1. define elastic collision

2. define inelastic collision

3. define law of conservation of momentum

4. write the equation for conservation of momentum and define all the variables.

Question

1. define elastic collision

2. define inelastic collision

3. define law of conservation of momentum

4. write the equation for conservation of momentum and define all the variables.

Accepted Answer

### 1. Define Elastic Collision
# Brief Explanations:
An elastic collision is a collision between two or more objects where both the total momentum and the total kinetic energy of the system are conserved. This means that after the collision, the objects may separate, and the kinetic energy before the collision is equal to the kinetic energy after the collision (no kinetic energy is lost to other forms like heat, sound, or deformation).
# Answer:
A collision where total momentum and total kinetic energy of the system are conserved (kinetic energy is not lost to other forms).

### 2. Define Inelastic Collision
# Brief Explanations:
An inelastic collision is a collision in which the total momentum of the system is conserved, but the total kinetic energy is not conserved. Some of the kinetic energy is transformed into other forms of energy, such as heat, sound, or work done to deform the objects. In a perfectly inelastic collision, the objects stick together after the collision.
# Answer:
A collision where total momentum is conserved, but total kinetic energy is not (kinetic energy is lost to other forms, e.g., heat, deformation).

### 3. Define Law of Conservation of Momentum
# Brief Explanations:
The Law of Conservation of Momentum states that in a closed system (a system where no external forces act on the objects within it), the total momentum of the system remains constant. This means that the total momentum before a collision (or interaction) is equal to the total momentum after the collision (or interaction). Mathematically, for a system of objects, $ \sum p_{\text{initial}}=\sum p_{\text{final}} $, where $ p = mv $ (momentum is the product of mass and velocity).
# Answer:
In a closed system (no external forces), total momentum before interaction equals total momentum after interaction ($ \sum p_{\text{initial}}=\sum p_{\text{final}} $).

### 4. Write the equation for Conservation of Momentum and define all the variables.
# Explanation:
## Step1: Recall the Law of Conservation of Momentum
For a system of two objects (1 and 2) interacting (e.g., colliding), the total initial momentum equals the total final momentum. The momentum of an object is given by $ p = mv $, where $ m $ is mass and $ v $ is velocity.
## Step2: Write the equation for two - object system
For two objects, the initial momentum of object 1 is $ m_1v_{1i} $ and the initial momentum of object 2 is $ m_2v_{2i} $. The final momentum of object 1 is $ m_1v_{1f} $ and the final momentum of object 2 is $ m_2v_{2f} $. So the equation for conservation of momentum is $ m_1v_{1i}+m_2v_{2i}=m_1v_{1f}+m_2v_{2f} $.
## Step3: Define the variables
- $ m_1 $: Mass of the first object (in kilograms, $ \text{kg} $).
- $ v_{1i} $: Initial velocity of the first object (in meters per second, $ \text{m/s} $).
- $ m_2 $: Mass of the second object (in kilograms, $ \text{kg} $).
- $ v_{2i} $: Initial velocity of the second object (in meters per second, $ \text{m/s} $).
- $ v_{1f} $: Final velocity of the first object (in meters per second, $ \text{m/s} $).
- $ v_{2f} $: Final velocity of the second object (in meters per second, $ \text{m/s} $).

For a general system with $ n $ objects, the equation can be written as $ \sum_{i = 1}^{n}m_iv_{i}=\sum_{i = 1}^{n}m_iv_{i}' $, where $ m_i $ is the mass of the $ i $-th object, $ v_i $ is the initial velocity of the $ i $-th object, and $ v_i' $ is the final velocity of the $ i $-th object.
# Answer:
### Equation:
For a two - object system: $ \boldsymbol{m_1v_{1i}+m_2v_{2i}=m_1v_{1f}+m_2v_{2f}} $
For a general $ n $-object system: $ \boldsymbol{\sum_{i = 1}^{n}m_iv_{i}=\sum_{i = 1}^{n}m_iv_{i}'} $

### Variable Definitions:
- $ m_1, m_2, m_i $: Mass of the object (in $ \text{kg} $).
- $ v_{1i}, v_{2i}, v_i $: Initial velocity of the object (in $ \text{m/s} $).
- $ v_{1f}, v_{2f}, v_i' $: Final velocity of the object (in $ \text{m/s} $).

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QUESTION IMAGE

Question

Explanation:

1. Define Elastic Collision

Answer:

2. Define Inelastic Collision