what is the relationship between displacement and the spring constant k
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Hooke's Law In contrast to the ball, moving a spring a distance, x (measured from its unstretched position) requires a non-constant force: the more you stretch/compress a spring, the more force it requires. For elastic springs, the relationship between the applied force and the distance the spring moves is called Hooke's Law. F = -kx (1). The negative sign is used because F is the restoring force of the spring, which is in the opposite direction from the applied force of the hanging mass. The restoring force is therefore in the opposite direction from the displacement of the spring. This relationship between restoring force and displacement depends on the physical properties of the spring. The more stiff a spring is, the more difficult it is to stretch or compress it.
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Work to Stretch a Spring The diagram at right shows a graph of force vs. stretch for a spring. The blue line represents the graph of F = kx (Hooke's Law). We know that the area shaded in red represents the work you would need to do to stretch the spring a distance x from its rest position.
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- 1 where k is called the spring constant. 2  It has units of Newtons per meter. 3  When a spring pulls something, or pushes something, over a distance x, it does work. 4  If a spring is compressed (or stretched) it stores energy equal to the work performed to compress (or stretch) it. 5  We might call this spring potential energy.
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- The equilibrium length of the spring about which it oscillates is different for the vertical position and the horizontal position. Assume an object attached to a spring exhibits simple harmonic motion. Let one end of the spring be attached to a wall and let the object move horizontally on a frictionless table.
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Spinal Fusion Fusion is a surgical technique in which one or more of the vertebrae of the spine are united together (“fused”) so that motion no longer occurs between them.The concept of fusion is similar to that of welding in industry. Spinal fusion surgery, however, does not weld the vertebrae immediately during surgery.usion is a surgical technique in which one or more of the vertebrae of the spine are united together (“fused”) so that motion no longer occurs between them.
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- When m 2 isplaced upon it, and all oscillation has died out, the length is 0.400 m. The mass m 1 is dropped 3.57 m and lands and stays on top of m 2. m 1 = 1.50 kg m 2 = 2.50 kg(a) Calculate the length of the spring at its maximum compression.(b) Calculate the energy lost to heat.
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Hooke's Law Explanation of Hooke's Law for springs. Hooke's Law Hooke's Law states that the force acting on a spring is directly proportional to its displacement from its equilibrium position (as long as the spring does not exceed its elastic limit). Mathematically, Hooke's law states that Where: F s is the force exerted by the spring k is the spring constant
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- Wien's Displacement Law Wien's displacement law says that the wavelength of the maximum emitted radiation is inversely proportional to the absolute (°K) temperature. If we plug in the temperatures of the earth and the sun, we will see that lambda max is 10µm and .49µm, respectively.
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- .If one of the springs has a bigger mass attached to it, the period will be longer; if m2 >. m1 then T2 > T1. Changing the spring constant also changes the period, if k2 > k1 then T2 < T1. For simple harmonic motion the period is independent of amplitude, i.e. extension does not affect the. period of oscillation, hence stretching the spring more to start with makes no difference to period. Accompanying sheet. Oscillations of a Spring-Mass System. Two identical objects are attached to identical springs.
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Springs The last thing we’re going to try doing regarding Hooke’s law is to try to create a spring between two moving targets. This is actually easier to do than you might think because we already talked about offsets. If we set the target of a spring to an offset of another moving part then we'll get a spring motion that always tries to converge to that offset.
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- Best Answer: force = kx [Hooke's Law] (where x is the amount of stretch) W(x) = work = 1/2 k x^2 = amount of work done in stretching the spring from its natural length to an amount of stretch of x. let L be the original length . (L < 8) 1 joule = 10000000 ergs stretching from 8 to 9: W(9-L) - W(8-L) = 0.05*10000000
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- A spring that has a spring constant of 440 N/m exerts a force of 88 N on a box. What is the displacement of the spring? 0.2 m5 m352 m528 m.
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Springs This gives the spring force its direction. If the spring is stretched in the positive direction (+x) the spring force pulls back in the negative direction (−F). If the spring is compressed in the negative direction (−x), the spring force pushes back in the positive direction (+F). Newton and Hooke.
