# What is Elastic potential energy: Definition and 92 Discussions

Elastic energy is the mechanical potential energy stored in the configuration of a material or physical system as it is subjected to elastic deformation by work performed upon it. Elastic energy occurs when objects are impermanently compressed, stretched or generally deformed in any manner. Elasticity theory primarily develops formalisms for the mechanics of solid bodies and materials. (Note however, the work done by a stretched rubber band is not an example of elastic energy. It is an example of entropic elasticity.) The elastic potential energy equation is used in calculations of positions of mechanical equilibrium. The energy is potential as it will be converted into other forms of energy, such as kinetic energy and sound energy, when the object is allowed to return to its original shape (reformation) by its elasticity.

U
=

1
2

k

Δ

x

2

{\displaystyle U={\frac {1}{2}}k\,\Delta x^{2}\,}
The essence of elasticity is reversibility. Forces applied to an elastic material transfer energy into the material which, upon yielding that energy to its surroundings, can recover its original shape. However, all materials have limits to the degree of distortion they can endure without breaking or irreversibly altering their internal structure. Hence, the characterizations of solid materials include specification, usually in terms of strains, of its elastic limits. Beyond the elastic limit, a material is no longer storing all of the energy from mechanical work performed on it in the form of elastic energy.
Elastic energy of or within a substance is static energy of configuration. It corresponds to energy stored principally by changing the interatomic distances between nuclei. Thermal energy is the randomized distribution of kinetic energy within the material, resulting in statistical fluctuations of the material about the equilibrium configuration. There is some interaction, however. For example, for some solid objects, twisting, bending, and other distortions may generate thermal energy, causing the material's temperature to rise. Thermal energy in solids is often carried by internal elastic waves, called phonons. Elastic waves that are large on the scale of an isolated object usually produce macroscopic vibrations sufficiently lacking in randomization that their oscillations are merely the repetitive exchange between (elastic) potential energy within the object and the kinetic energy of motion of the object as a whole.
Although elasticity is most commonly associated with the mechanics of solid bodies or materials, even the early literature on classical thermodynamics defines and uses "elasticity of a fluid" in ways compatible with the broad definition provided in the Introduction above.Solids include complex crystalline materials with sometimes complicated behavior. By contrast, the behavior of compressible fluids, and especially gases, demonstrates the essence of elastic energy with negligible complication. The simple thermodynamic formula:

d
U
=

P

d
V

,

{\displaystyle dU=-P\,dV\ ,}
where dU is an infinitesimal change in recoverable internal energy U, P is the uniform pressure (a force per unit area) applied to the material sample of interest, and dV is the infinitesimal change in volume that corresponds to the change in internal energy. The minus sign appears because dV is negative under compression by a positive applied pressure which also increases the internal energy. Upon reversal, the work that is done by a system is the negative of the change in its internal energy corresponding to the positive dV of an increasing volume. In other words, the system loses stored internal energy when doing work on its surroundings. Pressure is stress and volumetric change corresponds to changing the relative spacing of points within the material. The stress-strain-internal energy relationship of the foregoing formula is repeated in formulations for elastic energy of solid materials with complicated crystalline structure.

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1. ### Potential of particles moving on a circle attracted by elastic force

I use ##l-1## lagrangian coordinates ##\alpha_1,...,\alpha_{l-1}## . ##\alpha_i## is the angle between ##OP_{i-1}## and ##OP_{i}##. As the length of a chord between two rays with angle ##\alpha## is ##d=2Rsin(\alpha/2)##, I write the potential energy of the system as...
2. ### Elastic potential energy - different methods, different results

Can someone please tell me where I am wrong? I tried to solve the problem using velocity equation; ##v_{f}^2= v_{i}^{2} + 2as## and got a= 50m/s^2, F= 50 000N and therefore F=kx -> k=50 000N/m because dx=1. But it's not correct. When I do it using conservation of energy I get 100 000N/m. Which...
3. ### Why is the elastic potential energy in position 2 zero?

Hello, so we have two potitions right, if we take ##\theta = 90## as the first position (i.e. both rods are flat) and then the second position at ##\theta = 0##. I totally understand the exercise, not difficult. The only issue I am having is the torsional spring... it says that it is uncoiled...
4. ### Relationship between diameter and elastic potential energy of a wire

I think the answer is that the elastic potential energy will be a 1/16th of the original value. This is my reasoning: 1) If the diameter doubles, the cross sectional area is 4 times the original value. (from A= πr2). 2) F= stress/area. Force (load is the same). If cross sectional area...
5. ### Approximate energy loss ratio in mechanical springs

