BlogNCERTPotential Energy of a Spring

Potential Energy of a Spring

Introduction:

Whenever there is a compression or extension in a stretched spring there is a force produced which is equal to that applied force by us in the opposite direction. When a spring deviates from its mean position spring tends to restore its equilibrium by exerting a force that is equal and opposite of the external force. In this article, we will discuss more about this stored energy. And will learn about the work done by the spring.

A brief outline of the topic:

A spring is used in almost every mechanical work of our day-to-day life straight from the shock absorbers of a car to a gas lighter found in the kitchen. The spring is used due to its property to get deformed and come back to its natural state again. When the spring is compressed or stretched there is produced force in the opposite direction of this change. This happens due to the spring deviating from its mean position and it tries to come back there. This force is derived from Hooke’s law and helps us to analyze the energy stored in the spring.

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    The force is needed to stretch an elastic object such as a metal spring or rope. When an elastic object is compressed or stretched it will exert force to oppose that change in shape. This force is given by Hooke’s law. The force exerted by the spring is known as the restoring force since it is always present in the opposite direction of the deformation.

    The statement of Hooke’s law is given as follows,

    The force required to stretch an elastic object such as a metal spring is directly proportional to the extension of the spring for the short distances. Due to this restoring force in the opposite direction there is a use of negative signs.

    If x= the displacement relative to the unstretched length of the spring

    F= the force exerted by it.

    Then, F = -k x

    In the above mentioned equation k is the spring constant.

    A brief note of important concepts and laws:

    If the usual position is not stretched there will be no energy present in the spring. When the position is shifted from its usual position the spring is able to store energy by the virtue of its position. This stored energy is called the potential energy. The potential Energy of the spring is the potential energy stored as a result of the deformation of a particular elastic object, or of a spring. It describes the work done to stretch the spring and it depends on the spring constant K and the distance stretched.

    The potential energy is the stored energy which depends on the relative position of different parts of a system. The spring contains more potential energy when it is compressed or stretched. A steel ball has more potential energy raised above the ground than that of it has after falling to Earth.

    The concept of Spring Potential Energy:

    The spring is a common tool and generally their inertia is frequently neglected because of the negligible mass. It is a casual activity that spring when strained will undergo the displacement because of the compression. Then it will come to its equilibrium position. Hence the spring exerts an equal as well as an opposite force on a body that compresses or stretches it.

    This is the energy which is stored in a compressible or stretchable object like a spring or rubber band or molecule. Its other name is the elastic potential energy. It is almost equal to the force times the distance of the movement.

    If the general position that is without being stretched there will be no energy found in the spring. But when there is an alteration of the usual position from its original position then the spring will be able to store energy by the virtue of its position. This energy is known as the potential energy. This is the result of the deformation of the particular elastic object or a spring. It also defines the work done to stretch the spring. It is dependent on the spring constant k and the distance stretched.

    Potential Energy of a Spring Formula:

    The string potential energy is:

    P.E=1 ⁄ 2 k x 2

    The spring potential energy is a form of stored energy which is similar to the gravitational potential energy or electrical potential energy but one associated with springs and the elastic objects.

    Also read: Non-Conservative Forces

    FAQs (Frequently Asked Questions):

    Que 1:What is the formula to find potential energy?

    Ans: The formula is as follows:

    W = m × g × h = m g h

    Where,

    m = the mass in kilograms

    g = the acceleration due to gravity

    h = the height in meters

    Que 2: State Hooke’s law.

    Ans: Hooke’s law states that the strain of the material is directly proportional to the applied stress within the elastic limit of that material.

    Que: State the given statement is true or false: the potential energy is equal to the total external work done on the system.

    Ans: The above statement is true.

    Que: Write down the expression for the work done by spring.

    Ans: The expression for the work done by spring is given as follows:

    W ext=W p=V(x)=K(X) 22 W ext=W p=V(x)=K(X)22

    Que: Define spring constant.

    Ans: The characteristic property of the spring is spring constant. It is dependent on the material of construction and is measured in the units of N m-1.

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