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Spring Constant Formula Spring Constant Formula Questions: 1) Find the spring constant of a spring if it requires a 9000 N force to pull it 30.0 cm from equilibrium. Answer: The formula can be rearranged to solve for the spring constant, k: In this question, a 9000 N force is pulling on a spring. That means that the spring pulls back with an equal and opposite force of -9000 N. The displacement is 30.0 cm = 0.30 m. k = 30 000 N/m. The spring constant of this spring is 30 000 N/m.
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ANSWER KEY These were used to plot the line on the graph. The slope of the line, ignoring loads of less than 2kg, was found to be 22.2 ± 0.2 kg/m. From Equation 1, we see that we need to multiply this quantity by g to calculate a value for the spring constant of k = 217.4 ± 1.8 N/m.
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Physics spring problem? A block of mass 3.9 kg is sitting on a frictionless ramp with a spring at the bottom as shown, that has a spring constant of 575 N/m. The angle of ramp with respect to the horizontal is 39 degrees. a) The block, starting at rest, slides down the ramp a distance 31cm before hitting the spring. How far, in... show more A block of mass 3.9 kg is sitting on a frictionless ramp with a spring at the bottom as shown, that has a spring constant of 575 N/m.
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- The displacement as a function of time t in any simple harmonic motion—that is, one in which the net restoring force can be described by Hooke’s law, is given by. x t = X cos 2 πt T , x t = X cos 2 πt T , size 12{x left (t right )=Xcos { {2π`t} over {T} } } {}.
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- Changing the spring constant also changes the period, if k 2 k 1 then T 2 T 1 For simple harmonic motion the period is independent of amplitude, i.e. extension does not affect the period of oscillation, hence stretching the spring more to start with makes no difference to period.
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How to Calculate a Spring Constant Using Hookeâs Law The force exerted by a spring is called a restoring force; it always acts to restore the spring toward equilibrium. In Hooke’s law, the negative sign on the spring’s force means that the force exerted by the spring opposes the spring’s displacement. The direction of force exerted by a spring.
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- In this equation, S is the entropy of the system, k is a proportionality constant equal to the ideal gas constant divided by Avogadro's constant, ln represents a logarithm to the base e, and W is the number of equivalent ways of describing the state of the system.
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User Contributed Dictionary The specific dynamics of this spring-mass system are described mathematically by the simple harmonic oscillator and the regular periodic motion is known as simple harmonic motion. In the spring-mass system, oscillations occur because, at the static equilibrium displacement, the mass has kinetic energy which is converted into potential energy stored in the spring at the extremes of its path.
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Calculus - Hooke's Law , Spring Constant? Best Answer: force = kx [Hooke's Law] (where x is the amount of stretch) W(x) = work = 1/2 k x^2 = amount of work done in stretching the spring from its natural length to an amount of stretch of x. let L be the original length . (L < 8) 1 joule = 10000000 ergs.
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Cutting Quill Pens from Feathers I doesn't matter what the angle of incline is, the spring constant is the same. If you change the angle, both the sine of the angle and the amount of stretch will change together. The value of k that you find will be the same no matter what the angle. So if you've measured it once, that's enough.
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Coulomb's Law In equation form, Coulomb's law can be stated as. where Q1 represents the quantity of charge on object 1 (in Coulombs), Q2 represents the quantity of charge on object 2 (in Coulombs), and d represents the distance of separation between the two objects (in meters). The symbol k is a proportionality constant known as the Coulomb's law constant.
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- In Hooke's law, what does k represent? length, mass, stiffness or thickness of a springA constant, represents the some idiosynthesis of the object(s...
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For a spring, is it F=kx or is it F=-kx? The force exerted by a spring is called a restoring force; it always acts to restore the spring toward equilibrium. In Hooke’s law, the negative sign on the spring’s force means that the force exerted by the spring opposes the spring’s displacement. Hooke’s law says. F = –kx.