Energy is the ability to do work. An object can possess energy either because it is moving or because of its position or configuration.
The energy possessed by an object due to its position or shape is called potential energy.
For example:
- A book kept on a high shelf
- Water stored in a dam
- A stretched rubber band
- A compressed spring
All these objects possess energy even though they may not be moving.
Potential energy is the energy possessed by an object due to its position or configuration.
Potential energy is measured in Joules (\(J\)).
Types of Potential Energy:
(a) Gravitational Potential Energy:
An object raised above the ground possesses energy because work has been done against gravity.
Examples:
- Water stored in an overhead tank
- A flower pot kept on a balcony
- A suitcase placed on a shelf
(b) Elastic Potential Energy:
An elastic object stores energy when it is stretched or compressed.
Examples:
- Stretched rubber band
- Compressed spring
- Drawn bow
When released, this stored energy is converted into kinetic energy.
2. Derivation of the Expression for Gravitational Potential Energy:
Consider an object of mass '\(m\)' lying on the ground.
Suppose the object is lifted vertically through a height '\(h\)' at a constant speed.
Step 1: Force Required
To lift the object at constant speed, the applied upward force must be equal to its weight.
\(F\ =\ mg\)
where
- \(m\ =\) mass of the object
- \(g\ =\) acceleration due to gravity
Step 2: Work Done
The object is displaced vertically upward through a distance \(h\)
Work done is
\(W=F\times s\)
Substituting,
\(W=mg\times h\)
\(W\ =\ mgh\)
Step 3: Relation between Work Done and Potential Energy
The work done in lifting the object is stored in it as gravitational potential energy.
Therefore,
\(PE\ =\ mgh\)
where
- \(PE\ =\) Gravitational Potential Energy (\(J\))
- \(m\ =\) Mass (\(kg\))
- \(g\ =\) Acceleration due to gravity \(9.8m/s^{2} or 10m/s^{2}\)
- \(h\ =\) Height above the ground (\(m\))
SI Unit:
The SI unit of potential energy is Joule (\(J\))
Factors Affecting Gravitational Potential Energy:
Gravitational potential energy depends on:
1. Mass
Greater the mass, Greater the potential energy.
Example:
A \(20\ kg\) suitcase possesses more potential energy than a \(5\ kg\) suitcase kept at the same height.
2. Height
Greater the height, Greater the potential energy.
Example:
A flower pot kept on the third floor possesses more potential energy than the same flower pot kept on the first floor.
3. Acceleration due to Gravity
Potential energy also depends on gravitational acceleration.
Different planets have different values of \(g\).
Hence,
An object possesses different potential energies on the Earth and the Moon.
Conversion between Kinetic Energy and Potential Energy
Energy can change from one form to another.
One of the most common examples is the conversion between gravitational potential energy (PE) and kinetic energy (KE).
(A) During Free Fall
Consider a ball released from the top of a building.
Position A – At the Top
- Height = Maximum
- Speed = Zero
Therefore,
- Potential Energy = Maximum
- Kinetic Energy = Minimum (Zero)
Position B – Halfway Down
The ball falls due to gravity.
Its height decreases.
Its speed increases.
Therefore,
- Potential Energy decreases.
- Kinetic Energy increases.
Some of the stored potential energy has been converted into kinetic energy.
Position C – Just Before Reaching the Ground
Height is minimum.
Speed is maximum.
Therefore,
- Potential Energy = Minimum
- Kinetic Energy = Maximum
Almost all the gravitational potential energy has been converted into kinetic energy.
| Position | Potential Energy | Kinetic Energy |
|---|---|---|
| Top | Maximum | Minimum (Zero) |
| Halfway | Decreases | Increases |
| Just before the ground | Minimum | Maximum |
Law of Conservation of Energy
Energy can neither be created nor destroyed. It can only be transformed from one form to another.
The total energy of an isolated system remains constant.
Explanation using Free Fall
When a ball is released from the top of a building:
- Initially, it possesses maximum gravitational potential energy.
- As it falls, gravitational potential energy decreases.
- At the same time, kinetic energy increases.
- The loss in potential energy is equal to the gain in kinetic energy.
Hence,
\(Potential\ Energy\ +\ Kinetic\ Energy\ =\ Constant\)
Everyday Examples of the Law of Conservation of Energy
(a) Roller Coaster
- At the top: Maximum PE, minimum KE.
- While descending: PE decreases, KE increases.
- At the bottom: Minimum PE, maximum KE.
(b) Pendulum
- At the extreme positions: Maximum PE, minimum KE.
- At the mean position: Maximum KE, minimum PE.
Key Differences between Kinetic Energy and Potential Energy
| Kinetic Energy | Potential Energy |
| Energy due to motion | Energy due to position or configuration |
| Depends on speed | Depends on height or deformation |
| Zero for a stationary object | Can exist even when the object is at rest |
| Increases with speed | Increases with height (gravitational PE) |
Difference between KE and PE