potential energy of a spring

Introduction

Potential energy is the stored energy in a system defined by the relative locations of various system components. When a spring is compressed or stretched, its potential energy increases. When a steel ball is raised above the ground, it has more potential energy than when it is dropped to the bottom.

It is capable of accomplishing more work at the increased position. Potential energy is a property of a system, not an individual object or particle; for example, as the Earth and the higher ball are separated, the system has more potential energy.

In systems where parts exert forces on each other that are proportionate to their configuration or relative position, potential energy is formed. In the Earth-ball system, the gravitational force between the Earth and the ball is solely determined by the distance between them. The effort required to further separate them or raise the ball contributes to the system’s energy, which is stored as gravitational potential energy.

When an object repeats its motion in a predetermined cycle, it is said to be in periodic motion. Oscillation is another term for this type of motion. Spring and pendulum movement are simple examples, but there are numerous additional situations in which oscillations occur. One of the most significant characteristics of periodic motion is that the item maintains a stable equilibrium position. A restoring force is also at work for string, which means that string has potential energy.

Potential energy of a spring 

Spring is a common tool, and due to its small mass, their inertia is commonly overlooked. It’s a common occurrence that when a spring is strained, due to compression, it will deform. Then it comes to a point of equilibrium. As a result, a spring exerts an equal and opposite force when compressing or extending a body.

A compressible or stretchable item, such as a spring, rubber band, or molecule, stores energy. It’s also known as elastic potential energy. It’s the force multiplied by the movement’s distance.

Work done by spring:

The spring has no energy when it is in its usual position, that is, when it is not stressed. However, if we shift the spring from its usual place, the spring will be able to retain energy because of its new location. Potential energy is the name given to this type of energy.

This is caused by the deformation of a certain elastic object, such as a spring. It also refers to the process of stretching the spring. It is determined by the spring constant ‘k’ and the stretched distance.

Formula for potential entered of a spring

Potential energy of a string equals to  force   × displacement .

In addition, the force is equal to the displacement of the spring constant.

A spring’s potential energy is:

P.E = ½ ×kx²

Where,

P.E. is  spring’s potential energy is

k is the spring constant

Displacement in the spring is x

We must apply Hooke’s law to calculate the Spring potential energy. We acquire our force from Hooke’s law because potential energy is equivalent to the work done by a spring, and work is the product of force and distance. The term “distance” refers to the change in the spring’s position.

Hooke’s law:

When we state Hooke’s law, it is important to mention Robert Hooke. The law is named after British physicist Robert Hooke, who lived in the 17th century. Hooke’s equation holds in many different situations when an elastic body is deformed, such as wind blowing on a tall building or a musician plucking a guitar string (to some extent). A linear-elastic or Hookean body or substance is one for which this equation can be assumed.

The genuine reaction of springs and other elastic bodies to applied forces is only approximated by Hooke’s law, which is a first-order linear approximation. It will eventually fail if the forces surpass a certain limit because no material can be squeezed or stretched beyond a particular minimum or maximum size without irreversible distortion or change of state. Before the elastic limits are reached, many materials will diverge noticeably from Hooke’s rule.

For most solid solids, however, Hooke’s law is an accurate approximation as long as the forces and deformations are small enough. As a result, Hooke’s law is widely applied in all fields of research and engineering. It serves as the foundation for numerous fields such as seismology, molecular mechanics, and acoustics. The spring scale, the manometer, the galvanometer, and the balance wheel of a mechanical clock are all based on this idea.

Hooke’s law is generalised in the contemporary theory of elasticity, which states that the strain (deformation) of an elastic item or substance is proportional to the stress applied to it. Because generic stresses and strains may have a large number of independent components, the “proportionality factor” could be a linear map (a tensor) that can be represented by a matrix of real numbers rather than a single real number.

Hooke’s law, in its most general form, allows you to determine the relationship between strain and stress for complicated objects based on the intrinsic qualities of the materials they’re composed of. When a uniformly cross-sectioned homogeneous rod is stretched, it behaves like a simple spring, with a stiffness k that is proportional to the cross-section area but inversely related to the length.

Spring constant:

Fspring = -kx

Where, 

Fspring is the spring force

k is spring constant

x is spring stretch or compression

In order to define spring constant, the force exerted on the spring is denoted by the letter F, by something stretching or compressing it, and x is the distance the spring is stretched or compressed from its “rest” position in this equation. The letter k stands for the “spring constant,” which is a quantity that describes how “stiff” a spring is. If k is a large number, it signifies that stretching it to a specific length requires more force than stretching a less stiff spring to the same length. Unless the spring is broken in some manner, you can use that k number for all future calculations once you’ve discovered the spring constant.

Fapplied = +kx

To reach equilibrium, you must add a force that exactly balances the spring’s opposing force. This characteristic will be exploited in this experiment to determine the values of two spring constants.

Conclusion:

When a spring is extended or compressed, work is done. In the spring, elastic potential energy is stored. The work done is equal to the elastic potential energy stored, assuming no inelastic deformation has occurred.

The equation can be used to compute the elastic potential energy stored:

spring constant (extension)² = elastic potential energy

E = ½ kx²

This is when;

• In joules, elastic potential energy (Ee) is quantified (J)
• In newtons per meter (N/m), the spring constant (k) is expressed.
• The increase in length, referred to as extension (x), is measured in meters (m)