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## Class 11 Physics (India) - Hindi

### Course: Class 11 Physics (India) - Hindi>Unit 4

Lesson 9: Elastic and inelastic collisions (Hindi)

# Elastic collisions review

Review the key concepts, equations, and skills for elastic collisions, including how to predict objects' final velocities.

## Key terms

Term (symbol)Meaning
Closed systemSystem that is not acted on by a net external force. Also called an isolated system.
Conservation of momentumIn a closed (isolated) system, momentum is constant.
Elastic collisionCollision where both momentum and kinetic energy are conserved. There is no change in kinetic energy in the system as a result of the collision.

## Equations

EquationSymbolsMeaning in words
p, start subscript, i, end subscript, equals, p, start subscript, f, end subscriptp, start subscript, i, end subscript and p, start subscript, f, end subscript are the total initial and final momentumThe total initial momentum equals the total final momentum for a closed system. Commonly called the conservation of momentum.

## How to predict final velocities for an elastic collision

We know a collision is elastic if kinetic energy is conserved:
start fraction, 1, divided by, 2, end fraction, m, start subscript, 1, end subscript, v, start subscript, 1, i, end subscript, squared, plus, start fraction, 1, divided by, 2, end fraction, m, start subscript, 2, end subscript, v, start subscript, 2, i, end subscript, squared, equals, start fraction, 1, divided by, 2, end fraction, m, start subscript, 1, end subscript, v, start subscript, 1, f, end subscript, squared, plus, start fraction, 1, divided by, 2, end fraction, m, start subscript, 2, end subscript, v, start subscript, 2, f, end subscript, squared
and momentum is conserved:
m, start subscript, 1, end subscript, v, start subscript, 1, i, end subscript, plus, m, start subscript, 2, end subscript, v, start subscript, 2, i, end subscript, equals, m, start subscript, 1, end subscript, v, start subscript, 1, f, end subscript, plus, m, start subscript, 2, end subscript, v, start subscript, 2, f, end subscript
If we imagine ourselves sitting on object 1 moving at velocity v, start subscript, 1, end subscript, object 2 will look like it is moving at speed v, start subscript, 1, end subscript, minus, v, start subscript, 2, end subscript. The difference in the velocities of the two objects tells us how fast object 1 is moving relative to object 2, and is sometimes called the relative velocity. If kinetic energy and momentum are conserved, we can make some predictions about the relative velocity before and after the collision.
• The magnitude of the relative velocity is the same before and after the collision. That means if we are sitting on object 1 moving at velocity v, start subscript, 1, end subscript, object 2 will look like it is moving at the same speed both before and after the collision.
vertical bar, v, start subscript, 1, i, end subscript, minus, v, start subscript, 2, i, end subscript, vertical bar, equals, vertical bar, v, start subscript, 1, f, end subscript, minus, v, start subscript, 2, f, end subscript, vertical bar
• The relative velocity has opposite signs before and after the collision. If we are sitting on object 1 moving at v, start subscript, 1, end subscript, object 2 will look like it changes direction after the collision.
v, start subscript, 1, i, end subscript, minus, v, start subscript, 2, i, end subscript, equals, minus, left parenthesis, v, start subscript, 1, f, end subscript, minus, v, start subscript, 2, f, end subscript, right parenthesis
The relative velocity will have these properties before and after an elastic collision for any combination of masses.

## Common mistakes and misconceptions

Sometimes people forget that momentum is always conserved, but only in an isolated system. If there is a net external force on the system (an external impulse), then momentum is added to the system, and momentum is not conserved.