Elastic potential energy stored in a steel wire. 0 m/s is stretched through 2.

Elastic potential energy stored in a steel wire. Open in App Solution Verified by Toppr Click here👆to get an answer to your question ️ More lila UN OPLOH are shows the graph of elastic potential energy (U) stored versus extension, for a steel wire 0 y 1011 Pa) of volume 200 cc. 0 m in length is stretched through 2. For example, when you stretch a spring, it gains elastic potential energy which is released when the spring returns to its original position. Therefore, the ratio of elastic potential energies stored per unit volume in the steel wire to that in the copper wire A steel wire of 4. [3] Elastic potential energy is given by the equation: [3] E e l a s t i c = 1 2 k x 2 Hint: The elastic potential energy per unit volume of a wire stretched by hanging a weight from its end is given by half stress on the wire due to the weight ( i. e. 0× 1011N /m2 (a) the energy density of wire, (b) the elastic potential energy stored in the wire. The elastic potential energy stored in a steel wire of length 20 m stretched through 2 cm is 80 J . If α2 is the longitudinal strain and Y is its Young's modulus of elasticity , then show that the elastic potential energy per unit volume is given by 1/2 Y 2. 2 Extension (in mm) (a) A = 10-4 m2 (b) A = 10-3 m² (c) L = 1. Jun 28, 2021 · Calculate the work done in stretching a steel wire 100 cm in length and of cross sectional area 0. 5kx2, where PEel is the elastic potential energy, k is the force constant, and x is the displacement from equilibrium. For a wire under tension, stress is force/area and strain is change in length/original length. What is the resulting strain and elongation of the wire? The cross-sectional area of the wire is 1. Oct 19, 2020 · Figure shows the graph of elastic potential energy ` (U)` stored versus extension, for a steel wire ` (Y = 2xx10^ (11) Pa)` of volume `200 c c`. . The cross . Jul 3, 2023 · Figure shows the graph of elastic potential energy \\( (U) \\) stored versus extension, for a steel wire \\( \\left(Y=2 \\times 10^{11} \\mathrm{~Pa}\\right) \\) of Nov 7, 2023 · Problems related to elastic properties of material are solved in this chapter. 1: Stretched wire An object of mass 1. Solving for k, we find that k = 2000 N/m. What actually happens within some of the materials mentioned in the examples may be quite complex, but we can calculate the energy stored in a stretched metal wire where Hooke's law is obeyed as follows. If area of cross- section `A` and original length L, then Young's modulus = Stress / Strain Since the stress and strain are the same for both wires, the ratio of Young's modulus for steel to copper is 2:1. 03 cm2 when a load of 100 N is slowly applied without the elastic limit being reached. The elastic energy stored per unit volume of the material is About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features NFL Sunday Ticket © 2024 Google LLC A uniform steel wire of length 3 m and area of cross section 2 m m 2 is extended through 3 mm. The cross sectional area of the wire is ________ mm2. Implementing this on an industrial scale requires not only an understanding of the stretched wire theory but also manufacturing processes, cost, and material limitations. Answer Next, we can use the formula for the elastic potential energy stored in a wire under shear stress: U = (1/2)Gγ^2V where G is the modulus of rigidity, V is the volume of If strain in a matrial is not too great, the material will go back to the original shape when stress-causing force is removed. (Giv Nov 9, 2021 · A steel wire of length 2. Aug 25, 2025 · Solution For The elastic potential energy stored in a steel wire of length 20 m stretched through 2 cm is 80 J. Calculate the energy stored in the wire, if the elastic limit is not exceeded. So the steel spring lattice at the atomic level is at a higher energy level . If young's modulus of steel is 2. This constant is the amount of force required to stretch or compress a spring by one meter. Mar 19, 2025 · Three equal electric charges of each charge q q are placed at the vertices of an equilateral triangle of side length L L, then potential energy of the system is: To derive the expression for the elastic potential energy stored in a stretched wire under stress, we will follow these steps: Step 1: Understand the Concept of Work Done The elastic potential energy (U) stored in a stretched wire is equal to the work done (W) in stretching the wire. 0 mm2. 0 Joules. Calculate the energy stored in the wire, if elastic limit is not exceeded. 0mm2. 0x10^11Nm^-2` A steel wire of 4. 0 mm. The deformation could involve compressing, stretching or twisting the object. 