# Potential Energy and Conservation of energy

• msattar07
In summary, potential energy is the stored energy that an object possesses due to its position or state. It is calculated by multiplying the object's mass, the acceleration due to gravity, and the height or distance it is from the ground. Potential energy and kinetic energy are interrelated, with the law of conservation of energy stating that energy cannot be created or destroyed, only transformed between the two forms. The conservation of energy is applied to potential energy through the principle of conservation of mechanical energy, which states that the total amount of mechanical energy remains constant in a closed system. Examples of potential energy and its conversion to other forms include a stretched rubber band, a compressed spring, and a book on a shelf.
msattar07

## Homework Statement

How does the work required to stretch a spring 2cm compare with the work required to stretch a spring 1 cm?

?

## The Attempt at a Solution

i think its twice the work

Assuming that the two springs are the same and Hookean, you are wrong.

P.E. of a spring is 1/2kx^2 , which is directly proportional to the square of extension from the natural length

you can derive the expression for the potential energy of the spring by integrating the hooke law over the distance moved.

## 1. What is potential energy?

Potential energy is the energy that an object possesses due to its position or state. It is stored energy that can later be converted into other forms of energy, such as kinetic energy.

## 2. How is potential energy calculated?

Potential energy is calculated by multiplying the object's mass, the acceleration due to gravity, and the height or distance the object is from the ground. The formula for potential energy is PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height or distance.

## 3. What is the relationship between potential energy and kinetic energy?

Potential energy and kinetic energy are both forms of energy and are interrelated. As an object gains potential energy, it loses kinetic energy, and vice versa. This is known as the law of conservation of energy, which states that energy cannot be created or destroyed, only transformed from one form to another.

## 4. How is the conservation of energy applied to potential energy?

The conservation of energy applies to potential energy through the principle of conservation of mechanical energy. This principle states that the total amount of mechanical energy, which includes both potential and kinetic energy, remains constant in a closed system. This means that energy can be transferred between potential and kinetic energy, but the total amount remains the same.

## 5. What are some examples of potential energy and its conversion to other forms of energy?

Some examples of potential energy include a stretched rubber band, a compressed spring, and a book on a shelf. When a stretched rubber band is released, it converts its potential energy into kinetic energy as it snaps back to its original shape. A compressed spring converts its potential energy into kinetic energy when it is released. A book on a shelf has potential energy due to its position, and if it falls, it converts its potential energy into kinetic energy as it moves towards the ground.

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