**One Dimensional or Head-on Collision Definition Physics:**

If the initial and final velocities of colliding bodies lie along the same line, then the collision is called one dimensional or head-on collision.

We are giving a detailed and clear sheet on all Physics Notes that are very useful to understand the Basic Physics Concepts.

## Elastic and Inelastic Collisions in One Dimension | Physics – Work, Energy and Power

**Perfectly Elastic Collision in One Dimension**

Applying Newton’s experimental law, we have

v_{2} – v_{1} = u_{1} – u_{2}

Velocities after collision

v_{1} = \(\frac{\left(m_{1}-m_{2}\right) u_{1}+2 m_{2} u_{2}}{\left(m_{1}+m_{2}\right)}\)

and

v_{2} = \(\frac{\left(m_{2}-m_{1}\right) u_{2}+2 m_{1} u_{1}}{\left(m_{1}+m_{2}\right)}\)

**Special Cases of Elastic Collision in One Dimension:**

1. When masses of two colliding bodies are equal, then after the collision, the bodies exchange their velocities.

v_{1}, = u_{2} and v_{2} = u_{1}

2. If second body of same mass (m_{1} = m_{2}) is at rest, then after collision first body comes to rest and second body starts moving with the initial velocity of first body.

v_{1} = 0 and v_{2} = u_{1}

3. If a light body of mass m_{1} collides with a very heavy body of mass m_{2} at rest, then after collision

v_{1} = -u_{1} and v_{2}=0

It means light body will rebound with its own velocity and heavy body will continue to be at rest.

4. If a very heavy body of mass m1 collides with a light body of mass m_{2}(m_{1} > > m_{2}) at rest, then after collision

v_{1} = u_{1} and v_{2} = 2u_{1}

**In Inelastic Collision in One Dimensional**

Loss of kinetic energy

ΔK = \(\frac{m_{1} m_{2}}{2\left(m_{1}+m_{2}\right)}\left(u_{1}-u_{2}\right)^{2}\left(1-e^{2}\right)\)

**In Perfectly Inelastic One Dimensional Collision**

Velocity of separation after collision = 0.

Loss of kinetic energy = \(\frac{m_{1} m_{2}\left(u_{1}-u_{2}\right)^{2}}{2\left(m_{1}+m_{2}\right)}\)

If a body is dropped from a height h_{0} and it strikes the ground with velocity v_{0} and after inelastic collision it rebounds with velocity v_{1}, and rises to a height h_{1}, then

If after n collisions with the ground, the body rebounds with a velocity v_{n} and rises to a height h_{n}, then

\(e^{n}=\frac{v_{n}}{v_{0}}=\sqrt{\frac{h_{n}}{h_{0}}}\)

Height covered by the body after rath rebound, h_{n} = e^{2n}h_{0}

**Work, Energy and Power:**

Work, energy and power are the three quantities which are inter-related to each other. The rate of doing work is called power. An equal amount of energy is consumed to do a work. So, basically the power is the rate at which energy is consumed to complete a work.

Work | Energy |

Conservation of Energy | Power |

Collisions | Elastic and Inelastic Collisions in One Dimension |

Collisions in Two Dimensions |