Have you ever noticed that:
- A moving cricket ball can break a window.
- A speeding car is harder to stop than a slow-moving car.
- A running athlete can push another athlete with greater force than a standing person.
All these situations show that moving objects possess energy. This energy is called kinetic energy.
The faster an object moves, the greater its kinetic energy.
What is Kinetic Energy?
Kinetic energy is the energy possessed by an object due to its motion.
Any object that is moving possesses kinetic energy.
Example:
Moving car
Rolling ball
Flying bird
Running athlete
Flowing river water
Running athlete
Flowing river water
Objects with No Kinetic Energy
- Parked car
- Stationary bicycle
- Book resting on a table
- Standing person
Since these objects are not moving, their kinetic energy is zero.
Factors Affecting Kinetic Energy:
The kinetic energy of an object depends on:
1. Mass of the Object
For the same speed:
- Greater mass \(\rightarrow\) Greater kinetic energy
- Smaller mass \(\rightarrow\) Smaller kinetic energy
Example:
A truck and a bicycle moving at the same speed do not have the same kinetic energy.
The truck has a much larger mass, so it possesses greater kinetic energy.
2. Velocity of the Object
For the same mass:
- Higher speed \(\rightarrow\) Greater kinetic energy
- Lower speed \(\rightarrow\) Smaller kinetic energy
Example:
A cricket ball moving at \(40\ m/s\) has more kinetic energy than the same ball moving at \(20\ m/s\).
Derivation of the Expression for Kinetic Energy:
Consider an object of mass (\(m\)),
Suppose:
- Initial velocity \(=\) \(u\)
- Final velocity \(=\) \(v\)
- Force acting on object \(=\) \(F\)
- Displacement produced \(=\) \(s\)
Step 1: Apply the Formula for Work Done
Work done is:
\(W=Fs\)
Step 2: Use Newton's Second Law
\(F=ma\)
Substituting in the work equation:
\(W=mas\)
Step 3: Use the Equation of Motion
\(v^{2}-u^{2}=2as\)
Rearranging:
\(as=\frac{v^{2}-u^{2}}{2}\)
Substituting into the work equation:
\(W=m(\frac{v^{2}-u^{2}}{2})\)
Step 4: Simplify
\(W=\frac{1}{2}mv^{2}-\frac{1}{2}mu^{2}\)
Step 5: Object Initially at rest,
If the object starts from rest:
\(u=0\)
Therefore,
\(W=\frac{1}{2}mv^{2}\)
Thus,
\(K.E=\frac{1}{2}mv^{2}\)
This is the mathematical expression for kinetic energy.
Understanding the Formula:
\(K.E=\frac{1}{2}mv^{2}\)
Where:
\(KE\ =\ Kinetic\ Energy\)
\(m\ =\ Mass\ of\ object\ (kg)\)
\(v\ =\ Velocity\ m/s\)
Important Observations:
1. Kinetic Energy is Directly Proportional to Mass
\(KE\propto m\)
If mass doubles, kinetic energy doubles.
2. Kinetic Energy is Proportional to the Square of Velocity
\(KE\propto v^{2}\)
If velocity doubles:
\(KE=(2v)^{2}\)
\(KE=4v^{2}\)
Kinetic energy becomes four times.
If velocity triples:
\(KE=(3v)^{2}\)
\(KE=9v^{2}\)
Kinetic energy becomes nine times.
SI Unit of Kinetic Energy:
The SI unit of kinetic energy is: \(Joule\ (J)\)
Why?
From
\(KE=\frac{1}{2}mv^{2}\)
Unit of mass \(=\ kg\)
Unit of velocity \(=\ m/s\)
Therefore,
\(kg\times \frac{m^{2}}{s^{2}}\)
which is equivalent to a \(Joule\ (J)\)
Work and Energy:
When a force acts on an object and causes displacement, work is done.
Work transfers energy from one object to another.
Therefore:
\(Work\ Done\ =\ Energy\ Transferred\)
If positive work is done on an object, its energy increases.
If negative work is done on an object, its energy decreases.
Work–Energy Theorem:
The net work done on an object is equal to the change in its kinetic energy.
This important relationship is known as the Work–Energy Theorem.
\(W_{net}=\Delta K.E\)
Understanding the Work–Energy Theorem:
Case 1: Positive Work Done
\(W_{net}>0\)
then:
\(\Delta KE>0\)
The kinetic energy increases.
Example:
A football at rest is kicked. The foot does positive work on the ball. The ball gains kinetic energy and starts moving.
Case 2: Negative Work Done
\(W_{net}<0\)
then:
\(\Delta KE<0\)
The kinetic energy decreases.
Example:
Brakes are applied to a moving bicycle. The braking force does negative work. The bicycle slows down and loses kinetic energy.
Case 3: Zero Net Work Done
\(W_{net}=0\)
then:
\(\Delta KE=0\)
The kinetic energy remains constant.
Example:
A hockey puck moving with constant velocity on a frictionless surface. No net force acts on it. Its kinetic energy remains unchanged.
Real-Life Applications:
Sports
- Fast bowlers deliver cricket balls with high kinetic energy.
- Football players kick the ball by transferring energy through work done.
Transportation
- Brakes reduce a vehicle's kinetic energy.
- Seat belts help protect passengers during sudden changes in kinetic energy.
Machines
- Moving machine parts possess kinetic energy.
- Motors do work to increase the kinetic energy of moving components.
Daily Life
- Hammering a nail
- Kicking a ball
- Riding a bicycle
- Pushing a shopping cart
All involve work and changes in kinetic energy.