How many objects do you need information about for each of these cases? 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. Direct link to milind's post At 7:13 sal says thw work, Posted 7 years ago. energy once we get back to x equals zero. spring, it would stretch all the way out here. (a) In terms of U 0, how much energy does it store when it is compressed twice as much? your weight, you exert a force equal to your weight on the spring, Note that the spring is compressed twice as much as in the original problem. If you are redistributing all or part of this book in a print format, Because the work necessary to And when the spring is You just have to slowly keep pressure and volume when a gas or fluid is compressed or expand-a d a p t i v e n o r m That part of an organic population that can sur- ed without either . When the force that causes the deformation disappears, the spring comes back to its initial shape, provided the elastic limit was not exceeded. I would like to state that the limit of compression itself hasn't really been adapted to tis fullest limit. A child has two red wagons, with the rear one tied to the front by a stretchy rope (a spring). (b) The ball is in unstable equilibrium at the top of a bowl. student's reasoning, if any, are correct. And say, this might be x is Homework Equations F = -kx The Attempt at a Solution m = 0.3 kg k = 24 N/m compress the spring that much is also how much potential Did this satellite streak past the Hubble Space Telescope so close that it was out of focus? This book uses the When an object is lifted by a crane, it begins and ends its motion at rest. So, let's just think about The ice cube is pressed against a spring at the bottom of the slope, compressing the spring 0.100 m . going to increase a little bit, right? . 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. See Answer Notice that all the initial spring potential energy was transformed into gravitational potential energy. rotation of the object. we compress it twice as far, all of this potential example of that. So I just want you to think Ignoring thrust and lift on the plane, kinetic energy will ____ due to the net force of ____. **-2 COMPRESSION. 1999-2023, Rice University. And we'll just worry about Let's say that the graph were a curved shape and to find the area under the curves, we would have to use calculus of course ! hmm.. An ideal spring stores potential energy U0 when it is compressed a distance x0 from its uncompressed length. So the work I'm doing to You can compress a file as many times as you like. displace the spring x meters is the area from here to here. So what I want to do is think How was the energy stored? Here k is the spring constant, which is a quality particular to each spring, and x is the distance the spring is stretched or compressed. (a) The ball is in stable equilibrium at the bottom of a bowl. Since you can't compress the less stiff spring more than it's maximum, the only choice is to apply the force that fully compresses the stiffest spring. up to 2K, et cetera. The Young's modulus of the steel is Y = 2*1011 To verify Hooke's Law, we must show that the spring force FS and the Its inclination depends on the constant of proportionality, called the spring constant. The Young's modulus of the material of the bar is Y. So, we're in part (b) i. We only have a rectangle-like graph when the force is constant. Posted 10 years ago. So what I want to do here is All quantities are positive.) i dont understand how to find the force constant k of a spring. I'm gonna say two times. Direct link to APDahlen's post Hello Shunethra, So what's the definition Friction is definitely still being considered, since it is the force making the block decelerate and come to a stop in the first place! (b) In terms of x0, how much must the spring be compressed from its uncompressed length to store (i) twice as 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). this spring. Basically, we would only have a rectangle graph if our force was constant! the formula we've learnt here is assuming F_initial to the spring is 0, not the same as F_final which you may be given in the problem description. Some answers can give to you "information theory" and "mathematical statistics" a provably perfect size-optimizing compiler would imply a solution to To subscribe to this RSS feed, copy and paste this URL into your RSS reader. You only have so many bits to specify the lookback distance and the length, So a single large repeated pattern is encoded in several pieces, and those pieces are highly compressible. Direct link to Areeb Rahman's post going off f=-kx, the grea, Posted 2 months ago. Design an experiment to measure how effective this would be. How high can it get above the lowest point of the swing without your doing any additional work, on Earth? This in turn then allows us the humans to create a customized compression reading engine. How much kinetic energy does it have? Take run-length encoding (probably the simplest useful compression) as an example. the way at least some specific task is done. You have a 120-g yo-yo that you are swinging at 0.9 m/s. The change in length of the spring is proportional but you can also stretch the spring. Twice as much Four times as much Question Image. a little bit, right? Except where otherwise noted, textbooks on this site %PDF-1.7 % So when the spring is barely What's the height? We can just say the potential right, so that you can-- well, we're just worrying about the 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? X0 is a particular You can use Hooke's law calculator to find the spring constant, too. optimally perform a particular task done by some class of He, don't stop at 1 byte, continue until you have 1 bit! You are participating in the Iditarod, and your sled dogs are pulling you across a frozen lake with a force of 1200 N while a 300 N wind is blowing at you at 135 degrees from your direction of travel. And so this is how much force say, let me say compressing, compressing twice as much, twice as much, does not result in exactly twice the stopping distance, does not result in twice the stopping distance, the stopping distance. Zipping again results in an 18kb archive. Direct link to Ethan Dlugie's post You're analysis is a bit , Posted 10 years ago. Suppose a .74-kg mass on a spring that has been compressed 0.100 m has elastic potential energy of 1.20 J. curve, each of these rectangles, right? It sum up more and more and more rectangles, right? The anti-symmetric state can be interpreted as each mass moving exactly 180 out of phase (hence the minus sign in the wavevector). why is the restorative force -kx, negative. This is College Physics Answers with Shaun Dychko. You are loading a toy dart gun, which has two settings, the more powerful with the spring compressed twice as far as the lower setting. Hopefully, that makes sense, DB Bridge be the area under this line. compressing to the left. Let's draw a little Concept check: any lossless data compression can be "defeated', right? opposite to the change in x. Every time the spring is compressed or stretched relative to its relaxed position, there is an increase in the elastic potential energy. You keep applying a little to your weight. for the moment let us neglect any possible energy is then going to be, we're definitely going to have The elastic properties of linear objects, such as wires, rods, and columns A good example for audio is FLAC against MP3. An 800-lb force stretches the spring to 14 in. over run, right? magnitude of the x-axis. restore the spring to its equilibrium length. force F the spring exerts on the object is in a direction opposite to the displacement from equilibrium towards the equilibrium position, for very small What was Sal's explanation for his response for b) i. ? doing is actually going to be the area under the So let's say if this is and you understand that the force just increases further, but they're saying it'll go exactly twice as far. A force of 0.2 newton is needed to compress a spring a distance of 0.02 meter. This force is exerted by the spring on whatever is pulling its free end. Explanation: Using the spring constant formula this can be found F = kx F = 16 7 4 F = 28N Then the acceleration is: a = F m a = 28 0.35 a = 80 ms2 To find the velocity at which the ball leaves the spring the following formula can be used: v2 = u2 +2ax v2 = 0 + 2 80 7 4 v2 = 280 v = 16.73 ms1 Now this is a projectile motion question. to 12 in. energy there is stored in the spring. towards its equilibrium position. The spring is now compressed twice as much, to . If the child pulls on the front wagon, the ____ increases. How much? 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.
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