Hi!.. As known, a certain amount of energy is applied for compressing a mechanical spring. Thus mechanical spring is charged with energy and it stores it as elastic-potential energy. But whole energy, applied for compressing spring, can not be converted into potential energy. The reason is...
6. ### Calculating the elastic potential energy from a force-extension investigation

1. The student should use a rubber band, g-clamp, a retort stand, boss and clamp, a mass hanger, 100g masses and a metre rule. The rubber band should be positioned to hang freely from the retort stand, held in place by a g-clamp to the laboratory bench. Measure the length of the rubber band...
7. ### Issues Determining Change in Elastic Potential Energy

I've attached a screengrab of the problem (Specifically, Part B, as indicated in the image) and my attempt at a solution. Summarized, my thinking was based on using ##-\Delta U=\frac{Kx_i^2-Kx_f^2}{2}##. After using up all my attempts, the solution, as it turns out, was U2=4.91J. No variation...
8. ### Elastic potential energy and natural length of a spring- relation?

I figured out that the spring constant is inversely proportional to the natural length, but there’s still an unknown change in a quantity( most likely extension).
9. ### Understanding the derivation for Elastic Potential Energy.

Elastic Potential Energy of a Strained Body (A) Using ## Y = \frac {stress}{strain}## we get ##F = \frac {AY}{L} * x## where ##F## is the restoring force, ##x## is the distance the body is stretched by. Since Work = PE (spring force/ stress is conservative?) Thus ##W = \int_{0}^{x} \frac...
10. ### How do I calculate elastic potential energy?

Is this the correct formula to use, if not what is. I really just don't know where to start. I really just need to know where and how to start.
11. ### Elastic potential energy (spring) problem

Homework Statement A 0.200 kg object is attached to a horizontal spring with a spring constant of 77.0 N/m. The other end of the spring is attached to a wall in such a way that it rests on a frictionless horizontal surface. A 10.0 N force is exerted on the spring, causing it to compress a)...
12. ### Find the launch speed of a ball in a spring mechanism

Homework Statement I have a question asking me to find the launch speed of a ball (mass 0.39kg) when released by a spring mechanism made of 2 springs each with force constant 25Nm^-2. they are pulled back 12 cm. the ball is initially at rest.Homework Equations [/B] v^2=u^2+2as f=ma f=kx...
13. A

### Elastic potential energy problem

Homework Statement A 1.00kg mass and 2.00kg mass are set gently on a platform mounted on an ideal spring of force constant 40.0 N/m. The 2.00 kg mass is suddenly removed. How high above its starting position does the 1.00 kg mass reach? Related to it... An 87 g box is attached to a spring with...
14. ### Invariance of elastic potential energy

At non-relativistic speeds is the elastic potential energy of a compressed spring frame-invariant? That is, would all reference frames agree on how much elastic potential energy is stored in the spring?
15. ### Can Elastic Potential Energy Ever Be Negative?

Homework Statement Which of the following Graphs BEST illustrates the potential energy vs. time for the system in Figure 1, where t=0 is defined as the time at which the incident box 1st contacts the box on the spring? My question is why can't the Elastic PE be negative? The answer is A...
16. ### Motion with elastic potential energy and other forces

Homework Statement A 15.0 kg stone slides down a snow-covered hill leaving point A (at the top of the hill) with a speed of 10.0 m/s. There is no friction on he hill between point A and point B (at the foot of the hill). There is friction on the level ground at the bottom of the hill between...
17. ### [Mechanics] Tension in bungee jumping

Homework Statement A bungee jumper of mass 60kg jumps from a bridge 24 m above the surface of the water. The rope is 12 m long and is assumed to obey Hooke's law. What should the spring constant of the rope be if the woman is to just reach the water? Homework Equations Ep=mgh E=1/2 kx^2 The...
18. ### A really confusing question on potential energy,

Homework Statement A 975 g block is released from rest at height h0 above a vertical spring with spring constant k = 410 N/m and negligible mass. The block sticks to the spring and momentarily stops after compressing the spring 24.2 cm. How much work is done (a) by the block on the spring and...
19. ### Max speed and tension of bungee jump?

Just signed up, hi everyone! 1. Homework Statement A man weighs 150 lb, and attaches a bungee cord having a stiffness of k = 500 lb/ft, to his feet. If he jumps from rest off the side of a bridge, determine the required unstretched length of the cord so that he can just touch the surface of...
20. ### Conservation of energy - elastic potential energy and k.e.