0 x 10^11 N m-2 a) The extension of the wire b) The elastic energy stored in a wire given the Apr 25, 2023 · The elastic potential energy stored in a steel wire of length 20 m stretched through 2 cm is 80 J. If Young's modulus of steel is 2. The cross-sectional area of the wire is 2. (Given, y = 2. Young modulus of steel =2. The U = (1/2) × 2 × 10 11 × 10 -6 U = 10 5 J/m 3 Thus, the amount of elastic potential energy per unit volume of a steel wire of length 100 cm when stretched by 1 mm is 10 5 J/m 3. Apr 25, 2023 · The elastic potential energy stored in a steel wire of length 20 m stretched through 2 cm is 80 J. Calculate the elastic potential energy stored in the wire in the stretched condition. The cross sectional area of the wire is _____ mm 2 . Make sure to check out our potential energy calculator, too! Nov 14, 2024 · Elastic Potential Energy Elastic potential energy is defined as The energy stored within a material (e. The elastic potential energy is directly proportional to the Young's modulus. May 1, 2019 · A steel wire of length 2. The calculated value represents the amount of elastic potential energy per unit volume that the wire possesses due to the strain caused by elongation. 0 mm to calculate the elastic potential energy is stored in Sep 11, 2020 · Stress-strain Curve Example: The stress-strain curve illustrates the mechanical properties of materials, for example, steel, stainless steel or aluminium. #solid 9. 0 x 10¹¹ N m⁻² Jan 12, 2025 · The elastic potential energy stored in the steel wire, given its properties and Young's modulus, is calculated to be 8. 0mm. Mar 19, 2025 · Three equal electric charges of each charge q q are placed at the vertices of an equilateral triangle of side length L L, then potential energy of the system is: Apr 25, 2023 · The elastic potential energy stored in a steel wire of length 20 m stretched through 2 cm is 80 J. Evidently steel lattices can take a lot of deformation so must have many higher than ground state energies. Mar 19, 2025 · Three equal electric charges of each charge q q are placed at the vertices of an equilateral triangle of side length L L, then potential energy of the system is: Dec 8, 2014 · The energy is stored in the higher energy level attained by the interaction "lattice forrce". What is the elastic potential energy stored in a stretched steel wire of length 4 m The wire is stretched through 4 mm and consists of cross-sectional area of 8 mm 2 (Young's modulus of steel 2 0 10 11 N m - 2) A steel wire 4. To find: Calculate the elastic potential energy stored in the wire in the stretched condition. This is the area in which the material is stressed beyond its elastic loadability and the first plastic deformations occur. Dec 20, 2019 · Question From – DC Pandey PHYSICS Class 11 Chapter 15 Question – 003 ELASTICITY CBSE, RBSE, UP, MP, BIHAR BOARD QUESTION TEXT:- A steel wire` 4. This energy is most commonly observed in springs, rubber bands, and elastic materials. The shear strain is given by: γ = θr/L where θ is the angle of twist, r is the radius of the wire, and L is the length of the wire. 0 mm^2. or, Strain = Δl / l here, Δl = 2. 5×101 kg is hanging from one end of a steel wire. in a spring) when it is stretched or compressed It can be found from the area under the force-extension graph for a material deformed within its limit of proportionality A material within its limit of proportionality obeys Hooke’s law Therefore, for a material obeying Hooke’s Law A metallic wire is stretched by suspending a weight to it. Calculate the elastic potential energy stored in the wire in the stretched condition Mar 26, 2020 · Given, A steel wire of length 2. Complete step by step answer: Let us consider a stretchable wire attached to surface and a mass suspended from its end as shown in the We would like to show you a description here but the site won’t allow us. This work is stored in the wire in the form of elastic potential energy. Nov 21, 2024 · The elastic potential energy stored in a steel wire of length 20 m stretched through 2 cm is 80 I . Young modulus of steel `=2. Mar 19, 2025 · Three equal electric charges of each charge q q are placed at the vertices of an equilateral triangle of side length L L, then potential energy of the system is: The elastic potential energy stored in a steel wire of length 20 m stretched through 2 cm is 80 J. An elastic material of Young's modulus Y is subjected to a stress S. 0×1011N /m2 find (i) the energy density of wire (ii) the elastic potential energy stored in the wire. These elastic properties are characterized by Young’s modulus, shear modulus, bulk modulus, or Poisson’s ratio. The elastic potential energy stored in a stretched wire is given by: U = 1 2YAΔL2 L To solve the problem, we need to find the cross-sectional area of the steel wire given the elastic potential energy stored in it, its length, the amount it is stretched, and the Young's modulus of the material. 5 m (d) L = 2m Figure shows the graph of elastic potential energy (U) stored versus extension, for a steel wire (Y = 2×1011 Pa) of volume 200 cc. (Given, Y = 2 . The cross -sectional area of the wire is 2. 