Question

The spring extends by $x$ on loading, then energy stored by the spring is : (if $T$ is the tension in spring and $k$ is spring constant)

• A. $ \frac{T^{2}}{2k}$
• B. $ \frac{T^{2}}{2k^{2}}$
• C. $ \frac{2k}{T^{2}}$
• D. $ \frac{2T^{2}}{k}$

Answer 1

The Correct Option is A

The energy stored in the spring is

Answer 2

Ans. Extension of spring: x, tension on spring = T, and spring constant = k. Now the extension of spring, x = T/k and energy stored by the spring,

An item is considered to be in periodic motion when its motion repeats itself in a set cycle. Another name for this type of motion is oscillation. Simple instances of oscillations include spring and pendulum motion, but there are many more instances as well. The fact that the object maintains a constant equilibrium position is one of the most important aspects of periodic motion. String also has a restoring force at work, indicating that it possesses potential energy.

A ubiquitous tool, spring's inertia is frequently disregarded due to its little bulk. When a spring is under stress, compression causes deformation. Once there, it is at its balance. As a result, when a spring contracts or expands a body, it produces an equal and opposing force.

Energy is stored in a compressible or stretchy item, such as a spring, rubber band, or molecule. Additionally called elastic potential energy. It is the force times the distance of the movement.

When the spring is in its normal position, which is also when it is not strained, it has no energy. The spring, however, will be able to hold onto energy if we move it from its typical location because of the change in environment. This sort of energy, which is brought on by the deformation of an elastic object like a spring, is known as potential energy. The act of expanding the spring is sometimes referred to as this energy. The stretched distance and the spring constant 'k' serve as its determinants.

String potential energy is calculated by the product of force and distance of displacement, where the force is equal to the product of spring constant and spring displacement. 

P.E. = 1/2kx²

Here, 

P.E = Spring Potential Energy

k= Spring Constant 

χ= Spring Displacement