1. Homework Statement For part (iii) , I used the principle of conservation of energy, K.E of the 2 kg particle after collision + E.P.E = K.E of the 2 kg particle at the furthest distance away from A + E.PE, But the solution for this question did not include the E.P.E of the string...
21. ### A problem with Gravitational and Elastic Potential Energy

I am calculating the energy transfer in two different formulas and they are giving different results. What could be the reason of this difference? I would be grateful if someone tell me what i am missing here. http://s18.postimg.org/o4tknn77d/potential.jpg
22. ### Elastic Potential Energy to Aid Electromagnetic Induction

Matter can neither be created nor destroyed...but potential energy can be converted into a different kind of energy. Let's say we have a spring with a mass connected to it. This mass is a magnet, and the apparatus is inside a copper coil. It's a horizontal magnet with friction minimized at the...
23. ### Hooke's law vs. Elastic potential energy

Homework Statement I am currently learning about elastic potential energy and this is a question that was given to us by my teacher: When a 13.2-kg mass is placed on top of a vertical spring, the spring compresses 5.93 cm. Find the force constant of the spring. Homework EquationsThe Attempt...
24. ### [Problem] Elastic potential energy

Hi, I'm a second year Design Engineering student. This year we're having some basic physics class. We're doing projects on potential energy at this moment. I'm having a problem with the following; The assignment: The teacher assigned us that only 6 Joules of potential energy may be used to...
25. ### How Fast Can a Car Hit a Spring Bumper Without Damage?

Homework Statement A small truck is equipped with a rear bumper that has a spring constant of 8 x 10^5 N/m. The bumper can be compressed 15 cm without causing damage to the truck. What is the maximum velocity with which a solid 1000kg car can collide with the bumper without causing damage to...
26. ### Kinetic to Elastic Potential Energy

Homework Statement A moving car has 40,000 J of kinetic energy while moving at a speed of 7.0 m/s. A spring-loaded automobile bumper compresses 0.30 m when the car hits a wall and stops. What can you learn about the bumper’s spring using this information? Answer quantitatively and list the...
27. ### Elastic potential energy of a hanging cone

Homework Statement A cone of circular cross section having base radius R, mass M and height L is suspended from its base as shown in figure. The material of cone has Young's modulus Y. If the elastic potential energy stored in the cone can be expressed as: $$E=\frac{m^ag^bL^c}{d\pi^eY^fR^g}$$...
28. ### Elastic potential energy - springs

I know this problem has been asked before but i am trying to understand. Homework Statement A 2.00-kg block is pushed against a spring with negligible mass and force constant k = 400 N/m, compressing it 0.220 m. When the block is released, it moves along a frictionless, horizontal surface and...
29. ### Elastic potential energy of vertical spring

help is urgently needed please and thank u. 1. When a 13.2-kg mass is placed on top of a vertical spring, the spring compresses 5.93 cm. Find the force constant of the spring. 2. If a spring has a spring constant of 400 N/m, how much work is required to compress the spring 25.0 cm from...
30. ### * * Elastic potential energy with box going up an incline.

*URGENT* Elastic potential energy with box going up an incline. Homework Statement A spring having a force constant of 240 \frac{N}{m} is placed on a plane inclined at 67° to the horizontal. The spring is compressed 0.40 m and a 2.0 kg mass is placed on it. The coefficient of kinetic friction...
31. ### Ramp, block, and elastic potential energy

Homework Statement The spring in the figure below is initially compressed by 0.4 m in the position shown. If released from this position, block A travels 0.9 m before coming to a stop. The kinetic coefficient of friction is 0.8. What is the spring constant? (The spring is not fastened to...
32. ### Elastic Potential Energy of a Sprin

Homework Statement Two trolleys, of mass 1.2 kg and 4.8 kg, are at rest with a compressed spring between them, held that way by a string tied around both. When the string is cut, the trolleys move apart, if the force constant fo the spring is 2400 N/m, by how much must it have been compressed...
33. ### Gravitational Potential Energy, Elastic Potential Energy, and Kinetic Energy

Homework Statement A 4.0 kg mass is pressed down on a vertical spring of spring constant 400 N/m, compressing it to 0.250 m. After it is released, the amount of kinetic energy this mass would have when it leaves the spring is ___. Homework Equations mgy(final) + 1/2 kx^2 (final) + 1/2...
34. ### Total elastic potential energy of a compressed spring?