0×1011N/m2 find (i) the energy density of wire (ii) the elastic potential energy stored in the wire. The cross-sectional area of the wire is _ mm². The general formula is given by: U = 1 2 ×Stress×Strain×Volume Step 2: Define stress and strain - Stress (σ) is defined as the force (F Steel wire of length 2. Jul 12, 2023 · The storage and release of potential energy in the wire during stretching and subsequent release can be utilised in energy-efficient devices. 84m is suspended vertically from a fixed point and used to support a 60N weight hung from the lower end of the wire. ) Spring constant. This calculation follows from determining strain, stress, and the wire's volume. 0 x 1011 Nm-2) Jul 4, 2025 · Elastic potential energy is the energy stored in a material when it is stretched or compressed within its elastic limit. The energy stored in a spring depends on the: Distance the spring is deformed (stretched or compressed. The cross sectional area of the wire is mm . Solution: Strain can be given as change in dimension / original dimension. If area of cross-section (A) and original length (L), then What is elastic potential energy? Elastic potential energy is energy stored as a result of applying a force to deform an elastic object. The energy is stored until the force is removed and the object springs back to its original shape, doing work in the process. Energy stored in deformed elastic material is also considered. Example 26. (Given, y=2. The cross sectional area of the wire is 4. (Y s t e e l = 20 × 10 10 N / m 2) Mar 21, 2022 · Step 1/2 First, we need to find the shear strain in the wire due to the twisting. 0m` in length is stretched through `2. 0mm`. g. Apr 25, 2023 · The elastic potential energy stored in a steel wire of length 20 m stretched through 2 cm is 80 J. 0 m is stressed through 2. 4 ×10−2 cm2. the Young’s modulus times strain) multiplied by the strain on the wire due to its weight. In conclusion, by using Young's modulus and the strain formula, we can effectively determine the amount of elastic potential energy per unit volume of a steel wire under specified conditions. If area of cross-section A and original length L, then (Y = 2 x 1011 Pa) of volume 20 Elastic potential energy (in J) 0. 0×101Nm−1 Views: 5,358 students Updated on: Nov 21, 2024 Jan 30, 2011 · A steel wire diameter 0. 0 × 10 11 N m – 2 ), A uniform steel wire of length 3 m and area of cross section 2 mm? is extended through 3 mm. When a wire is put under a tensile stress, work is done against the inter-atomic forces. 0 m/s is stretched through 2. 6. Breaking Stress Definition: The minimum value of stress required to break a wire, is called breaking stress. 6 Elastic Potential Energy in a Stretched Wire When a wire is put under a tensile stress, e done against the inter-atomic forces. Elastic potential energy is the energy stored in an object when it is stretched, compressed, or deformed and can return to its original shape. The Young modulus for steel is 2. elastic potential energy:- it is the energy stored in a wire by applying a force on it. 0 mm = 2 * 10^-3 m , l Nov 23, 2019 · The work done by the external applied force during stretching is stored as potential energy (U) in the wire and is called as strain energy in the wire. Mar 19, 2025 · Three equal electric charges of each charge q q are placed at the vertices of an equilateral triangle of side length L L, then potential energy of the system is: Nov 1, 2023 · The elastic potential energy stored in a steel wire stretched through 2 cm can be calculated using the equation PEel = 0. 50 m . The energy stored in the strained material in the elastic region is just like the energy of a spring and is called elastic energy. 50mm and length 1. Jul 21, 2023 · Calculate the elastic potential energy stored in the wire in the stretched condition. Dec 19, 2024 · The elastic potential energy stored in a deformed material is given by (1/2) * stress * strain * volume. (Given, Y = 2. Breaking This elastic potential energy calculator makes it easy to determine the potential energy of a spring when stretched or compressed. 0x10^11Nm^-2 by Physics experts to help you in doubts & scoring excellent marks in Class 11 exams. Background The ability to transfer energy to this form depends on a material's elasticity. Read on to get a better understanding of this concept, including an elastic potential energy definition and an example of calculations. 0m in length is stretched through 2. To find the elastic potential energy of a stretched wire, we can follow these steps: Step 1: Understand the formula for elastic potential energy The elastic potential energy (U) stored in a stretched wire can be expressed in terms of stress and strain. The wire without the mass has an unstretched length of 0. yknrm cpwk dwoc qkki hnhf luap qpykppp hcmdaea rmoulo ldvwh