Homework Statement A spring with a spring constant of 4 Newtons per meter is compressed by a force of 1.2 Newtons. What is the total elastic potential energy stored in this compressed spring? k = 4 N/m F = 1.2 N PE = ? Homework Equations PE = (1/2)(k)(x)^2 The Attempt at a Solution...
35. ### Elastic Potential Energy and Energy Exchange

Homework Statement A 3 kg ball is dropped from a height of 0.8 m above the top of the spring onto a vertical coiled spring sitting on the floor. The spring constant of the spring is 1200 N/m. Determine the maximum compression of the spring as the ball comes momentarily to rest before rising...
36. ### Elastic Potential energy problem (simple)

Homework Statement A 1.20 kg piece of cheese is placed on a vertical spring of negligible mass and force constant k = 1800 N/m that is compressed 15 cm. When the spring is released, how high does the cheese rise from this initial position? (The cheese and the spring are not attached). I looked...
37. ### Elastic Potential Energy and velocity of spring

Homework Statement A spring, having a force constant of 6.0x102 N/m, is held in a vertical position and compressed 0.30m. A 5.0 kg mass is then placed on top of the spring. THe mass is then releases. Neglecting air resistance and the mass of the spring, calculate: a) the velocity of the...
38. ### Elastic Potential Energy Problem

Homework Statement A 1.2 kg spring laboratory cart is held against a wall. The spring constant is 65.0 N/m. The spring is compressed 8.0 cm when held against the wall. What is the compression of the spring when the cart's velocity is 42.0 cm/s? Homework Equations (1/2)mv^2=(1/2)kx^2...
39. ### How far does the marble travel horizontally before hitting the floor?

Homework Statement A horizontal spring, of force constant 12N/m, is mounted at the edge of a lab bench to shoot marbles at targets on the floor 93.0 cm below. A marble of mass 8.3 x 10^-3kg is shot from the spring, which is initially compressed a distance of 4.0 cm. how far does the marble...
40. ### Elastic Potential Energy of a system with 2 springs and 1 mass on an incline

Homework Statement IV. The block in the figure has a mass of 0.150 kg, and the surface it is on is frictionless. The force constant of the upper spring is 250 N/m, and the force constant of the lower spring is 450 N/m. The upper spring is initially compressed by a distance of 0.10 meters. The...
41. ### Question regarding elastic potential energy and work

Hi! This is probably something silly but here goes. My question involves elastic potential energy and work… So we know that a change in potential energy = Work done, as long as the forces are conservative... delta U = Work done Let’s say we have a spring… Work done/by on a spring is, W=...

Homework Statement An ore car of mass 4000 kg rolls downhill on tracks from a mine. At the end of the tracks, at 10 m elevation lower is a spring with k = 400,000 N/m. How much is the spring compressed in stopping the ore car? Ignore friction. Homework Equations First of all, I don't...
43. ### What is the Elastic Potential Energy Stored in a Compressed Spring?

Homework Statement A force of 5.00 N compresses a spring 5.00 cm. What is the elastic potential energy stored in the compressed spring? Homework Equations Ep=1/2kx2 The Attempt at a Solution Epelastic needs to calculated. I really do not know how to get there. K=f/x k=5N/ 0.05m...
44. ### What is the period of vibration for a 2.20 kg object on a 320 N/m spring?

Homework Statement A 2.20 kg object vibrates at the end of a horizontal spring whose force constant is 320 N/m. What is its period of vibration? Homework Equations Ep=1/2kx2 The Attempt at a Solution I don't even know where to start
45. ### Help with elastic potential energy

Homework Statement A child's toy shoots a rubber dart of mass 7.8g, using a compressed spring with a force constant of 3.5 x 10^2 N/m. The spring is initially compressed 4.5cm. All the elastic potential energy is converted into kinetic energy of the dart. What is the speed of the dart as it...
46. ### Elastic Potential Energy and Hooke's Law Problem

Homework Statement A small truck is equipped with a rear bumper that has a spring constant of 800,000 N/m. the bumper can be compressed up to 15cm without causing damage to the truck. What is the maximum velocity with which a solid 1000-kg car can collide with the bumper without causing damage...
47. ### Bungee Jumper - Elastic Potential Energy

Homework Statement In a "head dip" bungee jump from a bridge over a river the bungee cord is fastened to the jumper's ankles. The jumper than steps off and falls towards the river until the cord becomes taut. At that point, the cord begins to slow the jumper's decent, until his head just...
48. ### Using Hooke's Law and Elastic Potential Energy equations

I'm just having a bit of trouble understanding when to use F=kx and when to use W=.5kx^2 . I understand that Hooke's law is for the spring force and elastic PE is obviously for work, but you could use either one of these equations to solve for, for example, k: When solving for the spring...
49. ### Quick question about elastic potential energy?

Now when the spring recoils, it loses its elastic potential energy to the dart. If it loses its energy how does it come back to its original shape. I'm thinking it is the elastic potential energy that is used to make the coil come back to its orginal shape. Also let's say a spring was compressed...
50. ### Elastic potential energy of a spring

Hello, I'd relly appreciate some guidance on this one: [b]1. The length of a spring increases by 7.0 cm from its relaxed length when a mass of 1.7 kg is hanging in equilibrium from the spring. Spring constant 2.38 N/cm. How much elastic potential energy is stored in the spring? A...